Mean,Median and Mode - When and Where?

If you know only 'Average' and do not know much about the words  'Mean', 'Median' and 'Mode’, you are lucky!!  Those who know, always get confused about  When to use it? Which measure to use?
However, clarity helps understand things better.
Let us take the classical example of average income in two localities in Mumbai and try to understand these....

     Locality 1, say Mulund where multi-storied flats co-exist with slums around it.

     Locality 2, say South Mumbai where only Multi-storied flats exist and no slums.
Mean a.k.a Average

When to use Mean?  Mean is also called Average. 

You average out when things are similar or symmetrical. Isn’t it? 

So, in the above-mentioned localities where do you use mean? 

Obviously, in a locality where you find similarity in the population.

i.e. Locality 2 – only multi-storied flats.

Mean is the best measure when the distribution is not skewed.
This means, when symmetry exists use Mean.

Median

Median is the best choice in locality 1 because the distribution is skewed.

(High Income of the people residing in flats and presumably low income in people residing in slums). 

Few People who have disproportionately high income and few with very low income (these are called Outliers) can completely skew and distort the picture.

So , the moral of the story is next time when you are offered a job ask for the median salary of the post rather than the average salary for the post offered!

Mode 

Mode is most recurring or most often seen.

Mode is the least used measure of central tendency. 

Often you find it is not very meaningful.

Lets take the example: The salaries in an office with 6 people are as follows.

Rs.10,000, Rs.10,000, Rs.7,590, Rs.7,550, Rs.2,200 and Rs.7,565.

So, the Mode is most recurring i.e. Rs. 10,000 ( it appeared Twice).

This is not reflecting central tendency. It’s meaningless.

But where do you find Mode useful?

Let’s take this example which may be more meaningful for Gentlemen!

You are standing in a typical Mumbai Bus stop and watching women's dressing!

A Sari , Jeans, Chudidaar or Skirts.

At At the end of the day, if you are not arrested by Police, you come to a conclusion, that most women in Mumbai wear Jeans! (Quite an insight).

So, Mode is the best measure for Nominal data (such as Sex, Race, Ethnicity, Country etc.)

To summarize,

Mean is the Average, Median is Middle and Mode is Most often.

Mean tells the basic character of a population. It does not represent an individual from the population. In reality, you may not find anyone matching the mean in the population.

Median represents a typical Individual from the population.

Mode is most often observed.

Learn with this simple song for a better understanding..