The data set below shows the overall miles per gallon (MPG) of a new model of sm
ID: 3274394 • Letter: T
Question
The data set below shows the overall miles per gallon (MPG) of a new model of small SUVs. a. Compute the first quartile (Q_1), the third quartile (Q_3), and the interquartile range. b. List the five-number summary. c. Construct a boxplot and describe its shape. a. The first quartile is (Type an integer or a decimal.) The third quartile is (Type an integer or a decimal.) The interquartile range is (Type an integer or a decimal.) b. The five-number summary is (Type integers or decimals.) c. Construct a boxplot of the data. Choose the correct graph below. What is the shape of the data? A. The data distribution is left-skewed because the distance from the smallest value to the median is greater than the distance from the median to the largest value. B. The data distribution is symmetric because the distance from the smallest value to the median is equal to the distance from the median to the largest value. C. The data distribution is right-skewed because the distance from the smallest value to the median is less than the distance from the median to the largest value.Explanation / Answer
We can use excel to get the quartiles:
x
22
24
20
22
22
23
23
20
20
21
22
24
25
20
21
21
23
19
21
20
21
22
24
18
16
first quartile =
QUARTILE(D2:D26,1)
= 20
third quartile =
QUARTILE(D2:D26,3)
= 23
interquartile range =
D28-D27
= 3
Question a)
Answer:
The first quartile is 20
The third quartile is 23
The interquartile range is 3
Question b)
Here also we can use excel.
first quartile =
=QUARTILE(D2:D26,1)
= 20
third quartile =
=QUARTILE(D2:D26,3)
= 23
second quartile =
=QUARTILE(D2:D26,2)
= 21
Minimum =
=MIN(D2:D26)
= 16
Maximum =
=MAX(D2:D26)
= 25
The five number summary is 16, 20 , 21, 23, 25
Question c)
Answer: Option B
Answer: Option A. The data distribution is left-skewed because the distance from the smallest value of the median is greater than the distance from the median of the largest value.
x
22
24
20
22
22
23
23
20
20
21
22
24
25
20
21
21
23
19
21
20
21
22
24
18
16
first quartile =
QUARTILE(D2:D26,1)
= 20
third quartile =
QUARTILE(D2:D26,3)
= 23
interquartile range =
D28-D27
= 3
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