Statistics – Variance:

The average of the squared differences from the mean is known as the variance. Smaller the variance, closer the data points to the mean and from each other. Higher the variance indicates that the data points are very spread out from the mean and from each other.

The population Variance σ²  of a discrete set of numbers is :
σ²  = 
where x_i is the i^th unit, starting from the first observation to the last
μ – population mean
N -number of units in the population

The Variance of a sample s²  =
where x_i is the ith unit, starting from the first observation to the last
x̅ – sample mean
n – number of units in the sample.

This is known as Bessel’s correction.

To calculate manually:

Find the mean of the set.

Subtract each value from the mean to find its distance from the mean.

Square all distances.

Add all the squares of the distances.

Divide by the number of pieces of data.

The sum of actual deviations having both positive and negative values from the mean is zero. We use sum of squared deviations instead of the actual differences. Since square of the deviations is always positive, the variance is a positive for all data distributions.

Let’s check out variance in Excel:

We have function VARP for population variance