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Benchmark Six Sigma Expert View by Venugopal R Using median as a measure of central tendency helps to avoid effect of outliers. For those who need a clarity on fundamental behavior of mean and median, the following simple example will help. Consider as set of nine data points representing the minimum time in days between failures for nine similar equipment. 70, 248, 2400, 240, 2, 1460, 230, 180, 440 The mean for the above data is 586 whereas the median is 240. Now consider the data set below, which is same as above except that the maximum value has further increased from 2400 to 4800 70, 248, 4800, 240, 2, 1460, 230, 180, 440 The mean has shot up to 852, whereas the median remains unaffected at 240. In the above situation, the median is a more realistic representation as a measure of central tendency of the data. Few examples where the median may be a better choice: 1. Income data in an organization: It is quite possible that there could be a few high paid individuals, by which the mean could be severely biased, hence median is preferable. 2. Age of employees in a society: A few very senior citizens among a majority of people being in the lower middle age band, could give a non-normal distribution. 3. Customer satisfaction surveys using a Likert scale of 1 to 10: A very few customers voting on the upper or lower extreme could distort the reality – hence usage of median helps. 4. Life expectancy based on a specialized treatment: For instance if most patients had a post treatment life span in the range of 10 to 15, one odd patient living for 45 years could provide an unrealistic expectancy, unless we use median as a measure of performance. 5. The comparative tests performed on non-normal distributions, knows as non-parametric tests are based on usage of median. Examples of such tests are 1-Sample sign, Wilcoxon Signed rank, Mann Whitney, Kruskal Wallis, Moods Median.

Mean (Average) Mean is the best measure of central tendency in normally distributed data without significant outliers. As large number of distributions are symmetrical, mean represents the true estimate of distribution. Example: Mean height, weight etc. Mode Mode is the most repeated value in a set of data. Like, people become more inclined to things, that are undertaken by majority of the people. Median The median is the mid value that divides a set of values into top and bottom 50%. The income distribution in a country is asymmetrical, with 20% of population, accounting for major proportion of wealth in the country and remaining 80% of the people have lower income, in the way that wealth of top 20% is equal to bottom 80%. In this case, mean income will give a false and biased picture, due to distribution peaks in two different regions. Median will be the best representer of the income of the people in the country. In India, many educational institutes place their advertisements to attract students by stating the ''placement packages'' of their passing students either due to on campus selection attract students using “placement packages”. In this example, average placement package, which is commonly quoted, is a wrong way of assessing the students. Rather, median serves as the best measure, as the salary range is quite wide, for example for those selected for India location -20 students(salary up to 3 million INR) and those for USA location-5 students (Salary in range of 8 to 10 million INR after conversion of USD to INR) Median also finds use in measurement of commonly measured health indices such as blood pressure. If we measure the blood pressure of 5000 persons in a community health survey and tabulate the systolic and diastolic pressures separately, mean will give an erroneous impression, as 10-15%. of the patients may have very high systolic and diastolic blood pressures, much above the normal reference range( say, Systolic> 200mm of Hg and Diastolic> 140mm of Hg , which is not represented by majority) . Here, median will be the best measure for blood pressure levels of the community people and can be used to initiate health intervention for the community.

Q 225. As per Nash Equilibrium, one cannot predict the result of the choices of multiple decision makers if one analyzes those decisions in isolation. Instead, one must ask what each player would do, taking into account the decision-making of the others. What is the practical utility of Nash Equilibrium in Organizational Decision Making? Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday. All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/ Please visit the forum home page at https://www.benchmarksixsigma.com/forum/ to respond to the latest question open till the next Tuesday/ Friday evening 5 PM as per Indian Standard Time The best answer is always shown at the top among responses and the author finds honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term

Median is a statistical tool for data representation which is a measure for central tendency. In cases where, Mean which is the average of all the data, are not able to represent the correct picture of data requires Median as an indicator which is the central value in the entire data sets and make a clear distinction between first half and second half of the data sets. EXAMPLE 01 : The sales performance for 9 units of an apparel industry showed above average performance for last 3 quarters. So If Team goes by Mean as an indicator for statistical performance monitoring, management would assume that, the KPI is performing well. However if the team distributes the data for all 9 units using Median as an indicator, it was observed that 4 of the 5 units are performing very low in the sale performance, and the other 4 are performing exceedingly well. That kind of statistical representation gives a clear picture to the management that, those 4 units which are not performing well need to be prioritized and given special attention for improvement. But this kind of analysis would not have been possible, if merely we could have used Mean as an indicator. EXAMPLE 02 : One of the pharmaceutical manufacturing organisation has got 17 assembly lines. The management is worried about the Overall Equipment Effectiveness (OEE) performance of the Assembly line as a whole. Against the target OEE of 60%, consider if the average,i.e., Mean OEE of assembly lines come out for past one year comes out to be 63%, than obviously anyone can make out that, we are performing well in terms of average OEE performance of the site. However, if we would like to go into detail into details for bringing continuous improvement in the system, we will be extrapolating the data in terms of median representation. That will give us the clear picture in terms of Which assembly lines among 9 lines are giving poor performance in OEE against the central value and which of them are performing well. This will be a significant input for the management to focus on the assembly lines which are constraints/ poor performer. Hence, Median can be a good tool for ANALYZE phase of Problem solving. EXAMPLE 03 : Lets take another case from a service industry. Suppose there are 121 delivery boys for the Food delivery startup. Operational excellence team started to monitor the data for delivery time accuracy for each of the delivery boys in its dashboard. Even in this case, like above examples, Median can be a good tool to understand the best performers and least performer against the central value. Thus, being the med point in the entire data sets, Median helps in structural distribution of data, which brings more clarity to the problem solving team, on which area to be focused for improvement as a priority.