Humans and Bread

Food is a basic need for the creatures in the world to sustain their daily body methodology. Bread is a regarded as a symbol for life, symbol for prosperity and livelihood from ages. Bread, a food item was discovered primarily in the Middle East and the features of the bread were modified according to the regions it has been introduced. The bread was related to the divine source provided by the eternity. Since wheat is the cultivated in most part of the world and the bread is prepared with wheat. Bread therefore symbolizes food in various forms.Consumption of bread was known in the pre Christian era. In the initial times when bread was introduced to the English speaking countries the villages used to have to community kitchens where the women in every house used to bake their cakes at a common place. The women were regarded as the significant part in the family who nurture the family and their congregation was regarded as significant social involvement. The guests were welcomed in to the houses with a piece of bread and liquor to wish them a better life.The Russians regards bread and vodkha as a sacred combination. The bread which was prepared from wheat was considered basic food. Bread was used as a commodity in Egyptian ages. After the post harvest period people were provided with work and paid bread. Thus bread is considered as money. Bread or wheat was considered as basic ingredient for the livelihood and the rulers were at times conscious about the supply of the grains or bread to huge population in the kingdom.The bakers who tried to adulterate the bread making process were severely punished. The English used to introduce wheat cultivation and bread making in different parts of the world. Bread making even now is a daily routine affair for many families in different countries as it symbolizes a tradition, a habitual action. Now a days people in different parts prepare bread to suit their tastes to make it more nutritious and to include their and love and affection to share with family.

Meeting Scene Romeo and Juliet VS Gnomeo and Juliet Essay

The famous play Romeo and Juliet, written by William Shakespeare, is the tale of two star-crossed lovers. Romeo, the only heir of Montague, falls in love with Juliet, the heiress of Capulet, but their love is forbidden due to a rivalry between houses resulting in a double suicide. Two adaptations of William Shakespeare’s Romeo and Juliet are Asbury’s Gnomeo and Juliet (2011), portrayed as humorous through various film techniques, and Luhrmann’s Romeo and Juliet (1996), portrayed as a tragedy through similar film techniques. This will be shown through the use of film techniques like language, camera angles and mise-en-scene. Fristly, language features are used by both Luhrmann’s version of Romeo and Juliet and Asbury’s version of Gnomeo and Juliet. In Luhrmann’s Romeo and Juliet language features such as similes are being used in the meeting scene. Romeo is comparing Juliet to a saint and himself to a pilgrim. He is saying that as it’s a long last, when he finally found the object of his reverence. Romeo takes her hands, and offered to kiss away and damage he might of has caused or may have been committed in the process. This is evident when Romeo states, â€Å"If I profane with my unworthiest hand this holy shrine, the gentle sin is this: My lips, two blushing pilgrims, ready to stand to smooth that rough touch with a tender kiss.† Luhrmann’s version of Romeo and Juliet uses language to creates the feel of Romeo and Juliet falling in love with each other before they find out who they really are. The heartbreak and knowing that both parents won’t allow them together is tragic. In Asbury’s Gnomeo and Juliet play on words are used all throughout the film. In the meeting scene Gnomeo and Juliet are mucking around with each other as they both want the flower. As Juliet gets the flower from Gnomeo she states, â€Å"Who’s your Gnomeo now?† This used for when Juliet steals the Orchid from Gnomeo as they are play around with each other. This leads to Juliet flirting with Gnomeo as she develops feelings for him this creates a feel of happiness and cheerful between the character and the audience. The different language features that have been used in both films shows that the two have both constructed two different versions of William Shakespeare Romeo and Juliet. Secondly, the use of camera angles are used in Luhrmann’s Romeo and Juliet to show the tragic and emotion effect the film has on the audience. In Asbury’s Gnomeo  and Juliet the camera angle creates a romantic and humorous. This is shown in Luhrmann’s version through the low angle when Romeo and Juliet meet and realise who they actually are. The low angle is for Romeo when he runs after Juliet to see where she is going then finds her with her mother Mrs Capulet. The camera angle captures the Romeo’s facial expression, his confusion that his one true love is his family emery and now Romeo doesn’t understand why someone so prefect in his eyes could be his family worst emery of them all. In the Asbury’s version of Gnomeo and Juliet the camera angles are used to show that the film is humorous. The camera angle that has been used in the meeting scene Gnomeo and Juliet is an eye level angle; this is shown when Gnomeo and Juliet climbing up the glasshouse and when they both reach for the Orchid. The purpose behind using eye level angle is used to create the scene romantic when they touch for the first time. The camera angle is used to make the audience think that the two are in love and they are meant to be together forever right then and here. Camera angles are used in Luhrmann’s Romeo and Juliet to show the tragedy. The camera angles are used in Asbury’s Gnomeo and Juliet to show the humorous through the camera angles as Gnomeo and Juliet. In addition, the use of mise-en-scene things such as props, costumes, lighting, facial expressions and placement are used throughout both films. Luhrmann’s version of Romeo and Juliet the costumes played a big part in the meeting scene. In the scene Romeo is dressed up as a knight and Juliet is dressed up as an angel. Romeo see’s Juliet for what she really is, an angel in his eyes.

History Essay Example | Topics and Well Written Essays - 1250 words - 14

History - Essay Example Fundamentally, in the 20th century Russia was an exceedingly subjugated country managed by the Czars. Ruled by feudal tenets of dictatorship, the citizens’ of Russia were terribly oppressed, cold, poor, and starving, in addition they had no authentic course or hope. In essence, Russia had never undergone any open-minded revolutions, which were occurring in other parts of the globe. This made Russia remain as one of the real last remnants of the medieval European-American society. The rebels through acts of rebellion, revolutionist, and terrorism overthrew the Czars government. To start with, the Bolsheviks and Lenin were outside Russia when the revolution took place. Some of them were Russians while others were not Russians. They were socialists and Marxists revolutionaries existing in Europe studying sociology, science, economics, history, and many more from a Marxist viewpoint. The Bolsheviks did not necessitate the removal from power of the Russian government, after the coup, they came in with the intention of putting Marxist hypothesis and ideology to practice. Their major plan was to develop Russia into a social state through social revolution and spread their ideologies to Europe, America and eventually the whole world (Wiesner-Hanks & Wheeler 2007, 67). This portrays a major difference between the French revolution and the Russian revolution. Foreigners played a major role in the Russian revolution while only the French participated in the French revolution. Eventually, the Bolsheviks managed to overthrow the residual powers of Czars authoritarianism in October revolution. They began reforms through establishing legislative assemblies called the Soviets. The same way the French came up with representative units called the constituencies. These soviets consisted of openly elected officials who were in charge of the affaires of the citizens including peasants, soldiers, and workers. To add to that, they

Blog Essay Example | Topics and Well Written Essays - 500 words - 5

Blog - Essay Example In every fragment of the technology zone, leaders are beleaguered to concentrate on enhancing the processes that transport IT services to their industries, conglomerates and consumers. Reducing costs, giving speedier services, and increasing the value of a company or organization are all prerequisites in the world of Information Technology nowadays. The world is revolving so fast and the innovative advancements are comparable to an avalanche of new ideas and revolutionary approaches. A fluctuating and shifting demand is expected to take place. If these demands are left unaddressed, it can bring massive disasters toward a certain company. Seen this way, a necessity to align our IT services with the growing and varying tastes and trends of the consumers is imperative in maintaining the value of an organization. According to the Bloomberg BusinessWeek (2010), in a survey conducted in about 150 IT subdivisions at middle-sized companies, â€Å"IT Leadership Exchange found that 90 per cent of CIOs expect that the IT department will be misaligned with business needs in an economic recovery†¦this will threaten the business’s long-term competitiveness†. The job of bringing IT services and business precedence into line is more than scientific in context. Nevertheless, by way of continuing dialogue with the IT officials and by aligning our business objectives, the IT Leadership Exchange "finds that an IT department can boost its effectiveness to the company by 54 per cent" (Bloomberg, 2010). We see the importance of aligning our IT service and its management with the current inclinations of the consumers as part of the business goals of the company. But how do continual improvement on IT services and its management contribute in bettering the operational and process effectiveness? Also, how does it aid an organization to achieve cost effectiveness? In dealing with these critical points, there are manifold factors to consider: the IT

