Average, Weighted Average, Mean, Median

Mean, Median, Standard Deviation in Statistics

Category: Probability and Statistics Tags: Engineering Mathematics, GATE CS

Average or Mean

    Average is called mean in statistics, which is common center of measures. Dividing sum of elements in set/list by numbers of elements gives average.

Suppose a set of numbers S = {1, 4, 7, 8, 10} where n =5

So, Average or Mean given in image below:

Formula for Average or Mean
Formula for Average/Mean


Average/Mean of above set will be:

Calculation of Average/Mean

Standard Deviation

    Standard Deviation is square root of variance, standard deviation represents how close elements of a set are. High standard deviation means data points are spread to wide range.

So, Standard Deviation given in image below:


Formula of Standard Deviation
Formula of Standard Deviation


Standard Deviation from above set will be:


Calculation of Standard Deviation

Weighted Average

    Weighted Average is called Weighted Mean as well, only difference from Average is input data be in groups with different number of elements in group.

Let’s say age of girls and boys of a classroom given B = {10, 12, 8, 15, 5}, G = {2, 10}. So here two groups are boys and girls and 5, 2 are the number of elements in B and G respectively. Mean of B is 10 and Mean of G is 6.

So, Weighted Average or Weighted Mean in image below:


Formula of Weighted Average/Mean
Formula of Weighted Average/Mean


To calculate average weight of classroom, we will have to calculate weighted average of boys and girls, to do that we will multiply mean of each group with number of elements in respective group then sum all and then divide result by sum of number of elements in each group:


Calculation of Weighted Average/Mean



Calculation of Weighted Average/Mean


    Median is middle value of a series, suppose you have incremental series 1, 2, 4, 5, 7, 10, 13 then middle value is 5 which is called median. Series must be sorted so when we find median we can separate lower and upper half.

If series of n elements has odd number of elements, then median is in exactly in middle. i.e. median of 1,3,4,5,7 is 4

If series of n elements has even number of elements, then median is average of two middle numbers. i.e. median of 1,3,4,5,7,8 is (4+5)/2 = 4.5

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Last modified on 11 October 2018
Nikhil Joshi

Nikhil Joshi
Ceo & Founder at Dotnetlovers
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