Question

Consumer Reports uses a 100-point customer satisfaction score to rate the nations major chain stores. Assume that from the past experience with the satisfaction rating score, a population standard deviation of 12 is expected. In 2012, Costco with its 432 warehouses in 40 states was the only chain store to earn an outstanding rating for overall quality. A sample of 15 costco customer satisfaction scores follow:

95 90 83 64 95
98 80 83 82 93
86 80 94 75 62
(A) What is the sample mean customer satisfaction score for Costco?
(B) What is the sample variance?
(C) What is the sample standard deviation?

Answer 1

(A) Mean = 84

(B) Variance = 118.714

(C) Standard deviation = 10.89

Explanation:

Data provided:

number of observations, n = 15

sample of 15 costco customer satisfaction scores follow

X
`X-\bar{X}`
`(X-\bar{X})^2`

95 11 121

90 6 36

83 -1 1

64 -20 400

95 11 121

98 14 196

80 -4 16

83 -1 1

82 -2 4

93 9 81

86 2 4

80 -4 16

94 10 100

75 -9 81

62 -22 484

================================================

∑X = 1260 ∑= 1662

Now,

(A) Mean =
`\frac{\textup{Sum of all observations}}{\textup{Total number of observations}}`

or

Mean =
`\frac{\textup{1260}}{\textup{15}}` = 84

(B) Variance =
`\frac{\sum(X-\bar{X})^2}{n-1}`

or

Variance =
`(1662)/(15-1)`

or

Variance = 118.714

(C) Standard deviation = √Variance = √118.714 = 10.89