Question

Standard deviation is a useful concept in performance management. Let us say that a director in a local fire department wants to know any variation between the performance of this year and that of the last year. He draws a sample of 10 response times of this year ( in minutes): 3.0, 12.0, 7.0, 4.0, 4.0, 6.0, 3.0, 9.0, 11.0, and 15.0, comparing them with a sample of 10 response times last year ( in minutes): 8.0, 7.0, 8.0, 6.0, 6.0, 9.0, 7.0, 9.0, 8.0, and 6.0.

a. Does he see a performance variation by the mean? ( 10 points)

b. Does he see a performance variation by the standard deviation? If he does, is it performance improvement or deterioration from the last year? Why? ( 10 points)

Answer 1

In the given question, at first, we calculate the mean and standard deviation for response times of the current year and the last year. After calculating the mean and standard deviation for both the current year and last year we compare them. The calculation which is required to find mean and the standard deviation is done in the given table.