Question

The accompanying data represent the miles per gallon of a random sample of cars with a​ three-cylinder, 1.0 liter engine.

​(a)	Compute the​ z-score corresponding to the individual who obtained 35.9 miles per gallon. Interpret this result
​(b)	Determine the quartiles.
​(c)	Compute and interpret the interquartile​ range, IQR.
​(d)	Determine the lower and upper fences. Are there any​ outliers?

32.6
34.4
34.8
35.2
35.9
36.2
37.4
37.7
38.0
38.1
38.2
38.6
38.7
39.0
39.4
39.7
40.2
40.7
41.4
41.8
42.1
42.6
43.6
48.8

(a) Compute the​ z-score corresponding to the individual who obtained 35.9 miles per gallon. Interpret this result

The​ z-score corresponding to the individual is [ ] and indicates that the data value is [ ] standard​ deviation(s) [below/above] the [Median/Mode] ​(Type integers or decimals rounded to two decimal places as​ needed.)

​(b) Determine the quartiles.

Q1equals = [ ] mpg (Type an integer or a decimal. Do not​ round.)

Q2equals = [ ] mpg ​(Type an integer or a decimal. Do not​ round.)

Q3equals = [ ] mpg ​(Type an integer or a decimal. Do not​ round.)

​(c) Compute and interpret the interquartile​ range, IQR. Select the correct choice below and fill in the answer box to complete your choice.

(Type an integer or a decimal. Do not​ round.)

A.The interquartile range is [ ] mpg. It is the range of all of the observations in the data set.

B.The interquartile range is [ ] mpg. It is the range of the observations between the lower and upper fences.

C.The interquartile range is [ ] mpg. It is the range of the observations between either the lower or upper quartile and the middle​ quartile; it captures​ 25% of the observations.

D.The interquartile range is [ ] mpg. It is the range of the middle​ 50% of the observations in the data set.

​(d) Determine the lower and upper fences. Are there any​ outliers?

The lower fence is [ ] ​(Type an integer or a decimal. Do not​ round.)

The upper fence is [ ] ​(Type an integer or a decimal. Do not​ round.)

Are there any​ outliers? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.The​ outlier(s) is/are [ ] ​(Type an integer or a decimal. Do not round. Use a comma to separate answers as​ needed.)

B. There are no outliers.

Answer 1

∑x = 935.1  

∑x² = 36710.75  

n = 24  

Mean, x̅ = Ʃx/n = 935.1/24 = 38.9625

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(36710.75-(935.1)²/24)/(24-1)] = 3.4698

a)

z score = (35.9-38.9625)/3.4698 = -0.883

The​ z-score corresponding to the individual is -0.883 and indicates that the data value is 0.883 standard​ deviation below the Mean.

​(b) Quartiles:

First quartile, Q1 = 0.25(n+1)th value = 6.25 th value of sorted data = 36.5

Median, Q2 = 0.5(n+1)th value = 12.5 th value of sorted data = 38.65

Third quartile, Q3 = 0.75(n+1)th value = 18.75   th value of sorted data = 41.225

​(c)

IQR = Q3 - Q1 = 41.225 - 36.5 = 4.725

D.The interquartile range is 4.725 mpg. It is the range of the middle​ 50% of the observations in the data set.

​(d)

Lower Fence = Q1 - 1.5*IQR = 29.4125

Upper Fence = Q3 + 1.5*IQR = 48.3125

A.The​ outlier is 48.8