When the variable is height in centimetres, the unit of the standard deviation is

The correct answer is (d).

The standard deviation is a measure of how spread out a set of numbers is. It is calculated by taking the square root of the variance. The variance is calculated by taking the average of the squared deviations from the mean.

In the case of height in centimeters, the mean is the average height in centimeters. The squared deviations from the mean are the differences between each height and the mean, squared. The average of the squared deviations from the mean is the variance. The square root of the variance is the standard deviation.

The standard deviation has no units, because it is a measure of spread, not of size. It is a measure of how spread out the numbers are, not of how big or small they are.

(a) is incorrect because the unit of the standard deviation is not centimeters.
(b) is incorrect because the unit of the standard deviation is not centimeters squared.
(c) is incorrect because the unit of the standard deviation is not centimeters to the minus one.