概率与统计 习题

AP Statistics 8/31/00 Coley / P. Myers / Wylder Test #1 (Chapter 1) Name __________________________________________________________

Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.

1. Ms. Myers’ precalculus class had a s tandard deviation of

2.4 on a trigonometry test, while Ms. Gentry's precalculus had a standard

deviation of 1.2 on the same test. What can be said about these two classes?

(a) Ms. Myers’ class is more homogeneous than Ms. Gentry's class. (b) Ms. Gentry's class i s more homogeneous than Ms. Myers’ class. (c) Ms. Gentry's class did less well on the test than Ms. Myers’ class.

(d) Ms. Myers’ class performed twice as well on the test as Ms. Gentry’s class. (e) Ms. Myers’ class performed 1.2 points better on the test as Ms. Gentry’s class.

2. The following is the DataDesk statistical summary of thegold medal performance

in the men's long jump (measured in inches) for the modern Olympic series starting in 1900. Approximately what percent of the data lie between 298 and 334.64?

(a) 25% (b) 33% (c) 50% (d) 67% (e) 75%

3. Weights of seals are given in the following histogram.

For this data, which values are appropriate estimates of the data’s mean and standard deviation?

(a) 100, 50 (b) 100, 100 (c) 200, 50 (d) 200, 100 (e) 300, 50

4. A data set with seven data points has a mean of

5. One of the seven values in the data set is 8. What numerical contribution did

the data point 8 make to the variance?

(a) 1.25 (b) 1.50 (c) 1.75 (d) 2.00 (e) 2.25

5. In a frequency distribution of 3000 scores, the mean is 78 and the median as 95. One would expect this distribution to be:

(a) skewed to the right (b) skewed to the left

(c) symmetrical and mound-shaped (d) symmetrical and uniform

6. A study was conducted on the weights of three different species of fish

found in a lake in Finland. These three fish (bream, perch and roach) are

commercial fish. Their weights are displayed in the boxplots below. Which

of the following statements comparing these boxplots is NOT correct?

(a) The median weights of the three species differ.

(b) The spread of roach is less than the spread of the other two species.

(c) The distributions of weights are approximately symmetric for all three

species.

(d) There are no outliers in weight for the three species.

(e) The variability in the weights for the three species exceeds the variation in

the three species’ means.

7. The mean age of 12 of the members attending a mathematics department

faculty meeting is 37. Mr. Myers, who is 50, arrives late. What is the average of all 13 members?

(a) 37

(b) 38

(c) 39

(d) 40

(e) 41

8. Which of the following are true statements?

I.The standard deviation is the square root of the variance.

II.The standard deviation is zero only when all values are the same.

III.The standard deviation is strongly affected by outliers.

(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.

of the 50 states. Which of the following best describes the data?

(a)Skewed distribution, mean greater than median

(b)Skewed distribution, median greater than mean

(c)Symmetric distribution, mean greater than median

(d)Symmetric distribution, median greater than mean

(e)Symmetric distribution with outliers on high end

10. In order to rate TV shows, phone surveys are sometimes used. Such a survey might record several variables, some of which are

listed below. Which of these variables are categorical?

I.The type of show being watched

II.The number of persons watching the show

III.The ages of persons watching the show

IV.The name of the show being watched

V.The number of times the show has been watched in the last month

(a)II, III, and V

(b)I only

(c)I and V

(d)I and IV

(e)None of the above describes the complete set of correct responses

Part II – Free Response (Questions 11-14) – Show your work and explain your results clearly.

11. Is it easier for the best National Basketball Association (NBA) players to get a rebound or an assist? The data was taken during

the 1994-1995 season.

The top 20 rebounding leaders averaged the following numbers of rebounds per game:

16.8 (Rodman), 12.6, 11.4, 11.1, 11.0, 10.9, 10.9, 10.9, 10.8, 10.8, 10.6, 10.6, 10.6, 10.4, 10.3, 9.9, 9.7, 9.7, 9.6, and 9.4

The top 20 assist leaders averaged the following number of assists per game:

12.3 (Stockton), 9.4, 9.3, 8.8, 8.7, 8.3, 8.2, 7.9, 7.7, 7.7, 7.6, 7.5, 7.3, 7.2, 7.1, 6.9, 6.4, 6.2, 6.1, and 5.7

Compare these data using back-to-back stemplots.

Comment and shape and outliers.

Woodward Academy families.

How many families are represented in this study?

Determine the mean, median, mode, standard deviation, IQR,

and range of the data and comment on the most appropriate

measures to report and the shape of the data.

13. Determine, with explanation, which values (if any) in the following dataset of test scores are outliers.

52, 75, 79, 83, 98, 86, 74, 77, 80, 99, 83, 85, 72, 46, 84

14. Five hundred randomly selected middle-aged men and five hundred randomly selected young adult men were rated on a scale from

1 to 10 on their physical flexibility, with 10 being the most flexible. Their ratings appear in the frequency table below. For

example, 17 middle-aged men had a flexibility rating of 1.

(a)Display these data graphically so that the flexibility of middle-aged men and young adult men can be easily compared.

(b) Based on an examination of your graphical display, write a few sentences comparing the flexibility of middle-aged men with the flexibility of young adult men.