Business Intelligence in the Company's Management Practices Essay - 1

Business Intelligence in the Company's Management Practices - Essay Example Whole Foods Market depends on organizational structure to ensure performance that would impact employees and customers.   Since January 2001 Whole Food Market has experienced an increase in sales, profits, and stock prices.   The success of the company has flourished from the hard work of team members and strong leadership throughout the company.  Ã‚  Whole Foods Market depends on organizational structure to ensure performance that would impact employees and customers.   Since January 2001 Whole Food Market has experienced an increase in sales, profits, and stock prices.   The success of the company has flourished from the hard work of team members and strong leadership throughout the company.  Ã‚   The Executive Team, also known as the E-Team, consists of the Ceo, Co-Ceo, Company President, Vice President of Growth and Development and the Financial Officer.   These five leaders work together to improve the company’s performance and production through decision ma king.   Unlike many companies, Whole Foods’ E-team discusses and debates their ideas until they all come together in agreement as a team.   In doing so, they are able to provide the company, customers and team members with the proper attention and performance needed. Co-CEO Walter Robb and Company President A.C. Gallo, are responsible for operating the company’s marketing process, purchasing products from suppliers and vendors, and distributing products to all twelve regions.     These twelve regions include the United Kingdom, Southern Pacific, Northern California, Pacific Northwest, Rocky Mountain, Southwest, Midwest, South, Florida Northeast, Mid Atlantic and North Atlantic.   Within these regions, there are over three hundred stores, five commissaries, nine distribution centers and over fifty-four thousand team members.     Robb and Gallo’s goal and commitment are to purchase and distribute from local vendor and suppliers quality products that will attract customers to shop at local Whole Foods stores.   When customers are satisfied with products this makes an impact on the company which in turn produces growth, productivity and prosperity. As the years continue to move forward, E-team will keep working together as a collaborative leadership team to influence and lead Whole Foods Market into remarkable growth and success.   Because of its well-developed structure, Whole Foods Market will continue to make a great impact on customers, employees and suppliers.

International Intellectual Property Law Essay Example | Topics and Well Written Essays - 2000 words

International Intellectual Property Law - Essay Example One is that emerging countries might not have the same technology as advanced countries, and need to copy advanced companies to innovate. This is an issue that is addressed below. However, the bulk of this article will deal with copyrights, especially with regards to British Law regarding the same. Intellectual property rights have become one of the buzzwords surrounding globalization. Globalization may be defined as â€Å"an extent of internationalisation at a level where boundaries are blurred or appear close, where networks and solidarities are communicating, [and] where interdependencies are increasing.†1 On a technological basis, modern globalization is dependent upon the structures for communication, transportation, computation and enforcement interlocking.2 Globalization has reached many sectors, including intellectual property, financial services, money capital, goods and financial instruments.3 There are obvious positive aspects of globalization, and negative ones as well, as globalization leads to clashes, prejudices, tension and cultural misunderstandings such as those seen on 9/11, and the Bali, Madrid and London bombings.4 Intellectual property is one of the core businesses in the World Trade Organisation (WTO), in which one of the WTOs founding element with regards to intellectual property is the Trade Related Aspects of Intellectual Property Rights (TRIPS) Agreement.5 The TRIPS Agreement, in a nutshell, establishes a global harmonisation of protection for Intellectual Property and enforcement, as well as created international standards regarding patent, copyright, trademark and design protections.6 The existing regimes of the United States, Europe and Japan with regards to intellectual property were largely the same, so their laws did not need as much harmonising. However, there were some areas that were a problem, as far as different countries having different rules, and they were â€Å"first to invent systems, scope of

Key Literature on Strategies to Reduce Carbon Emissions review

Key on Strategies to Reduce Carbon Emissions - Literature review Example The policy was introduced by then Minister for Finance, Brian Lenihan. The Irish scrappage policy was meant to reduce the level of carbon emissions in Ireland as well as boost domestic demand. Hennessy and Tol (2011) constructed an empirical model (based on history of data) to anticipate the impact of three policies in Ireland to reduce carbon emissions. The first policy is the 2009 reform of vehicle registration and motor tax; the second policy is the electrification of transports; and the third policy is the scrappage scheme. The model sought to characterize the impact of the three policies on the Irish car stock from 2010 to 2025. Based on the empirical model developed by Hennessy and Tol, the first policy or the 2009 reform of vehicle registration and motor tax will lead to a dramatic shift in Irish vehicle stock: the main vehicle stock will be transformed from petrol to diesel cars (Hennessy and Tol 2011, p. 135). According to the model, fuel efficiency will improve with the fir st policy. However, although carbon emissions will be reduced, the reduction will not be substantial (Hennessy and Tol 2011, p. 135). The reduction in carbon emission through a policy of reform of vehicle registration and motor tax will be such that by 2020, Irish carbon emissions will be only roughly equal to the carbon emissions of 2007 or the carbon emissions of four years ago. ... 135). Hennessy and Tol’s model indicated that the third policy or the scrappage scheme will have little effect because it applies only to a tiny fraction of the car stock. While the Hennesy and Tol study employed their model to anticipate or project the possible impact of three policies on carbon emissions, the Rogan et al. (2011) investigated the impact of taxation on private cars proportionate to their carbon emissions based on the results after a year of the tax rate change that was started to be implemented in July 2008. According to Rogan et al. (2011), the taxation proportionate to carbon emission policy that was started to be implemented in July 2008 reduced the emissions from new cars to only 145 g/km as short as one year from the start of the implementation of the policy (Rogan et al. 2011, p. 583). According to Rogan et al., the reduction was brought about not by a decrease in engine size but by through the shift to diesel cars. However, the policy led to a 33% decre ase in tax revenue equivalent to â‚ ¬166 million (Rogan et al. 2011, p. 583). Earlier, Giblin and McNabola (2009) attempted to anticipate the possible impact of the 2008 policy that was the subject of the Rogan et al. (2011) analysis. In contrast to the one-year after results of the policy analysis of Rogan et al. (2011), however, Giblin and McNabola anticipated or forecasted the possible impact of the policy using a model. In the Giblin and McNabola model, the carbon emission-differentiated vehicle tax system that was implemented beginning July 2008 was forecasted to result into a 3.6 to 3.8% carbon dioxide emission intensity and a reduction in tax revenue of â‚ ¬ 191 million. Licandro and Sampayo (2005) used a mathematical car replacement model to analyze the impact of

The impact of point of view in a story Essay Example | Topics and Well Written Essays - 500 words

The impact of point of view in a story - Essay Example Meanwhile, Sarah shifts into the new barn and turns that into a home. As Adomiram returns, he finds himself helpless and submits his will in the hands of his family. Women should not just voice their thoughts, but should also take practical measures in order to get their rights. Main body: Sarah and Adoniram played the traditional gender roles. Although Sarah later made the new barn into a home without the consent of her husband, she had initially abandoned her long cultivated dream of building a house over that place when Adoniram had conflicting plans about the utility of that space. Sarah had been dreaming of a decent home to live in for over forty years because Adoniram had promised her one. However, when the time came, Adoniram did not feel it necessary even to ask the opinion of Sarah. So she made the pies faithfully, while across the table she could see, when she glanced up from her work, the sight that rankled in her patient and steadfast soul — the digging of the cell ar of the new barn in the place where Adoniram forty years ago had promised her their new house should stand. (Wilkins). Sarah, as usual, believed that the only rational thing is to follow her husband and suppress her feelings. She was not only an obedient wife, she would spare her dreams for the sake of Adoniram’s happiness.

Viola Assignment Example | Topics and Well Written Essays - 250 words

Viola - Assignment Example In describing her love for Orsino, she states that â€Å"†¦ she sat like patience on a monument. Smiling at grief. Was not this love indeed?† (II. iv. 60). This shows how sincere her love for Orsino was. She claimed that her state was desperate for her master’s love. Viola is also used to illustrate how violent and frustrating love can be. Although Viola, who disguises as Cesario, is in love with her master, she remains loyal to him. This makes Olivia, the Orsino’s lover, like her for her boldness, thinking she is a man. This makes Orsino accuse Viola (Cesario), of taking Oliviia away from him. This leads to a chaotic confrontation between Orsino and Viola. Shakespeare is thus able to portray the good and bad side of love through Viola. Finally, because of her disguise, Viola is able to influence other characters in the play. She is used to highlight the kind of love men have for women and vice versa. For instance, the fact that she acts as a man, she is able to reveal to the audience the kind of love that exists between Olivia and Orsino, and the feelings they have for one

