Statistical Sampling


What is the formula for the variance?

2 years ago


1 Reply




Steve Wolff

1 Answer

Anirudh Lakra

Variance is a measure of how far the data points, on average, vary around the mean.

Let us construct the formula from variance using this definition. First of all, let us assume that there are n data points in our dataset and the value xi represents the ith data value. Finally, we will let mu represent the mean value of our dataset.

We can measure how each data point varies around the mean by computing mu - xi for each data point. We generally want this value to be positive so we will square it as well. We need to do this for every single data point and add them all up.

So far: sum ((mu - xi) ^2).

However, we are not done yet. We need to find the average variance and we do this by dividing what we have computed thus far by n (which is the number of data values).

Hence: Variance = (1/n) * sum((mu - xi) ^2).

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