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**

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(b)
Determine the quartiles.
(c)
Compute and interpret the interquartile range, IQR.
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Determine the lower and upper fences. Are there any
outliers?
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34.7
35.7
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36.3
37.3
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