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A. P. StatisticsChapter 1 Test Review

On this test you will be expected to:

1) demonstrate understanding of the following terms and concepts* individuals and variables* categorical and quantitative variables* center, shape, spread, and outlier* mean and median* five-number summary and interquartile range

* variance and standard deviation

2) construct and interpret the following graphs* histogram* stemplot and back-to-back stemplot* dot plot* box plot and modified box plot* time plot* cumulative frequency plot

3) compare and contrast the above graphs

4) match a data set to a graph

5) estimate the mean and median of a graph and demonstrate

understanding of how the mean and median are related to eachother

6) demonstrate understanding of the concept ofresistance

7) determine whether or not a data value is an outlier

8) use your calculator to find the 5 number summary for data

given in a frequency table

Things you should do:

Look at the sections summaries on pages 24 and 47 andread through the Chapter Review which begins on p. 51.

Look over old quizzes and handouts.

Work through the practice multiple choice questions and

check your answers. Ask questions if you dontunderstand!

Work through sample short answer questions. Payattention to details such as labeling graphs, showing work,and justifying your answers with complete sentences.

Practice Multiple Choice Questions

1. Ms. Sweets biology class had a standard deviation of 2.4 on astandardized test and Ms. Sours biology class had a standarddeviation of 1.2 on the same test. What can be said about thesetwo classes?a. Ms. Sweets class is more homogeneous than Ms. Sours

class.b. Ms. Sours class is more homogeneous than Ms. Sweets

class.c. Ms. Sours class on the average scored lower on the test

than did Ms. Sweets class.d. Ms. Sweets class performed twice as well as did Ms.

Sours class.e. Ms. Sours class performed twice as well as did Ms.

Sweets class.

2. For a symmetric distribution, the mean and the median area. the same

b. always differentc. sometimes the same, sometimes differentd. greater than the standard deviatione. insufficient information to determine the correct answer

Use the stem plot below to answer questions 3 and 4. You shouldnot try to enter the data into your calculator; rather you should beable to determine the answer by simply looking at the graph. (In

fact, on the test if you did this problem by punching in the data, youprobably wouldnt have enough time to finish the test.)

A B

3 2

6 2 3 37 4 2 6

9 0 5 79 9 2 0 6 0 9

9 7 5 4 3 7 0 2 9 98 3 8 3 4 5 7 9

9 3 8

3. Which of the following statements about the stem plot are true?I. Distributions A and B have the same range

II. Distributions A and B have the same medianIII. Distributions A and B have the same

standard deviationa. I only

b. II onlyc. I and II onlyd. I and III onlye. I, II, and III

4. Which of the following statements would be true about thedistribution of data set B in the stem plot above?a. The distribution is skewed to the right and the mean is

less than the median.b. The distribution is skewed to the left and the mean is less

than the median.c. The distribution is skewed to the right and the mean is

greater than the median.d. The distribution is skewed to the left and the mean is

greater than the median.e. The distribution is skewed to the right and the mean is

equal to the median.

5. Find the mean and median of the following sample:

X Frequency

2 13 24 3

a. median = 3; mean = 3b. median = 4; mean 3.3c. median = 4; mean = 3d. median = 3.5; mean = 3e. median = 3.5; mean 3.3

6. The mean, median, and mode of a distribution are 5, 6, and 7respectively. The distribution isa. skewed left

b. uniformc. skewed rightd. symmetricale. bimodal

7. Which of the following statistics are notresistant?I. Mean

II. MedianIII. Standard deviationIV. Interquartile range

a. I onlyb. I and IV onlyc. I and II onlyd. III and IV onlye. I and III only

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8. In a group of 12 scores, the largest score is increased by 36points. What effect will this have on the mean of the scores?a. The mean will increase by 12 points.

b. The mean will remain unchanged.c. The mean will increase by 3 points.d. The mean will increase by 36 points.e. There is no way of knowing by exactly how many points

the mean will increase.

9. A teacher computes the mean of a set of scores and thensubtracts this mean from each students score. What is true

about the sum of the resulting set of adjusted scores?a. The sum will be zero.

b. The sum will equal the number of scores.c. The sum will be the mean.d. The sum will be negative.e. The sum will be positive.

10. If the variance of a distribution is 9, the standard deviation isa. 3

b. 6c. 9d. 81e. It is impossible to determine the standard deviation

without knowing the number of data points.