Problem Solving and Decision Making Essay Example for Free

Problem Solving and Decision Making Essay Background I work for a company called npower and we are an energy supplier in the UK. Specifically, I work within the Blended Services department and we deal with various types of inbound contact from our customers such as email, letters and telephone calls. I manage a team of 15 people advisors and their role is to effectively deal with customer enquiries that come in via the different methods of contact. Due to the large volumes of correspondence that we have come in, it’s not always practical to respond to customers via a written response and we therefore ask the advisors to call as many customers as possible and resolve their enquiries by phone, this allows the advisors not only deal with the customer’s original enquiry but to also answer any subsequent questions that may arise when they are presented with the answer we give them. Description of the problem When advisors call a customer there are regulations around data protection and also keeping customer contact details up to date that we must adhere to, we refer to these regulations as compliance. This is a very black and white subject, we must be compliant in all we do 100% of the time. The problem that has come to light that in our department, is that our advisors are not 100% compliant 100% of the time. They will fully cover data protection and request up to date contact information on some calls but not others. This presents a problem for the department and me as a manager as well as the advisors in question as these inconsistencies can lead to varying degrees of disciplinary action for the advisors and the company. The impact of this for the advisors is that it can lead to disciplinary action such as informal warnings, up to more formal action such as written warnings and even loss of their job. In extreme cases offending advisors can even face personal fines. As a manager, I then have to consider the potential knock on effects of such action which can include loss of advisor confidence, a reduction in staff morale, and opportunity for progression may be reduced or taken away and all of these in turn may affect an advisors attendance. For me as a manager the concerns are that these actions could affect my time as I am required to carry out investigations in to each case of non-compliance. This is turn could leave other members of my team to feel neglected as my time becomes consumed with investigations and carrying out disciplinary action. Potentially, this could lead to a general loss of morale within my team as a whole and go on to impact their performance. This issue also affects our customers as if we are seen to be breaking such important regulations as data protection, and then this could cause an increase in complaints, damage our customer’s confidence in us as a company, lead to a decrease in customer loyalty and ultimately the loss of their business. From a company point of view the impacts are possibly the greatest. Just a few potential knock on effects from non-compliance are loss of customers, brand damage, legal consequences including large fines and potentially losing out license to trade. Disciplinary action can lead to loss of staff and this brings further impacts such as the time and cost of recruiting and training new staff and all of these could eventually impact our ability to provide a desired service to our customers. Analysis of the problem In trying to identify options to solve the problem of advisors inconsistently adhering to compliance regulations, I first looked at gathering as much information as I could in to how much it was affecting my department and if there were any contributing factors to the problem. I liaised with our quality analysts. The QA team had recently marked a sample of the calls we make within the department and informed me that in the month of September they sampled four calls from each team within the department. This was made up of one inbound call (calls where the customer calls npower) and one outbound call (calls where we call the customer) for two advisors on each team. There are 18 teams so this is 36 advisors that were sampled and scored. The results showed that of the advisors monitored only 69% were fully compliant. This is cause for concern then as the target is 100%. Following on from this, I needed to do further investigation. My time, however, is very valuable and for me to take on such an investigation alone is not feasible. I discussed the problem with my manager and we came up with an idea to help us follow up the results from the QA Teams quality checks. Within our own operations group (5 Teams) we asked each manager to mark two calls for each of their advisor focussing solely on whether or not the advisors were following compliance regulations that we must adhere to. In the first week of October, each manager carried out the quality checks for their teams. The results showed that we were 50% compliant as an operations group. Following these results each manager went out to the advisors that were not following the compliance regulations and gave them a training session as well as an informal warning that this kind of action was not acceptable and that compliance must be adhered to at all times. The managers including myself then left the advisors for a couple of weeks and then went back and completed the same quality checks once more. The second time around we noticed an improvement as we scored 70%. However, we were and still are a long way short of our ultimate goal. Following on from this, I devised what I saw to be a simple yet effective questionnaire that would be completed by a sample group of advisors. The purpose of the questionnaire was to establish possible reasons why the advisors failed to be consistent in regards to meeting compliance when speaking to customers on the telephone. I looked to address such matters as how confident they were that they were personally 100% complaint 100% of the time, were they aware of the tools that npower provide to assist them in being complaint, what barriers they have encountered that make it difficult to be compliant and what do they feel would ensure that they were 100% compliant 100% of the time going forward. The results of the questionnaire showed that the advisors knew what was required of them to be compliant and that they recognised the implications of not being compliant. It also showed that all of the advisors were aware of the various support tools that npower provides them to help with compliance though not all of them used them. This suggests then that the problem of being inconsistent in regards to compliance may be down to advisor attitude or focus but at this point I wanted to avoid making assumptions. With all of this information, I used a simple fishbone to drill down for possible reasons for these inconsistencies. I looked at the following headings and then added the possible reasons: Confidence (lack of) * Inconsistent message * Unclear on what’s expected * Cannot deal with conflict (from customers) * DPA doesn’t feel natural (in call structure) * Situations outside of the norm (3rd party calling on behalf of the customer) Knowledge (lack of) * No or little training (new to business) * Lack of communication (not advised of possible changes) * Inconsistent message (unsure what is correct) Skill * Unsure how to resolve conflict * Not certain how to incorporate data protection in to their call structure * Not able to control a call (allows a customer to drive a conversation, potentially skipping past vital areas for not wanting to interrupt) Attitude/Behaviour * Doesn’t understand potential consequences * Doesn’t like change * Refuses to comply After considering all of the above the potential solutions to my problem could be creating a guide that points out to advisors what they must do to be fully compliant but that isn’t rigid in its delivery so that the advisors can make it their own. Ensuring that the guide and its use is trained out in a clear manner that makes sure there are no questions unanswered. Providing the advisors with additional training to enable them to capably and confidently deal with situations of conflict i.e. if a customer refuses to go through data protection. Finally, making sure that the consequences of non-compliance for both advisors and the company are clearly communicated. Resolution of the problem I went to manager with my findings and stated what I wanted to achieve. I needed the goal to realistic and to be measurable. Remembering that QA Team reported the department to be 69% compliant for the month of September my goal statement was this: * To decrease the compliance fail rate in our department by 15% during the month of November based upon 36 evaluations. In making this statement, I ensured that if would be a fair reflection since it would match the original investigation completed by the QA Team. It’s SMART, because I have a specific goal that can be measured against previous findings. It’s both achievable and realistic as all managers will make numerous quality checks throughout the month and I’m trying to achieve the ultimate goal of 100% compliance but instead make a small but reasonable step towards it and finally, it’s time bound as all steps will be put in place and measured throughout November. Once the goal had