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

Answer:

(A) Mean = 84

(B) Variance = 118.714

(C) Standard deviation = 10.89

Step-by-step 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 = $\frac{1662}{15-1}$

or

Variance = 118.714

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