Units of measure change numeric values of a standard deviation.

Calculate the standard deviations of the batches of numbers here.

Which batch has the greatest variability?

This exercise demonstrates a potential problem when comparing standard deviations for variables using different units of measurement. The three batches of numbers describe identical information, but their standard deviations differ. Reporting units of measure mitigates the problem: Batch A has a standard deviation of 1 year, batch 2 has a standard deviation of 12 months, and batch 3 has a standard deviation of 365 days.
When it is necessary to compare standard deviations of measurements on different scales, convert each standard deviation to a coefficient of variation (CV), defined as The CV removes the units of measure and expresses the standard deviation in relation to the size of the mean. This allows for direct comparison of numerical results. In Exercise 4.11, batch A has CV = 1 year/1 year = 1, batch 2 has CV = 12 months/12 months = 1, and batch 3 has CV = 365 days/365 days = 1. All three CVs are equal to 1.