been set, my manager and I held a brain storming session to look at possible options to resolve the problem. Further to those I mentioned earlier, we came up with these additional ideas: * Speech Analytics * Scripts for data protection * A specific inbound call team * A specific outbound call team * Feedback, coaching and evaluations * An inbound and outbound call decision making tree * Brief to include what’s expected and what the consequences are for non-compliance * Compliance champs * Compliance tick sheet After we had come up with these various options I went away and decided which would be the best course of action. To help me decide I used a simple Pro’s and Con’s method. I put each of the above options in to a table and then listed what the advantages and disadvantages were. Below, I have just briefly outlined some of the key points for each one. Speech analytics Pros * It saves time (it’s all automated, listening to and identifying key words and phrases in conversations) so managers don’t have to do manual checks. * A large sample is gathered (it pulls data from all recorded calls) therefore the reflection is very accurate. * Reports can easily be pulled, since all data is compiled and exported in excel spread sheet format. Cons * It’s not an immediate solution. Speech analytics for npower is in early testing stages and it’s unlikely to be available for at least another year. * Cost – It’s very expensive to implement and so even to run in a small test environment is currently unlikely. Scripts for data protection Pros * It would clearly set out what needs to be said (no grey area) * Advisors would have something to reference at all times * Can easily be updated when changes occur * Managers could easily cover this in a coaching session Cons * Advisors may not feel it comes across as natural * Advisors may forget to keep it on their desk each day * It would need to be updated with each new change (potentially old ones could be in circulation) * Repeat contact customers would have to go through the exact same process each time and may feel it comes across as robotic Specific inbound/outbound call teams Pros * Advisors would deal with only one call type (one set of compliance regulations, more specialised, less chance of failure) * Becoming specialised may increase confidence Cons * It may not be feasible to have a enough specialised teams to deal with the workload * We would lose multi-skilled advisors, impacting our ability to deal with other work volumes * Specialised teams leave us vulnerable to outside influences such as absence. Compliance Champs Pros * Position of responsibility for trusted advisors * Someone on hand to reference in uncertain situations Cons * Those not chosen may feel disappointed * The cost of taking advisors away from completing work may not be feasible in such a busy time * Having to wait for a ‘Champ’ may impact customer wait times and thus service * Takes ownership and responsibility away from the advisors Compliance Checklist Pros * Advisors already use something similar, so it would be familiar * Advisors could clearly track what they have and haven’t asked * Peace of mind as it states clearly what they must ask * Natural, as it states what they must ask but doesn’t tell them how to do it * Cheap and easy to implement * Easy to amend when changes occur * Advisors can easily keep it with them either paper based or electronically * Puts the responsibility on the advisor * Best use can be coached around Cons * Must be altered with each change (old ones could be left in circulation) * Puts the responsibility on the advisors (must be trusted to use it) After evaluating the options and the pros and cons to each. I decided to go with a compliance checklist. Once I had decided on what I believed to be the best solution I asked myself two important questions, in various decision making models these are also known as Acid Tests 12. Acid Test 1 – If I implement all of my plans for action will my problems be overcome? In considering the answer I thought back to areas that I had identified earlier that linked into the problem of inconsistent compliance. To recap these were things such as: * Advisors were unsure what they should be asking. * They lacked confidence that they were saying all the right things. * They could often miss important information if interrupted by a customer before the compliance checks were complete. * The solution needed to be simple and easy to implement, so that it was clear and simple to train out. The majority of my advisors already use a checklist of sorts to capture the work they complete and how they contacted the customer, by adding compliance prompts to this it creates a visual aid for the advisors reminding them of what they need to ask and it remains in a setting that they find familiar. Also, because the advisors are able to tick off the various requirements as they go along it makes it very clear what must be asked and it’s less likely that they’ll miss things out if they are interrupted as they can simply go back along the list and pick up where they left off. It’s also likely to come across as more natural when the advisors are talking to them customers as well as again it only prompts them with what they need to ask rather than telling them how to say it. Finally, it’s relatively cheap to implement, it isn’t very time consuming to put in place and it’s something that can be done immediately. A copy of the checklist is attached (Appendix A) Acid test 2 – If I get rid of all my problems will I achieve my objectives? Again, the answer should be yes. My solution will give advisors something black and white, that’s clear and easy to understand and familiar to them in their day to day role. This should in turn give them the added confidence when talking to customer’s on the phone. There is, however, a human element. This is that the solution once trained out and implemented, relies upon the advisor taking some ownership and making sure that use it every day even if they feel confident that they are fully compliant. Because this is a personal choice there is no plan that I can implement that will solve this. However, as a company we do have measures already in place to manage this. If an advisor is proven to have the skills and the knowledge to be fully compliant and yet for whatever reason chooses not to, then I or any other manager would need to ensure that this is managed in the proper fashion. Implementation and communication of the solution As previously stated the advisor already usage a data capture sheet in their day to day jobs. I have taken that and added some simple yet clear checklist boxes that prompt the advisors on what they need to be asking when speaking to customers on the telephone. I will start off with a trial in my operations group and then if the desired results are proven then I will discuss with my manager a plan to roll it out to the whole department. I’ll start by holding a small group meeting with my fellow team managers, briefly describing the problem that I’ve been looking in to. I’ll present my solution and tell them how I would like it to be used. The managers including me can then go out to our own teams and deliver the message in a brief team meeting. The compliance checklist will be distributed via email to the managers and advisors alike. This way the advisors can choose to print it off and fill it in manually or they can simply fill in in on their PC’S. This also means that they will always be able to access a copy even if they have to move desks as it will be saved to their email. Following this, I would plan to follow up with some side by side observations. This would be to ensure that the advisors are using the checklist as intended and it also gives me the chance to answer any questions that they may have as well as offer advice and praise where they are doing things well and hopefully begin to build that confidence in their ability back up. As far as monitoring and reviewing of the situation, this should be quite straight forward. I know what the problem is and I have identified a list of causes. I also know clearly what I expect to achieve from the solution. I perform at least one quality check on each of my advisors each week, so these will prove useful when monitoring progress in this area and the results should be clear to see. These quality checks are always given to the advisors as feedback and trends from multiple quality checks are used to build useful coaching sessions. The feedback that I receive from the advisors at this point should also allow me to monitor if they are using my solution as expected and how confident they feel with it. As a department, we also receive daily, weekly and monthly reports. These will enable me to view the progress of the other teams in my operations group to see if they are showing the results that are expected. I will raise the matter for discussion in the weekly operations group meeting and this will allow me to receive feedback from my fellow managers and get their thoughts on what is and potentially isn’t going well. Finally, the QA Team will perform another quality check across a random sample of the department. This will perhaps be the ultimate mark of whether or not my solution has been successful. If so, then there should be a significant increase in the percentage of advisors that pass compliance.