11. The standard deviation of a group of scores is 10. If 5 weresubtracted from each score, the standard deviation of the newset of scores would bea. 2

b. 10/25c. 5d. 20e. none of these

12. Ms. Smartt calculates the standard deviation for 5 studentsscores on a recent test to be 8. She then discovers that sheomitted one students paper, and now she must recalculate thestandard deviation since there are really 6 students. If theomitted students score is equal to the mean, what effect willthe addition of this students score have on the standard

deviation?a. The addition of this students score will have no effect on

the standard deviation.b. The addition of this students score will cause the

standard deviation to increase.c. The addition of this students score will cause the

standard deviation to decrease.d. It is impossible to know the effect of this students score

without knowing the mean.e. It is impossible to know the effect of this students score

without knowing all of the students scores.

13. Which of the following are true statements?I. Approximately 50% of the data is between

Q1 and Q3.

II. The interquartile range is half the distancebetween the first quartile and the thirdquartile.

III. While the range is affected by outliers, theinterquartile range is not.

a. I onlyb. II onlyc. III onlyd. I and II onlye. I and III only

14. Mr. Hatts third period class has 10 students and the averagescore on a test in their class was 80. His fifth period class has15 students and their average score was 90. If Mr. Hattcombines the two classes, what will the average of thecombined scores be?a. 85

b. 85.5c. 86d. 86.5e. There is insufficient information to answer this question.

15. If the standard deviation of a set of observations is 0, you canconcludea. 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.

16. Which of the following distributions are more likely to beskewed to the left than skewed to the right?

I. Household incomesII. Home prices in a suburban area

III. Ages of teenage drivers

a. III only

b. I and II onlyc. I and III onlyd. II and III onlye. I, II, and III

17. Consider the following parallel boxplots illustrating the dailytemperatures (in degrees Fahrenheit) of an upstate New Yorkcity during January and July.

Which of the following are true statements?I. The ranges are the same.

II. The interquartile ranges are the same.III. Because of symmetry, the medians are the

same

a. I onlyb. II onlyc. I and II onlyd. I and III onlye. II and III only

18. Which of the following statements are true?I. If the right and left sides of a histogram are

mirror images of each other, the distribution isskewed on both sides.

II. A distribution spread far to the right side is saidto be skewed to the right.

III. If a distribution is skewed to the right, its mean isgreater than its median.

a. I onlyb. I and II onlyc. I and III onlyd. II and III onlye. None of the above gives the complete set of true

responses.19. The graph below shows cumulative proportions plotted against

GPAs for high school seniors.

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What is the interquartile range?a. 0.85

b. 2.25c. 2.70d. 2.75e. 3.1

20. Following is a histogram of test scores.

Which of the following statements are true?I. The median score is 75.

II. If the passing score was 60, most students failed.III. More students scored between 50 and 60 than

between 90 and 100.

a. I onlyb. II onlyc. I and III onlyd. II and III onlye. None of the above gives the complete set of true

responses.

21. A stemplot for the 1988 per capita personal income (inhundreds of dollars) for the 50 states is shown below.

11 0 712 6 2 7 8 2 7 5 7 8 5 013 3 7 714 9 7 8 1 615 0 9 0 5 2 5 0 4 416 4 5 9 4 8 2 8 617 7 6 4 618 919 5 3 0 320 721 922 8

Which of the following describes the data?a. Skewed distribution, mean greater than the median.

b. Skewed distribution, median greater than the mean.c. Symmetric distribution, mean greater than the median.d. Symmetric distribution, median greater than the mean.e. Symmetric distribution with outliers on the high end.

22. Look back at the stemplot in number 21. What is the relativefrequency of states with per capita personal incomes of at least$1800?a. 0.02

b. 0.14c. 0.16d. 7e. 8

23. The 5-number summaries for 3 sets of data are given. Forwhich set(s) of data would an observation of 6 be an outlier

(using the IQR rule)?I. 4, 12, 13, 14, 16

II. 4, 11, 12, 15, 16III. 4, 10, 13, 14, 16

a. I onlyb. III onlyc. I and II onlyd. I and III onlye. None of the above gives the complete set of correct

responses

24. Since the distribution of housing prices in a community isusually skewed right, which measure of center should you usefor housing prices?

a. meanb. medianc. moded. IQR e. None of the above

25. In a samples distribution of incomes, the modal income (mostfrequently occurring income) is $27,000 a year, the medianincome is $35,000 a year, and the mean income is $45,000 ayear. Which statistic do you think is the best estimate ofaverage income, and based on this information, would you saythat distribution of incomes is mound-shaped, skewed to theleft, or skewed to the right?a. $27,000; skewed right

b. $35,000; skewed right

c. $45,000; mound-shapedd. $35,000; skewed lefte. $45,000; skewed left