Table of Contents

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Application of median in real life

Consider the case of a suburb having 9 similar eateries.Assume that a lunch for a person costs - say,60, 50, 70, 90, 80, 100, 80, 120, 110 rupees.

Few hundred meters away from these eateries, there lies a posh hotel that charges - say Rs.

500 per lunch.

Now, what is the average cost of lunch for one person - in this locality? Average cost -> Arithmetic mean, or, simply mean would be:,(60+50+70+.

.

.

.

+110+500)/10.

0 --> 1260/10 --> 126.

,If you have to find the median price, you have to sort the price in ascending order - 50, 60, 70, 80, 80, 90, 100, 110, 120, 500; Then, find the middle item - 6th item - 90 would be your median.

,For mode, the item with the maximum frequency would be your mode.

Here, it would be 80.

It is totally possible that there could be more than one mode in a data set.

,Now, for the interpretation part:,From the values of mean and median, is it okay to say that the average cost of lunch is Rs.

126.

Here 126 is much more than the 9th item in the list.

If you take median here, we could say that the median price of food in the locality is Rs.

90 - which means there are equal number of observations to both the left and right of 90 (above and below).

This gives a feel that the median cost/lunch is not that bad as observed through mean.

,What is happening here?,Mean is sensitive to extreme observations.

Data point: 500 is an outlier, and it skews the entire data set.

However, in case of median, it is totally resistant to extreme observations.

All it matters in Median, is each numbers relative standing with respect to the Median.

In this example, Median would be the right choice for central tendency and not mean.

,Similarly, the housing prices in a locality - may have few outliers (for now - treat them as numbers that are far off from mean/median), and hence, Median price would be the right way to represent the central tendency of housing prices.

Also, in a group within an organization, median income would be the right choice for the central tendency.

,NOTE:,1.

I hope this sounds as laymen as possible and relate to real life.

,2.

Central tendency - defines how data is distributed around the mean or median.

,3.

In a normal distribution, both mean and median would be the same.

,4.

Choice of mean or median as central tendency would vary depending on how the data is distributed.

##
Real life example of mean

All measures of central tendency are trying to find one number that minimizes error.And here error is what you think error is - how wrong you are.

Each minimizes a different type of error.

,The mode (most common response) minimizes the odds you guess wrong.

For example, if I need to guess how tall a person is and Iu2019m going to be either right or wrong, guessing the modal height (5u20194u201d, say) would give the most correct and fewest incorrect guesses.

,The median is the response that divides the population into the top and bottom 50%.

Here Iu2019m interested in minimizing my summed TOTAL error.

In this case, the error is the distance of my guess (the median) from how tall people actually are.

If I have a group of people and am asked how tall each person is, I subtract the median (my guess) from each personu2019s height.

The distance of their true height from my guess is each personu2019s error.

Adding those errors together gives me my summed error.

The median will give me a smaller summed error than any other number.

So if I just want to be as correct as possible, thatu2019s going to be my choice.

,The mean minimizes LARGE errors.

Like the median, error is determined by the distance of your guess (the mean) from peopleu2019s true scores.

However, instead of just adding together all the errors to get a total summed error, you SQUARE the errors prior to summing them.

This exaggerates the influence of large deviations between my guess (the mean) and the true score).

The mean is the number the minimizes summed SQUARED error, thus it will tend to move towards the outliers.

This will my choice for making the best guess of a population if my goal is to minimize large errors in the guess.

,Grades are an example I often use to help people think about which measure of central tendency works best.

Say a student has the following assignment grades:,90,90,90,80,80,70,0 (missing assignment),If I used a mode, the student would earn a 90 for the class.

If I used a median, they would earn an 80.

If I used a mean, they would earn a 71.

4.

Which do you think best represents their work? You can make an argument for each of those grades, but they are each minimizing a different type of error.

,(As a practical matter, I believe the effective range of grades is 50u2013100, not 0 to 100.

One could reassign the missing assignment a 50 instead of a 0.

That penalizes students for missing work but doesnu2019t heavily weight missing assignments by making them huge outliers.

Then one could use a mean to calculate the grades, giving the student a 78.

6.

)

##
uses of mean, median and mode pdf

First, neither of those parameters are averages.(The mean of a random process can be estimated by computing the mean of a sample from that distribution, but is just a estimate of the actual mean.

),Second, some distribution have those parameters in their distribution functions, or derivable from the distributionu2019s PDF, and estimates of them can be computed from observations.

For other distributions, those parameters do not exist.

,So the appropriate circumstance is u201cwhen you have a sample from a distribution where those parameters are meaningful.

u201d

##
Using mean, median and mode in healthcare

Interview - IIM Lucknow (in Noida Campus),Status - Converted,Background - Engineer, Business Analyst in Healthcare insurance,I was the last in my panel.Document verification took a lot of time.

