Mean, Median and Mode

Let’s get into little elementary stuff which is basic but important.


It is the average of all entries or data points. For example :- 9,2,3,1,2,2,4,1,5,6,3

Mean = (9+2+3+1+2+2+4+1+5+6+3)/11 = 3.455


It is the mid point of the data. For example :- considering previous data i.e 9,2,3,1,2,2,4,1,5,6,3

Median = sort the data then pick the mid element.

Sorted data = 1,1,2,2,2,3,3,4,5,6,9

Mid element = 3 , in this case we have odd number of elements but if we have even number of elements then we take average of the two mid elements.


The element which is occurring maximum number of times is the mode. For example :- considering previous data i.e 9,2,3,1,2,2,4,1,5,6,3

1 = 2 times, 2 = 3 times, 3 = 2 times, 4 = 1 time, 5  = 1 time, 6  = time, 9 = 1 time

So Mode = 2

We usually found mode of discrete numerical data. Mode is not that much in use.

Median gives more reliable information then mean. If our data have some outliers then mean we mislead us but there will be no effect on the median. Let’s discuss this with an example.

Consider income of citizens of any country. There will some people which are very rich, their income will effect the mean and we can not get a correct picture of the incomes. These will act as outliers. But these values have no effect on median. Therefore median is better than mean. Let’s discuss this with considering our example data i.e 9,2,3,2,2,4,1,5,6,3

Now mean is 3.455 and median is 3. If we add 100 to the data then our mean will be (9+2+3+2+2+4+1+5+6+3+100)/12 = 11.5  and median will be 1,1,2,2,2,3,3,4,5,6,9,100 = (3+3)/2 = 3. There is no effect on median but mean changed drastically. Therefore median is better then mean.  


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