The ages of all patients in the isolation ward of the hospital are 38, 26, 13, 41 and 22.

Question

What is the population variance?

Answer 1

The variance will be based on this standard formula, which is no doubt in your text book:

s^2 = (sum (x^2) - (sum x)^2 / N) / N - 1

The numbers 38, 26, 13, 41 and 22 - there are 5 of them, and that's N.

The sum of the 5 numbers is sum x = 140.

You also need the sum of the squares of the 5 numbers, and the squares are

1444, 676, 169, 1681 and 484 - so the sum of the squares is 4454.

The variance is found by

s^2 = (4454 - (140^2 / 5)) / 4 = (4454 - 3920) / 4 = 133.5