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)

c. Now, imagine that you are a citizen receiving fire protection services from the local fire department. How do you evaluate the response times of the fire department, by the mean, by the standard deviation, or by both? Please explain. ( 20 points).

Answer 1

Given that :

Sample size = 10

a)Mean for the year = 7.4

i.e (3 + 12 + 7 + 4 + 4 + 6 + 3 + 9 + 11 + 15) / 10 = 74 / 10 = 74

mean for last year = 7.4

i.e ( 8 + 7 + 8 + 6 + 6 + 9 + 7 + 9 + 8 + 6) / 10 = 74 / 10 = 7.4

Therefore Here,

Ans : No

Because,The mean for both years is 7.4

b)YES,

The standard deviation of reaction times this year is larger,indicating a presentation crumbling from the last year.This implies that reaction times have moved toward becoming unstable,unpredictable,and unreliable.There are three long reactions this year.

c)Citizens ought to be concerned on the grounds that they could be possibly influenced by longer responses.Management should utilize the both the mean and standard deviation in assessment.