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 36.3 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?

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32.5	35.9	38.0	38.6	39.9	42.4
34.4	36.3	38.1	38.7	40.6	42.7
34.6	37.5	38.2	39.5	41.4	43.8
35.2	37.7	38.5	39.8	41.6	49.3

(a) Compute the​ z-score corresponding to the individual who obtained

36.336.3

miles per gallon. Interpret this result.The​ z-score corresponding to the individual is

nothing

and indicates that the data value is

nothing

standard​ deviation(s)

▼

the

▼

​(Type integers or decimals rounded to two decimal places as​ needed.)

​(b) Determine the quartiles.

Q1equals=nothing

mpg

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

Q2equals=nothing

mpg

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

Q3equals=nothing

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

nothing

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.

B.

The interquartile range is

nothing

mpg. It is the range of the observations between the lower and upper fences.

C.

The interquartile range is

nothing

mpg. It is the range of the middle​ 50% of the observations in the data set.

D.

The interquartile range is

nothing

mpg. It is the range of all of the observations in the data set.

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

The lower fence is

nothing.

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

The upper fence is

nothing.

​(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

nothing.

​(Type an integer or a decimal. Do not round. Use a comma to separate answers as​ needed.)

B.

There are no outliers.

Answer 1

First we need to find the mean and SD of data. Let X is a random variable shows the given data. Following table shows the calculations:

	X	(X-mean)^2
	32.5	41.8609
	35.9	9.4249
	38	0.9409
	38.6	0.1369
	39.9	0.8649
	42.4	11.7649
	34.4	20.8849
	36.3	7.1289
	38.1	0.7569
	38.7	0.0729
	40.6	2.6569
	42.7	13.9129
	34.6	19.0969
	37.5	2.1609
	38.2	0.5929
	39.5	0.2809
	41.4	5.9049
	43.8	23.3289
	35.2	14.2129
	37.7	1.6129
	38.5	0.2209
	39.8	0.6889
	41.6	6.9169
	49.3	106.7089
Total	935.2	292.1336

Sample size: n =24

The sample mean is:

The standard deviation is:

The z-score for x = 36.3 is

The​ z-score corresponding to the individual is -0.66 and indicates that the data value is 0.66 standard​ deviations below the mean.

(b)

Following is the ordered data set:

S.No.	X
1	32.5
2	34.4
3	34.6
4	35.2
5	35.9
6	36.3
7	37.5
8	37.7
9	38
10	38.1
11	38.2
12	38.5
13	38.6
14	38.7
15	39.5
16	39.8
17	39.9
18	40.6
19	41.4
20	41.6
21	42.4
22	42.7
23	43.8
24	49.3

There are 12 data values in first half so first quartile will be average of 6th and 7th data values. That is first quartile is:

There are 24 data values so median will be average of 12th and 13th data values. That is median will be

There are 12 data values in second half so third quartile will be average of 18th and 19th data values. That is first quartile is:

(c)

The inter quartile range is:

C.

The interquartile range is 4.1 mpg. It is the range of the middle​ 50% of the observations in the data set.

(d)

Lower fence:

Upper fence:

A: The outlier is: 49.3