It is average of squared differences from the mean. In simple words we subtract mean from every element and which give us the distance of every element from mean. Then we square each to avoid negative numbers and then find average. For example :- 1,2,3,4,5,6,7,8,9

Mean = 5

Distance from mean :- -4,-3,-2,-1,0,1,2,3,4

If we find average now then negative and positive will cancel out each other. So, we will square all and then find average.

Square :- 16,9,4,1,0,1,4,9,16

Average :- 6.667

So, Variance = 6.667

Standard Deviation

It is square root of variance.

Considering previous example, Standard Deviation = 2.582

So question is what Standard Deviation actually gives : –

let we have some spread data and we know it’s mean which gives average or somewhat the middle point of the data. Now to know on an average how far or spread our data is from mean we find standard deviation.