Measures of Central Tendency

Measures of Central Tendency The one single value that reflects the nature and characteristics of the entire given data is called as central value. Central tendency refers to the middle point of a given distribution. It is other wise called as ‘measures of location. The nature of this value is such that it always lies between the highest value and the lowest value of that series. In other wards, it lies at the centre or at the middle of the series. CHARACTERISTICS OF A GOOD AVERAGE: Yule and Kendall have pointed out some basic characteristics which an average should satisfy to call it as good average. They are: Average is the easiest method to calculate It should be rigidly defined. This says that, the series of whose average is calculated should have only one interpretation. One interpretation will avoid personal prejudice or bias. It should be representative of the entire series. In other wards, the value should lie between the upper and lower limit of the data. It should have capable of further algebraic treatment. In other wards, an ideal average is one which can be used for further statistical calculations. It should not be affected by the extreme values of the observation or series. DEFINITIONS: Different experts have defined differently to the concept of average. Gupta (2008) in his work has narrated Lawrence J. Kaplan definition as ‘one of the most widely used set of summery figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose of computing an average value for a set of observation is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point of location around which the individual items cluster. This opinion clearly narrates the basic purpose of computing an average. Similarly, Croxton and Cowden define the concept as ‘an average is a single value within the range of the data that is used to represent all of the values in the series. Since the average is somewhere within the range of data, it is sometimes called a measure of central value. TYPES OF AVERAGES: Following five are frequently used types of an average or measure of central tendency. They are Arithmetic mean Weighted arithmetic mean Median Mode Geometric Mean and Harmonic Mean All the above five types are discussed below in detail. THE ARITHMETIC MEAN: Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. It can be computed in a several ways. Commonly it can be computed by dividing the total value by the number of observations. Let ‘n be the number of items in a case. Each individual item in a list can be represented in a relationship as x1, x2, x3, ,xn. In this relationship, ‘x1 is one value, ‘x2 is another value in the series and the value extends upto a particular limit represented by ‘xn. The dots in the relationship express that there are some values between the two extremes which are omitted in the relationship. Some people interprets the same relationship as, which can be read as ‘x-sub-i, as i runs from 1 upto n. In case the numbers of variable in list is more, then it requires a long space for deriving the mean. Thus the summation notation is used to describe the entire relationship. The above relationship can be derived with the help of summation as: , representing the sum of the ‘x values, using the index ‘i to enumerate from the starting value i =1 to the ending value i = n. thus we have and the average can be represented as The symbol ‘i is again nothing but a continuing covariance. The readers should not be confused while using the notation , rather they can also use or or any other similar notation which are of same meaning. The mean of a series can be calculated in a number of ways. Following are some basic ways that are commonly used in researchers related to management and social sciences, particularly by the beginners. However, the readers should not be confused on sample mean and population mean. A sample of a population of ‘n observations and the mean of sample is denoted by ‘. Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol ‘Â µ, which is pronounced as ‘mue and is derived from the Greek letter ‘mu. Below we are discussing the concepts of sample mean. Type-1: In case of individual observation: a. Direct method- Mean or average can be calculated directly in the following way Step-1: First of all the researcher has to add all the observations of a given series. The observations are x1, x2, x3, xn. Step-2- Count how many observations are their in that series (n) Step-3- the following procedure than adopted to get the average. Thus the average or mean denoted as ‘and can be read as ‘x bar is derives as: Thus it can be said that the average mark of the final contestants in the quiz competition is 67.6 marks which can be rounded over to 70 marks. b. Short-cut method- The average or mean can also be calculated by using short-cut method. This method is applicable when a particular series is having so many observations. In other wards, to reduce calculations this method is generally used. The steps of calculating mean by this method is as follows: i. The research has to assume any one value from the entire series. This value is called as assumed value. Let this value be denoted here as ‘P. ii. Differentiate each a value from this assumed vale. That is find out individual values of each observation. Let this difference value be denoted as ‘B. Hence B=xn-P where n= 1,2,3,n. iii. Add all the difference value or get sum of B and count the number of observation ‘n. iv. Putting the values in the following formula and get the value of mean. Type-2: In case of discrete observations or series of data: Discrete series are the variables whose values can be identified and isolated. In such a case the variant is a whole number, but is form frequency distribution. The data set derived in case-1 above is called as ungrouped data. The computations in case of these data are not difficult. Where as, if the data set is having frequencies are called as groped data. a. Direct method: Following are some steps of calculating mean by using the direct method i. In the first step, the values of each row (X) are to be multiplied by its respective frequencies (f). ii. Calculate the sum of the frequencies (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*f values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula b. Short cut method: Arithmetic mean can also be calculated by using the short cut method or assumed mean method. This method is generally used by the researchers to avoid the time requirements and calculation complexities. Following are the steps of calculating mean by this method. i. The first step is to assume a value from the ‘X values of the series (denoted as A= assumed value) ii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘X to that of assumed value (A) i.e., D = X-A iii. Multiply each D with f i.e., find our Df iv. Calculate the value of sum of at the end of respective columns. v. Mean can be calculated by using the formula as Type-3: In case of continuous observations or series of data: Another type of frequency distributions is there which consists of data that are grouped by classes. In such case each value of an observation falls somewhere in one of the classes. Calculation of arithmetic mean in case of grouped data is some what different from that of ungrouped data. To find out the arithmetic mean of continuous series, one has to calculate the midpoint of each class interval. To make midpoints come out in whole cents, one has to round up the value. Mean in continuous series can be calculated in two ways as derived below: a. Direct method: In this method, mean can be calculated by using the steps as i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Multiply the mid points of each class interval (m) with its respective frequencies (f) i.e., find out mf iii. Calculate the value of sum of at the end of respective columns. iv. Mean can be calculated by using the formula as b. Short cut method: Mean can also be calculated by using short cut method. Following are the steps to calculate mean by this method. i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Assume a value from the ‘m values of the series (denoted as A= assumed value) iii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘m to that of assumed value (A) i.e., D = m A iv. Multiply each D with f i.e., find our Df v. Calculate the value of sum of at the end of respective columns. vi. Put the values in the following formula to get mean of the series THE WEIGHTED ARITHMETIC MEAN: In real life situation in management studies and social sciences, some items need more importance than that of the other items of that series. Hence, importance assigned to different items with the help of numerical value as per the priority basis in a series as called as weights. The arithmetic mean on the other hand, gives equal weightage or importance to each observation of the series. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. Following is the procedures of computing mean of a weighted series. By the way, an important problem that arises while using weighted mean is regarding selection of weights. Weights may be either actual or arbitrary, i.e., estimated. The researcher will not face any difficulty, if the actual weights are assigned to the set of data. But in case, if actual data is not assigned than it is advisable to assign arbitrary or imaginary weights. Following are some steps of calculating weighted mean: i. In the first step, the values of each row (X) are to be multiplied by its respective weights (W) ii. Calculate the sum of the weights (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*W values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula Advantages of Arithmetic mean: Following are some advantages of arithmetic mean. i. The concept is more familiar concept among the people. It is unique because each data set has only one mean. ii. It is very easy to compute and requires fewer calculations. As every data set has a mean, hence, as a measure mean can be calculated. iii. Mean represents a single value to the entire data set. Thus easily one can interpret a data set its characteristics. iv. An average can be calculated of any type of series. Disadvantages of Arithmetic mean: The disadvantages are as follows. i. One of the greatest disadvantages of average is that it is mostly affected by the extreme values. For example let consider Sachin Tendulkars score in last three matches. Let it be, 100 in first match, 2 in second match and 10 in third match. The average score of these three matches will me 100+2+10/3=37. Thus it implies that Tendulkars average score is 37 which is not correct. Hence lead to wrong conclusion. ii. It is not possible to compute mean for a data set that has open-ended classes at either the high or low end of the scale. iii. The arithmetic average sometimes gives such value which cannot be found from the data series from which it is calculated. iv. It is unrealistic. v. It cannot be identified observation or graphic method of representing the data and interpretation. THE MEDIAN: Another one technique to measure central tendency of a series of observation is the median. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. In other wards, it is the exactly middle value of the series. Hence, fifty percent of the observations in the series are above the median value and other fifty or half observations are remains below the median value. However, if the series are having odd numbers of observations like 3,5,7,9,11,13 etc., then the median value will be equal to one of the exact value from the series. On the other hand, if the series is having even observations, then median value can be calculated by getting the arithmetic mean of the two middle values of the observations of the series. Median an a technique of measuring central tendency can be best used in cases where the problem sought for more qualitative or psychological in nature such as health, intelligence, satisfaction etc. Definitions: The concept of median can be clearer from the definitions derived below. Connor defined it as ‘the median is the value which divides the distribution into two equal parts, one part comprising all values greater, and the other values less than the median. Where as Croxton and Cowden defined it as ‘the median is that value which divides a series so that one half or more of the items are equal to or less than it and one half or more of the items are equal to or greater than it. Median can be computed in three different series separately. All the cases are discussed separately below. Computation of Median in Individual Series Computation of Median in Discrete Series and Computation of Median in Continuous Series Computation of Median in Individual Series: Following are some steps to calculate the median in individual series. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. Than the median value can be calculated by using the formula th value or item from the series. Where, N= Number of observation in that series. When N is odd number (like 5, 7,9,11,13 etc.) median value is one of the item within that series, but in case N will be a even number than median is the arithmetic mean of the two middle value after applying the above formula. The following problem can make the concept clear. Computation of Median in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Following are the steps of computing the median when the series is discrete. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies of the series. Computation of Median in Continuous Series: Continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of median is little bit different from that of the other two cases discussed above. Following are some steps to get median in continuous series of data. