Sample Variance

The Sample Variance, s², is used to calculate how varied a sample is,
and it's useful to estimate the Population Variance.

Since the Sample Variance is kind of estimation, so its formula is bit different.

Why do we need to divide by n-1?

Refer to Quora: Why is the formula of sample variance different from population variance?

“The sample variance is an estimator for the population variance. When applied to sample data, the population variance formula is a biased estimatorof the population variance: it tends to UNDERESTIMATE the amount of variability. "

For solving this Underestimation problem, the statisticians found out that by dividing n-1 we will solve this problem, regards to the idea of degrees of freedom (DF).

Easy way to calculate Sample Variance

This formula is better for handwriting calculation:

Sample Standard Deviation

Example

Solve:

The age of any gorilla in our sample is likely to be closer to the average of the 4 gorillas we looked at instead of the average of all the gorillas in the zoo.
Because of that, the squared deviations from the mean we calculated will probably underestimate the actual deviations from the population mean.
To compensate for this underestimation, rather than simply averaging the squared deviations from the mean, we total them and divide by n-1.