Whenever we are asked to find the variance then the first thing you have to keep in mind that variance is always defined for large population. As we can treat any population as Random variables so our first task is to have a little knowledge about Random Variable. After performing the experiment we will be getting a numeric value if that value is fixed then the experiment is called as random variable and if not fixed then it is called as infinite random variable. Now our task is how to find variance, for finding the variance we need to find the Standard Deviation first and after that we can find variance. Here I want to tell you a very important Point about variance that it is the only parameter which describes Probability distribution. Variance is denoted by ‘σ2’.
The first thing we need to find before finding variance is Mean, as we all know that we can find the mean of any data by adding all the terms and then divide it by number of terms. Now we will see one example in which we will be finding the variance of a data.
Example: find the variance of 4, 5, 6, 7, 8, 6
Firstly we will find mean
4 + 5 + 6 + 7 + 8 + 6/6
So mean will be 6
Now for calculating the variance we will be subtracting all the term by mean and then we will find the Square of each term,
So the variance will be,
σ2= ((6 - 4)2 + (6 - 6)2 + (6 - 6)2 + (7 - 6)2 + (8 - 6)2 + (6-6)2)/6,
σ2= 4 + 1 +0 + 1 + 4 + 0/6
σ = 0.527
Using this we can calculate variance of any data.