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies column of the series. Form the cumulative frequencies, one can get the median class i.e., in which class the value lies. This class is called as median class and one can get the lower value of the class and the upper value of the class. The following formula can be used to calculate the median We have to get the median class first. For this, median class is N/2 th value or 70/2= 35. The value 35 lies in the third row of the table against the class 30-40. Thus 30-40 is the median class and it shows that the median value lies in this class only. After getting the median class, to get the median value we have to apply the formula . Advantages of Median: Median as a measure of central tendency has following advantages of its own. It is very simple and can be easily understood. It is very easy to calculate and interpret. It Includes all the observations while calculation. Like that of arithmetic mean, median is not affected by the extreme values of the observation. It has the advantages for using further analysis. It can even used to calculate for open ended distribution. Disadvantages of Median: Median as a means to calculate central tendency is also not free from draw backs. Following are some important draw backs that are leveled against median. Median is not a widely measure to calculate central tendency like that of arithmetic mean and also mode. It is not based on algebraic treatment. THE MODE: Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. Like that of median, mode is also more useful in case of qualitative data analysis. It can be used in problems generally having the discrete series of data and particularly, problems involving the expression of psychological determinants. Definitions: The concept of mode can be clearer from the definitions derived below. Croxten and Cowden defined it as ‘the mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded as the most typical of a series of value. Similarly, in the words of Prof. Kenny ‘the value of the variable which occurs most frequently in a distribution is called the mode. Mode can be computed in three different series separately. All the cases are discussed separately below. Computation of Mode in Individual Series Computation of Mode in Discrete Series and Computation of Mode in Continuous Series Computation of Mode in Individual Series: Calculation of mode in individual series is very easy. The data is to be arranged in a sequential order and that value which occurs maximum times in that series is the value mode. The following example will make the concept clear. Computation of Mode in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Hence directly, mode will be that value which is having maximum frequency. By the way, for accuracy in calculation, there is a method called as groping method which is frequently used for calculating mode. Following is the illustration to calculate mode of a series by using grouping method. Consider the following data set and calculate mode by using the grouping method. The calculation carried out in different steps is derived as: Step-1: Sum of two frequencies including the first one i.e., 1+2=3, then 4+3=7, then 2+1=3 etc. Step-2: Sum of two frequencies excluding the first one i.e., 2+4=7, then 3+2=5, then 1+2=3 etc. Step-3: Sum of three frequencies including the first one i.e., 1+2+4=7, then 3+2+1=6 etc. Step-4: Sum of two frequencies excluding the first one i.e., 2+4+3=9, then 2+1+2=5 etc. Step-5: Sum of three frequencies excluding the first and second i.e., 4+3+2=9, then 1+2+1=4. Computation of Mode in Continuous Series: As already discussed, continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of mode is little bit different from that of the other two cases discussed above. Following are some steps to get mode in continuous series of data. Select the mode class. A mode class can be selected by selecting the highest frequency size. Mode value can be calculated by using the following formula Advantages of Mode: Following are some important advantages of mode as a measure of central tendency. It is easy to calculate and easy to understand. It eliminates the impact of extreme values. It is easy to locate and in some cases we can estimate mode by mere inspection. It is not affected by extreme values. Disadvantages of Mode: Following are some important disadvantages of mode. It is not suitable for further mathematical treatment. It may lead to a wrong conclusion. Some critiques criticized mode by saying that mode is influenced by length of the class interval. THE GEOMETRIC MEAN: Geometric mean, as another measure of central tendency is very much useful in social science and business related problems. It is an average which is most suitable when large weights have to be assigned to small values of observations and small weights to large values of observation. Geometric mean best suits to the problems where a particular situation changes over time in percentage terms. Hence it is basically used to find the average percent increase or decrease in sales, production, population etc. Again it is also considered to be the best average in the construction of index numbers. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. For example, if a series is having only two observations then N will be two or we will take square root of the observations. Similarly, when series is having three observations then we have to take cube root and the process will continue like wise. Geometric mean can be calculated separately for two sets of data. Both are discussed below. When the data is ungrouped: In case of ungrouped series of observations, GM can be calculated by using the following formula: where X1 , X2 , X3, XN various observations of a series and N is the Nth observation of the data. But it is very difficult to calculate GM by using the above formula. Hence the above formula needs to be simplified. To simplify the formula, both side of the above formula is to be taken logarithms. To calculate the G.M. of an ungrouped data, following steps are to be adopted. Take the log of individual observations i.e., calculate log X. Make the sum of all log X values i.e., calculate Then use the above formula to calculate the G.M. of the series. When the data is grouped: Calculation of geometric mean in case of grouped data is little bit different from that of calculation of G.M. in case of ungrouped series. Following are some steps to calculate the G.M. in case of grouped data series. To calculate the G.M. of a grouped data, following steps are to be adopted. Take the mid point of the continuous series. Take the log of mid points i.e., calculate log X and it can also be denoted as log m Make the sum of all log X values i.e., calculate or Then use the following formula to calculate the G.M. of the series. Advantages of G.M.: Following are some advantages of G.M. i. One of the greatest advantages of G.M. is that it can be possible for further algebraic treatment i.e., combined G.M., can be calculated when there is availability of G.M., of two or more series along with their corresponding number of observations. ii. It is a very useful method of getting average when the series of observation possess rates of growth i.e., increase or decrease over a period of time. iii. Since it is useful in averaging ratios and percentages, hence, are more useful in social science and business related problems. Disadvantages of G.M.: G.M., as a technique of calculating central value is also not free from defects. Following are some disadvantages of G.M. i. It is very difficult to calculate the value of log and antilog and hence, compared to other methods of central tendency, G.M., is very difficult to compute. ii. The greatest disadvantage of G.M., is that it cannot be used when the series is having both negative or positive observations and observations having more zero values. THE HARMONIC MEAN: The last technique of getting the central tendency of a series of data is the Harmonic mean (H.M.). Harmonic mean, like the other methods of central tendency is not clearly defined. It is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. H.M., is very much useful in those cases of observations where the nature of data is such that it express the average rate of growth of any events. For example, the average rate of increase of sales or profits, the average speed of a train or bus or a journey can be completed etc. Following is the general formula to calculate H.M.: When the data is ungrouped: When the observations of the series are ungrouped, H.M., can be calculated as: The step for calculating H.M., of ungrouped data by using the derived formula is very simple. In such a case, one has to find out the values of 1/X and then sum of 1/X. When the data is grouped: In case of grouped data, the formula for calculating H.M., is discussed as below: Take the mid point of the continuous series. Calculate 1/X and it can also be denoted as 1/m Make the sum of all 1/X values i.e., calculate Then use the following formula to calculate the H.M. of the series. Advantages of H.M.: Harmonic mean as a measure of central tendency is having following advantages. i. Harmonic mean considers each and every observation of the series. ii. It is simple to compute when compared to G.M. iii. It is very useful for averaging rates. Disadvantages of H.M.: Following are some disadvantages of H.M. i. It is rarely used as a technique of measuring central tendency. ii. It is not defined clearly like that of other techniques of measuring central value mean, median and mode. iii. Like that of G.M., H.M., cannot be used when the series is having both negative or positive observations and observations having more zero values. CONCLUSION: An average is a single value representing a group of values. Each type of averages has their own advantages and disadvantages and hence, they are having their own usefulness. But it is always confusing among the researchers that which average is the best among the five different techniques that we have discussed above? The answer to this question is very simple and says that no single average can be considered as best for all types of data. However, experts opine two considerations that the researchers must be kept in mind while going for selecting a technique to determine the average. The first consideration is that of determining the nature of data. If the data is more skewed it is better to avoid arithmetic mean, if the data is having gap around the middle value of the series, then median should be avoided and on the other hand, if the nature of series is such that they are unequal in class-intervals, then mode is to be avoided. The second consideration is on the type of value req uired. When there is need of composite average of all absolute or relative values, then arithmetic mean or geometric mean is to be selected, in case the researcher is in need of a middle value of the series, then median may be the best choice, but in case the most common value is needed, then will not be any alternative except mode. Similarly, Harmonic mean is useful in averaging ratios and percentages. SUMMERY: 1. Different experts have defined differently to the concept of average. 2. Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. 3. The best use of arithmetic mean is at the time of correcting some wrong entered data. For example in a group of 10 students, scoring an average of 60 marks, in a paper it was wrongly marked 70 instead of 65. the solution in such a cases is derived below: 4. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. 5. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. 6. Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. 7. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. 8. Harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. QUESTIONS: 1. In a class containing 90 students following heights (in inches) has been observed. Based on the data calculate the mean, median and mode of the class. 2. In a physical test camp meant for selection of army solders the following heights of the candidates have been observed. Find the mean, median and mode of the distribution. 3. From the distribution derived below, calculate mean and standard deviation of the series. 4. The following table derives the marks obtained in Indian Economy paper by 90 students in a class. Calculate the mean, median and mode of the following distribution. 5. The monthly profits of 180 shop keepers selling different commodities in a city footpath is derived below. Calculate the mean and median of the distribution. 6. The daily wage of 130 labourers working in a cotton mill in Ahmadabad cith is derived below. Calculate the mean, median and mode. 7. There is always controversy before the BCCI before selection of batsmen between Rahul Dravid and V.V.S. Laxman. Runs of 10 test matches of both the players are given below. Suggest who the better run getter is and who the consistent player is. 8. Calculate the mean, median and mode of the following distribution. 9. What do you mean by measure of central tendency? How far it helpful to a decision-maker in the process of decision making? 10. Define measure of central tendency? What are the basic criteria of a good average? 11. What do you mean by measure of central tendency? Compare and contrast arithmetic mean, median and mode by pointing out the advantages and disadvantages. 