,2 Panelists - Male professor, M and Female professor, F (Senior in terms of expertise),I know work experience is my strong suit, so i end my introduction in work experience, or try to link, if possible my answers to work experience.

,M - Introduce yourself.

,Me - Ended in me being an analyst for 3 years, and have used Regression, Text Analytics, other M/C learning techniques.

,M (clearly an expert on M/C learning techniques) - Tell me the formula for standard deviation.

,*Told the one with N in denominator,M - There are 2, one where you also divide by (N-1),*Told the difference, Sample Vs.

Population,M - Asked the reason,*Didnt knew at that time,Me - I am not aware about it.

,M - Range of Correlation; What does -1.

5 correlation coefficient mean; R square Vs.

Adjusted R square; Difference between Mean, Median and Mode, with examples from Data preparation in Regression;,*Told,F was listening all this time.

Suddenly barged in to check my basics.

,F - Equation of Linear regression, she wanted to know if we add the terms after multiplying the coefficients with independent variables.

,*I told the various counterpoints, like adding an intercept term, eliminating the not significant variables etc.

,F - Yes or No? **slightly angry,Me - Yes,F - We are done with you.

Thank you.

,Me - Thank you for your time.

*left*,**This lasted for only 4 minutes.

,**I knew either it was a blunder or i simply did awesome.

,**Converted today, 28th April**,**Latter it is.

:p

##
Applications of mode in real life

Consider the case of a suburb having 9 similar eateries.Assume that a lunch for a person costs - say,60, 50, 70, 90, 80, 100, 80, 120, 110 rupees.

Few hundred meters away from these eateries, there lies a posh hotel that charges - say Rs.

500 per lunch.

Now, what is the average cost of lunch for one person - in this locality? Average cost -> Arithmetic mean, or, simply mean would be:,(60+50+70+.

.

.

.

+110+500)/10.

0 --> 1260/10 --> 126.

,If you have to find the median price, you have to sort the price in ascending order - 50, 60, 70, 80, 80, 90, 100, 110, 120, 500; Then, find the middle item - 6th item - 90 would be your median.

,For mode, the item with the maximum frequency would be your mode.

Here, it would be 80.

It is totally possible that there could be more than one mode in a data set.

,Now, for the interpretation part:,From the values of mean and median, is it okay to say that the average cost of lunch is Rs.

126.

Here 126 is much more than the 9th item in the list.

If you take median here, we could say that the median price of food in the locality is Rs.

90 - which means there are equal number of observations to both the left and right of 90 (above and below).

This gives a feel that the median cost/lunch is not that bad as observed through mean.

,What is happening here?,Mean is sensitive to extreme observations.

Data point: 500 is an outlier, and it skews the entire data set.

However, in case of median, it is totally resistant to extreme observations.

All it matters in Median, is each numbers relative standing with respect to the Median.

In this example, Median would be the right choice for central tendency and not mean.

,Similarly, the housing prices in a locality - may have few outliers (for now - treat them as numbers that are far off from mean/median), and hence, Median price would be the right way to represent the central tendency of housing prices.

Also, in a group within an organization, median income would be the right choice for the central tendency.

,NOTE:,1.

I hope this sounds as laymen as possible and relate to real life.

,2.

Central tendency - defines how data is distributed around the mean or median.

,3.

In a normal distribution, both mean and median would be the same.

,4.

Choice of mean or median as central tendency would vary depending on how the data is distributed.

##
use of mean, median, mode in education

CAT Percentile: 99.82,Background: X- 90% (CBSE), XII -95.

6(State Board), Engg - 8.

6, Mech Engg, Bits Pilani, Goa Campus.

Work Exp - 6 Months by January of that year (I remember this to be considered for consolidated scores),WAT & GD - Had a WAT and GD Topic about Govt.

providing subsidies and its advantages and disadvantages for the whole country.

I used couple of data based facts in the WAT and used similar points in GD as well, along with good counter arguments to some of the points raised by other participants.

,Interview -,Panelists - Accounting Prof with serious face and Operations Prof with relatively neutral face (This is the toughest expression to deal with as you wonu2019t understand whether interview is going great or not),Started with simple Tell me about yourself, my typical working day, my company and its details (It was a private firm in education space and panel wouldnu2019t know a lot about the firm),Then, I had a rapid fire round :,Mean, Median and Mode,Standard Deviation (SD),Why do we square and then add all deviations and apply square root again for Standard Deviation,Two batsmen with similar average and different SD, whom would you prefer in the team?,Who is the current World Chess Champion ? (Mentioned Chess as a hobby in the form),Who is the guy that leaked about NSA abusing privacy of people? (Mentioned about my interest in following technology related news in the form and expect this to appear from that),Where is he currently living after moving out of US?,I answered all these questions correctly and interview ended.

I felt happy for the way I answered these questions, but the difficult part was with handling their expressions.

,It was a short and quick one.

And I made it to IIM Kozhikode and had the luck to attend Accounting Prof classes as well.

,Hope it helps !!