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AP Statistics

**AP Review – Center, Spread, Boxplots **

1) Suppose the average score on a national test is 500 with a standard deviation of 100. If each score is increased by 25, what are the new mean and standard deviation?

A) 500, 100

B) 500, 125

D) 525, 105

E) 525, 125

C) 525, 100

2) Suppose the average score on a national test is 500 with a standard deviation of 100. If each score is increased by 25%, what are the new mean and standard deviation?

A) 500, 100

B) 525, 100

C) 625, 100

D) 625, 105

E) 625, 125

3) In a certain southwestern city the air pollution index averages 62.5 during the year with a standard deviation of 18. Assuming that the empirical rule is appropriate, the index falls within what interval 95% of the time?

A) (8.5, 116.5)

B) (26.5, 98.5)

C) (44.5, 80.5)

D) (45.4, 79.6)

E) There is insufficient information to answer this question.

4) The average cost per ounce for glass cleaner is 7.7 cents with a standard deviation of 2.5 cents. What is the *z*-score of Windex with a cost of 10.1 cents per ounce?

A) 0.96

B) 1.31

C) 1.94

D) 4.04

E) None of these

5) Suppose the average height of policemen is 71 inches with a standard deviation of 4 inches, while the average height for policewomen is 66 inches with a standard deviation of 3 inches. If a committee looks at all ways of pairing up on male with one female officer, what will be the mean and standard deviation for the difference in heights for the set of possible partners?

A) Mean of 5 inches with a standard deviation of 1 inch

B) Mean of 5 inches with a standard deviation of 3.5 inches

C) Mean of 5 inches with a standard deviation of 5 inches

D) Mean of 68.5 inches with a standard deviation of 1 inch

E) Mean of 68.5 inches with a standard deviation of 3.5 inches

6) Consider these parallel boxplots of gasoline mileage for three makes of cars. Which of the following are true statements?

22 24 26 28

Miles per gallon

30

I.

All three have the same range.

II.

All three have the same interquartile range.

III.

The difference in the medians between the first and third distributions is equal to the interquartile range of the second distribution.

A) I and II

B) I and III

C) II and III

D) I, II, and III

E) None of the above gives the complete set of true responses.

7) When a set of data has suspect outliers, which of the following are preferred measures of central tendency and of variability?

A) mean and standard deviation

B) mean and variance

C) mean and range

D) median and range

E) median and interquartile range

8) If the standard deviation as a set of observations is 0, you can conclude

A) that there is no relationship between the observations.

B) that the average value is 0.

C) that all the observations are the same value.

D) that a mistake in arithmetic has been made.

E) none of the above.

9) A teacher is teaching two AP Statistics classes. On the final exam, the 20 students in the first class averaged 92 while the 25 students in the second class averaged only 83. If the teacher combines the classes, what will the average final exam score be?

A) 87

B) 87.5

C) 88

D) 85

E) There is insufficient information to answer this question.

10) Suppose *X* and *Y* are random variables with μ

*X*

10 , σ

*X*

3 , μ

*Y*

15 , and σ

*Y*

4 .

Given that *X* and *Y* are independent, what are the mean and standard deviation of the random variable *X* + *Y*?

A) μ

*X Y*

25 , σ

*X Y*

3 .

5

B) μ

*X Y*

25 , σ

*X Y*

5

C) μ

*X Y*

25 , σ

*X Y*

7

D) μ

*X Y*

12 .

5 , σ

*X Y*

7

E) There is insufficient information to answer this question.

11) The *1992 NAEP Trial State Assessment* calculated a state-by-state average mathematics proficiency score for students in the eighth grade.

The resulting boxplot is below. Which of the following statements are true?

280

270

260

250

I.

II.

The state score 273 has a percentile rank of 75.

The mean state score is 270.

III.

The lowest state score is 245.

A) III only

B) I and II

C) I and III

D) II and III

E) I, II, and III

12) A survey was conducted to gather ratings of the quality of service at a local restaurant. Respondents were to rate overall service using the values between 0 (terrible) and 100 (excellent). The ratings are:

The value 82 is

A) the maximum but not an outlier

B) the maximum and an outlier

C) one of two outliers

D) not a data value

Stem Leaf

3

4

5

6

2 4

0 3 4 7 8 9 9 9

0 1 1 2 3 4 5

1 2 5 6 6 8

E) none of these.

7

8 0 2

Stem: tens

Leaf: ones