Question

3.12 The file SUV contains the overall miles per gallon (MPG) of 2015 small SUVs: 26 22 24 22 26 21 24 25 28 24 22 21 22 21 24 23 23 22 21 22 Source: Data extracted from "Which Cars Is Right for You,” Consumer Reports, April 2015, pp. 60-61. 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 3.11 (a) through (c) that refer to the MPG of midsized sedans.

Answer 1

The given data is:

data
26
22
24
22
26
21
24
25
28
24
22
21
22
21
24
23
23
22
21
22

Using Excel<data<megastat<descriptive statistics

Here is the output:

Descriptive statistics
	data
count	20
mean	23.15
sample standard deviation	1.95
sample variance	3.82
minimum	21
maximum	28
range	7
skewness	0.94
kurtosis	0.40
coefficient of variation (CV)	8.44%
1st quartile	22.00
median	22.50
3rd quartile	24.00
interquartile range	2.00
mode	22.00

confidence interval 95.% lower	22.24
confidence interval 95.% upper	24.06
margin of error	0.91
t(df = 19)	2.093

Answers:

a) Mean=Sum of all observations/Total number of observations =463/20=23.15

Mode=22

Median=22.50

b) Variance=3.82

Standard deviation=1.95

Range=7

Coefficient of variation=8.44%

Z scores=2.093 (n<30)

c) The skewness can be found with the help of a box plot:

ejep ZE DE L 87 97 07. ? 0 BoxPlot

Skewed to right. Skewed data show a lopsided boxplot, where the median cuts the box into two unequal pieces. If the longer part of the box is to the right (or above) the median, the data is said to be skewed right.