Find the variance of ungrouped data

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

Find the variance of the following 5 data: 21, 22, 9, 4, 24

Remember: Find the mean, square each deviation from the mean, then take the mean of those squares. Variance is the square of the standard deviation.

The mean is 80 ÷ 5 = 16.
Taking the mean from each datum gives 5, 6, −7, −12, 8, and the squares of these add up to 318.
The variance is 318/5.

Common mistakes

Stopped at the sum of the squared deviations. It still has to be divided by N.
Averaged the squares of the data. The mean has to be taken off each datum first.
Averaged the sizes of the deviations without squaring them.