12. The expenditure on purchase of snacks by a group of hosteller per week is Measures of Central Tendency Measures of Central Tendency The one single value that reflects the nature and characteristics of the entire given data is called as central value. Central tendency refers to the middle point of a given distribution. It is other wise called as ‘measures of location. The nature of this value is such that it always lies between the highest value and the lowest value of that series. In other wards, it lies at the centre or at the middle of the series. CHARACTERISTICS OF A GOOD AVERAGE: Yule and Kendall have pointed out some basic characteristics which an average should satisfy to call it as good average. They are: Average is the easiest method to calculate It should be rigidly defined. This says that, the series of whose average is calculated should have only one interpretation. One interpretation will avoid personal prejudice or bias. It should be representative of the entire series. In other wards, the value should lie between the upper and lower limit of the data. It should have capable of further algebraic treatment. In other wards, an ideal average is one which can be used for further statistical calculations. It should not be affected by the extreme values of the observation or series. DEFINITIONS: Different experts have defined differently to the concept of average. Gupta (2008) in his work has narrated Lawrence J. Kaplan definition as ‘one of the most widely used set of summery figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose of computing an average value for a set of observation is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point of location around which the individual items cluster. This opinion clearly narrates the basic purpose of computing an average. Similarly, Croxton and Cowden define the concept as ‘an average is a single value within the range of the data that is used to represent all of the values in the series. Since the average is somewhere within the range of data, it is sometimes called a measure of central value. TYPES OF AVERAGES: Following five are frequently used types of an average or measure of central tendency. They are Arithmetic mean Weighted arithmetic mean Median Mode Geometric Mean and Harmonic Mean All the above five types are discussed below in detail. THE ARITHMETIC MEAN: Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. It can be computed in a several ways. Commonly it can be computed by dividing the total value by the number of observations. Let ‘n be the number of items in a case. Each individual item in a list can be represented in a relationship as x1, x2, x3, ,xn. In this relationship, ‘x1 is one value, ‘x2 is another value in the series and the value extends upto a particular limit represented by ‘xn. The dots in the relationship express that there are some values between the two extremes which are omitted in the relationship. Some people interprets the same relationship as, which can be read as ‘x-sub-i, as i runs from 1 upto n. In case the numbers of variable in list is more, then it requires a long space for deriving the mean. Thus the summation notation is used to describe the entire relationship. The above relationship can be derived with the help of summation as: , representing the sum of the ‘x values, using the index ‘i to enumerate from the starting value i =1 to the ending value i = n. thus we have and the average can be represented as The symbol ‘i is again nothing but a continuing covariance. The readers should not be confused while using the notation , rather they can also use or or any other similar notation which are of same meaning. The mean of a series can be calculated in a number of ways. Following are some basic ways that are commonly used in researchers related to management and social sciences, particularly by the beginners. However, the readers should not be confused on sample mean and population mean. A sample of a population of ‘n observations and the mean of sample is denoted by ‘. Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol ‘Â µ, which is pronounced as ‘mue and is derived from the Greek letter ‘mu. Below we are discussing the concepts of sample mean. Type-1: In case of individual observation: a. Direct method- Mean or average can be calculated directly in the following way Step-1: First of all the researcher has to add all the observations of a given series. The observations are x1, x2, x3, xn. Step-2- Count how many observations are their in that series (n) Step-3- the following procedure than adopted to get the average. Thus the average or mean denoted as ‘and can be read as ‘x bar is derives as: Thus it can be said that the average mark of the final contestants in the quiz competition is 67.6 marks which can be rounded over to 70 marks. b. Short-cut method- The average or mean can also be calculated by using short-cut method. This method is applicable when a particular series is having so many observations. In other wards, to reduce calculations this method is generally used. The steps of calculating mean by this method is as follows: i. The research has to assume any one value from the entire series. This value is called as assumed value. Let this value be denoted here as ‘P. ii. Differentiate each a value from this assumed vale. That is find out individual values of each observation. Let this difference value be denoted as ‘B. Hence B=xn-P where n= 1,2,3,n. iii. Add all the difference value or get sum of B and count the number of observation ‘n. iv. Putting the values in the following formula and get the value of mean. Type-2: In case of discrete observations or series of data: Discrete series are the variables whose values can be identified and isolated. In such a case the variant is a whole number, but is form frequency distribution. The data set derived in case-1 above is called as ungrouped data. The computations in case of these data are not difficult. Where as, if the data set is having frequencies are called as groped data. a. Direct method: Following are some steps of calculating mean by using the direct method i. In the first step, the values of each row (X) are to be multiplied by its respective frequencies (f). ii. Calculate the sum of the frequencies (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*f values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula b. Short cut method: Arithmetic mean can also be calculated by using the short cut method or assumed mean method. This method is generally used by the researchers to avoid the time requirements and calculation complexities. Following are the steps of calculating mean by this method. i. The first step is to assume a value from the ‘X values of the series (denoted as A= assumed value) ii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘X to that of assumed value (A) i.e., D = X-A iii. Multiply each D with f i.e., find our Df iv. Calculate the value of sum of at the end of respective columns. v. Mean can be calculated by using the formula as Type-3: In case of continuous observations or series of data: Another type of frequency distributions is there which consists of data that are grouped by classes. In such case each value of an observation falls somewhere in one of the classes. Calculation of arithmetic mean in case of grouped data is some what different from that of ungrouped data. To find out the arithmetic mean of continuous series, one has to calculate the midpoint of each class interval. To make midpoints come out in whole cents, one has to round up the value. Mean in continuous series can be calculated in two ways as derived below: a. Direct method: In this method, mean can be calculated by using the steps as i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Multiply the mid points of each class interval (m) with its respective frequencies (f) i.e., find out mf iii. Calculate the value of sum of at the end of respective columns. iv. Mean can be calculated by using the formula as b. Short cut method: Mean can also be calculated by using short cut method. Following are the steps to calculate mean by this method. i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Assume a value from the ‘m values of the series (denoted as A= assumed value) iii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘m to that of assumed value (A) i.e., D = m A iv. Multiply each D with f i.e., find our Df v. Calculate the value of sum of at the end of respective columns. vi. Put the values in the following formula to get mean of the series THE WEIGHTED ARITHMETIC MEAN: In real life situation in management studies and social sciences, some items need more importance than that of the other items of that series. Hence, importance assigned to different items with the help of numerical value as per the priority basis in a series as called as weights. The arithmetic mean on the other hand, gives equal weightage or importance to each observation of the series. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. Following is the procedures of computing mean of a weighted series. By the way, an important problem that arises while using weighted mean is regarding selection of weights. Weights may be either actual or arbitrary, i.e., estimated. The researcher will not face any difficulty, if the actual weights are assigned to the set of data. But in case, if actual data is not assigned than it is advisable to assign arbitrary or imaginary weights. Following are some steps of calculating weighted mean: i. In the first step, the values of each row (X) are to be multiplied by its respective weights (W) ii. Calculate the sum of the weights (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*W values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula Advantages of Arithmetic mean: Following are some advantages of arithmetic mean. i. The concept is more familiar concept among the people. It is unique because each data set has only one mean. ii. It is very easy to compute and requires fewer calculations. As every data set has a mean, hence, as a measure mean can be calculated. iii. Mean represents a single value to the entire data set. Thus easily one can interpret a data set its characteristics. iv. An average can be calculated of any type of series. Disadvantages of Arithmetic mean: The disadvantages are as follows. i. One of the greatest disadvantages of average is that it is mostly affected by the extreme values. For example let consider Sachin Tendulkars score in last three matches. Let it be, 100 in first match, 2 in second match and 10 in third match. The average score of these three matches will me 100+2+10/3=37. Thus it implies that Tendulkars average score is 37 which is not correct. Hence lead to wrong conclusion. ii. It is not possible to compute mean for a data set that has open-ended classes at either the high or low end of the scale. iii. The arithmetic average sometimes gives such value which cannot be found from the data series from which it is calculated. iv. It is unrealistic. v. It cannot be identified observation or graphic method of representing the data and interpretation. THE MEDIAN: Another one technique to measure central tendency of a series of observation is the median. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. In other wards, it is the exactly middle value of the series. Hence, fifty percent of the observations in the series are above the median value and other fifty or half observations are remains below the median value. However, if the series are having odd numbers of observations like 3,5,7,9,11,13 etc., then the median value will be equal to one of the exact value from the series. On the other hand, if the series is having even observations, then median value can be calculated by getting the arithmetic mean of the two middle values of the observations of the series. Median an a technique of measuring central tendency can be best used in cases where the problem sought for more qualitative or psychological in nature such as health, intelligence, satisfaction etc. Definitions: The concept of median can be clearer from the definitions derived below. Connor defined it as ‘the median is the value which divides the distribution into two equal parts, one part comprising all values greater, and the other values less than the median. Where as Croxton and Cowden defined it as ‘the median is that value which divides a series so that one half or more of the items are equal to or less than it and one half or more of the items are equal to or greater than it. Median can be computed in three different series separately. All the cases are discussed separately below. Computation of Median in Individual Series Computation of Median in Discrete Series and Computation of Median in Continuous Series Computation of Median in Individual Series: Following are some steps to calculate the median in individual series. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. Than the median value can be calculated by using the formula th value or item from the series. Where, N= Number of observation in that series. When N is odd number (like 5, 7,9,11,13 etc.) median value is one of the item within that series, but in case N will be a even number than median is the arithmetic mean of the two middle value after applying the above formula. The following problem can make the concept clear. Computation of Median in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Following are the steps of computing the median when the series is discrete. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies of the series. Computation of Median in Continuous Series: Continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of median is little bit different from that of the other two cases discussed above. Following are some steps to get median in continuous series of data. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies column of the series. Form the cumulative frequencies, one can get the median class i.e., in which class the value lies. This class is called as median class and one can get the lower value of the class and the upper value of the class. The following formula can be used to calculate the median We have to get the median class first. For this, median class is N/2 th value or 70/2= 35. The value 35 lies in the third row of the table against the class 30-40. Thus 30-40 is the median class and it shows that the median value lies in this class only. After getting the median class, to get the median value we have to apply the formula . Advantages of Median: Median as a measure of central tendency has following advantages of its own. It is very simple and can be easily understood. It is very easy to calculate and interpret. It Includes all the observations while calculation. Like that of arithmetic mean, median is not affected by the extreme values of the observation. It has the advantages for using further analysis. It can even used to calculate for open ended distribution. Disadvantages of Median: Median as a means to calculate central tendency is also not free from draw backs. Following are some important draw backs that are leveled against median. Median is not a widely measure to calculate central tendency like that of arithmetic mean and also mode. It is not based on algebraic treatment. THE MODE: Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. Like that of median, mode is also more useful in case of qualitative data analysis. It can be used in problems generally having the discrete series of data and particularly, problems involving the expression of psychological determinants. Definitions: The concept of mode can be clearer from the definitions derived below. Croxten and Cowden defined it as ‘the mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded as the most typical of a series of value. Similarly, in the words of Prof. Kenny ‘the value of the variable which occurs most frequently in a distribution is called the mode. Mode can be computed in three different series separately. All the cases are discussed separately below. Computation of Mode in Individual Series Computation of Mode in Discrete Series and Computation of Mode in Continuous Series Computation of Mode in Individual Series: Calculation of mode in individual series is very easy. The data is to be arranged in a sequential order and that value which occurs maximum times in that series is the value mode. The following example will make the concept clear. Computation of Mode in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Hence directly, mode will be that value which is having maximum frequency. By the way, for accuracy in calculation, there is a method called as groping method which is frequently used for calculating mode. Following is the illustration to calculate mode of a series by using grouping method. Consider the following data set and calculate mode by using the grouping method. The calculation carried out in different steps is derived as: Step-1: Sum of two frequencies including the first one i.e., 1+2=3, then 4+3=7, then 2+1=3 etc. Step-2: Sum of two frequencies excluding the first one i.e., 2+4=7, then 3+2=5, then 1+2=3 etc. Step-3: Sum of three frequencies including the first one i.e., 1+2+4=7, then 3+2+1=6 etc. Step-4: Sum of two frequencies excluding the first one i.e., 2+4+3=9, then 2+1+2=5 etc. Step-5: Sum of three frequencies excluding the first and second i.e., 4+3+2=9, then 1+2+1=4. Computation of Mode in Continuous Series: As already discussed, continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of mode is little bit different from that of the other two cases discussed above. Following are some steps to get mode in continuous series of data. Select the mode class. A mode class can be selected by selecting the highest frequency size. Mode value can be calculated by using the following formula Advantages of Mode: Following are some important advantages of mode as a measure of central tendency. It is easy to calculate and easy to understand. It eliminates the impact of extreme values. It is easy to locate and in some cases we can estimate mode by mere inspection. It is not affected by extreme values. Disadvantages of Mode: Following are some important disadvantages of mode. It is not suitable for further mathematical treatment. It may lead to a wrong conclusion. Some critiques criticized mode by saying that mode is influenced by length of the class interval. THE GEOMETRIC MEAN: Geometric mean, as another measure of central tendency is very much useful in social science and business related problems. It is an average which is most suitable when large weights have to be assigned to small values of observations and small weights to large values of observation. Geometric mean best suits to the problems where a particular situation changes over time in percentage terms. Hence it is basically used to find the average percent increase or decrease in sales, production, population etc. Again it is also considered to be the best average in the construction of index numbers. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. For example, if a series is having only two observations then N will be two or we will take square root of the observations. Similarly, when series is having three observations then we have to take cube root and the process will continue like wise. Geometric mean can be calculated separately for two sets of data. Both are discussed below. When the data is ungrouped: In case of ungrouped series of observations, GM can be calculated by using the following formula: where X1 , X2 , X3, XN various observations of a series and N is the Nth observation of the data. But it is very difficult to calculate GM by using the above formula. Hence the above formula needs to be simplified. To simplify the formula, both side of the above formula is to be taken logarithms. To calculate the G.M. of an ungrouped data, following steps are to be adopted. Take the log of individual observations i.e., calculate log X. Make the sum of all log X values i.e., calculate Then use the above formula to calculate the G.M. of the series. When the data is grouped: Calculation of geometric mean in case of grouped data is little bit different from that of calculation of G.M. in case of ungrouped series. Following are some steps to calculate the G.M. in case of grouped data series. To calculate the G.M. of a grouped data, following steps are to be adopted. Take the mid point of the continuous series. Take the log of mid points i.e., calculate log X and it can also be denoted as log m Make the sum of all log X values i.e., calculate or Then use the following formula to calculate the G.M. of the series. Advantages of G.M.: Following are some advantages of G.M. i. One of the greatest advantages of G.M. is that it can be possible for further algebraic treatment i.e., combined G.M., can be calculated when there is availability of G.M., of two or more series along with their corresponding number of observations. ii. It is a very useful method of getting average when the series of observation possess rates of growth i.e., increase or decrease over a period of time. iii. Since it is useful in averaging ratios and percentages, hence, are more useful in social science and business related problems. Disadvantages of G.M.: G.M., as a technique of calculating central value is also not free from defects. Following are some disadvantages of G.M. i. It is very difficult to calculate the value of log and antilog and hence, compared to other methods of central tendency, G.M., is very difficult to compute. ii. The greatest disadvantage of G.M., is that it cannot be used when the series is having both negative or positive observations and observations having more zero values. THE HARMONIC MEAN: The last technique of getting the central tendency of a series of data is the Harmonic mean (H.M.). Harmonic mean, like the other methods of central tendency is not clearly defined. It is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. H.M., is very much useful in those cases of observations where the nature of data is such that it express the average rate of growth of any events. For example, the average rate of increase of sales or profits, the average speed of a train or bus or a journey can be completed etc. Following is the general formula to calculate H.M.: When the data is ungrouped: When the observations of the series are ungrouped, H.M., can be calculated as: The step for calculating H.M., of ungrouped data by using the derived formula is very simple. In such a case, one has to find out the values of 1/X and then sum of 1/X. When the data is grouped: In case of grouped data, the formula for calculating H.M., is discussed as below: Take the mid point of the continuous series. Calculate 1/X and it can also be denoted as 1/m Make the sum of all 1/X values i.e., calculate Then use the following formula to calculate the H.M. of the series. Advantages of H.M.: Harmonic mean as a measure of central tendency is having following advantages. i. Harmonic mean considers each and every observation of the series. ii. It is simple to compute when compared to G.M. iii. It is very useful for averaging rates. Disadvantages of H.M.: Following are some disadvantages of H.M. i. It is rarely used as a technique of measuring central tendency. ii. It is not defined clearly like that of other techniques of measuring central value mean, median and mode. iii. Like that of G.M., H.M., cannot be used when the series is having both negative or positive observations and observations having more zero values. CONCLUSION: An average is a single value representing a group of values. Each type of averages has their own advantages and disadvantages and hence, they are having their own usefulness. But it is always confusing among the researchers that which average is the best among the five different techniques that we have discussed above? The answer to this question is very simple and says that no single average can be considered as best for all types of data. However, experts opine two considerations that the researchers must be kept in mind while going for selecting a technique to determine the average. The first consideration is that of determining the nature of data. If the data is more skewed it is better to avoid arithmetic mean, if the data is having gap around the middle value of the series, then median should be avoided and on the other hand, if the nature of series is such that they are unequal in class-intervals, then mode is to be avoided. The second consideration is on the type of value req uired. When there is need of composite average of all absolute or relative values, then arithmetic mean or geometric mean is to be selected, in case the researcher is in need of a middle value of the series, then median may be the best choice, but in case the most common value is needed, then will not be any alternative except mode. Similarly, Harmonic mean is useful in averaging ratios and percentages. SUMMERY: 1. Different experts have defined differently to the concept of average. 2. Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. 3. The best use of arithmetic mean is at the time of correcting some wrong entered data. For example in a group of 10 students, scoring an average of 60 marks, in a paper it was wrongly marked 70 instead of 65. the solution in such a cases is derived below: 4. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. 5. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. 6. Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. 7. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. 8. Harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. QUESTIONS: 1. In a class containing 90 students following heights (in inches) has been observed. Based on the data calculate the mean, median and mode of the class. 2. In a physical test camp meant for selection of army solders the following heights of the candidates have been observed. Find the mean, median and mode of the distribution. 3. From the distribution derived below, calculate mean and standard deviation of the series. 4. The following table derives the marks obtained in Indian Economy paper by 90 students in a class. Calculate the mean, median and mode of the following distribution. 5. The monthly profits of 180 shop keepers selling different commodities in a city footpath is derived below. Calculate the mean and median of the distribution. 6. The daily wage of 130 labourers working in a cotton mill in Ahmadabad cith is derived below. Calculate the mean, median and mode. 7. There is always controversy before the BCCI before selection of batsmen between Rahul Dravid and V.V.S. Laxman. Runs of 10 test matches of both the players are given below. Suggest who the better run getter is and who the consistent player is. 8. Calculate the mean, median and mode of the following distribution. 9. What do you mean by measure of central tendency? How far it helpful to a decision-maker in the process of decision making? 10. Define measure of central tendency? What are the basic criteria of a good average? 11. What do you mean by measure of central tendency? Compare and contrast arithmetic mean, median and mode by pointing out the advantages and disadvantages. 12. The expenditure on purchase of snacks by a group of hosteller per week is