Question

The file Sedans contains the overall miles per gallon
(MPG) of 2013 midsized sedans:
38 26 30 26 25 27 22 27 39 24 24 26 25
23 25 26 31 26 37 22 29 25 33 21 21
Source: Data extracted from “Ratings,” Consumer Reports, April
2013, pp. 30–31.
a. Compute the mean, median, and mode.
b. Compute the variance, standard deviation, range, coefficient of
variation, and Z scores.
c. Are the data skewed? If so, how?
d. Compare the results of (a) through (c) to those of Problem 3.12
(a) through (c) that refer to the miles per gallon of small SUVs.

Answer 1

Solution:-

Given Data

22

22

23

25

25

25

26

26

26

26

27

27

29

30

31

37

38

39

Here using Excel for all calculation

a.)

Mean=28 (Use;'=AVERAGE()' , formula in excel)

Median=26 (use '=Median()' formula in excel)

Mode=26 (most frequent data in the given data set)

b.)Variance=26.94 (use '=Var.s()' in excel)

Standard Deviation =sqrt(Variance)

=5.19

Range=Maximum value-Minimum value

=39-22

=17

Coefficient of variation=(Standard Deviation/Mean)

=15.19/28

=0.5425

Z Score=(X-Mean)/Std. Deviation

X	Z=X-Mean)/Standard Deviation
22	-1.16
22	-1.16
23	-0.96
25	-0.58
25	-0.58
25	-0.58
26	-0.39
26	-0.39
26	-0.39
26	-0.39
27	-0.19
27	-0.19
29	0.19
30	0.39
31	0.58
37	1.73
38	1.93
39	2.12

c.)Skewness=(Mean-Mode)/Std. Deviation

=(28-26)/5.19

=0.3853

here positive sign indicate that the data is right skewed.

d.)

I have solved the whole parts, now compare it with your problem 3.12, as you have not provided that question.