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# One-Variable Data Analysis Free Response Practice Problems for AP Statistics

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By — McGraw-Hill Professional
Updated on Feb 5, 2011

Review the following concepts if necessary:

### Problems

1. Mickey Mantle played with the New York Yankees from 1951 through 1968. He had the following number of home runs for those years: 13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18. Were any of these years outliers? Explain.
2. Which of the following are properties of the normal distribution? Explain your answers.
1. It has a mean of 0 and a standard deviation of 1.
2. Its mean = median = mode.
3. All terms in the distribution lie within four standard deviations of the mean.
4. It is bell-shaped.
5. The total area under the curve and above the horizontal axis is 1.
3. Make a stemplot for the number of home runs hit by Mickey Mantle during his career (from question ?1, the numbers are: 13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18). Do it first using an increment of 10, then do it again using an increment of 5. What can you see in the second graph that was not obvious in the first?
4. A group of 15 students were identified as needing supplemental help in basic arithmetic skills. Two of the students were put through a pilot program and achieved scores of 84 and 89 on a test of basic skills after the program was finished. The other 13 students received scores of 66, 82, 76, 79, 72, 98, 75, 80, 76, 55, 77, 68, and 69. Find the z-scores for the students in the pilot program and comment on the success of the program.
5. For the 15 students whose scores were given in question #4, find the five-number summary and construct a boxplot of the data. What are the distinguishing features of the graph?
6. Assuming that the batting averages in major league baseball over the years have been approximately normally distributed with a mean of 0.265 and a standard deviation of 0.032, what would be the percentile rank of a player who bats 0.370 (as Barry Bonds did in the 2002 season)?
7. In problem #1, we considered the home runs hit by Mickey Mantle during his career. The following is a stemplot of the number of doubles hit by Mantle during his career. What is the interquartile range (IQR) of this data? (Hint: n =18.)
8. For the histogram pictured below, what proportion of the terms are less than 3.5?
9. The following graph shows boxplots for the number of career home runs for Hank Aaron and Barry Bonds. Comment on the graphs. Which player would you rather have on your team most seasons? A season in which you needed a lot of home runs?
10. Suppose that being in the top 20% of people with high blood cholesterol level is considered dangerous. Assume that cholesterol levels are approximately normally distributed with mean 185 and standard deviation 25. What is the maximum cholesterol level you can have and not be in the top 20%?
11. The following are the salaries, in millions of dollars, for members of the 2001–2002 Golden State Warriors: 6.2, 5.4, 5.4, 4.9, 4.4, 4.4, 3.4, 3.3, 3.0, 2.4, 2.3, 1.3, .3, .3. Which gives a better "picture" of these salaries, mean-based or median-based statistics? Explain.
12. The following table gives the results of an experiment in which the ages of 525 pennies from current change were recorded. "0" represents the current year, "1" represents pennies one year old, etc.
13. Describe the distribution of ages of pennies (remember that the instruction "describe" means to discuss center, spread, and shape). Justify your answer.

14. A wealthy woman is trying to decide whether or not to buy a coin collection that contains 1450 coins. She will buy the collection only if at least 225 of the coins are worth more than \$170. The present owner of the collection reports that the average coin in the collection is worth \$130 with a standard deviation of \$15. Should the woman buy the collection?
15. The mean of a set of 150 values is 35, its median is 33, its standard deviation is 6, and its IQR is 12. A new set is created by first subtracting 10 from every term and then multiplying by 5. What are the mean, median, variance, standard deviation, and IQR of the new set?
16. The following graph shows the distribution of the heights of 300 women whose average height is 65" and whose standard deviation is 2.5". Assume that the heights of women are approximately normally distributed. How many of the women would you expect to be less than 5'2" tall?
17. Which of the following are properties of the standard deviation? Expain your answer.
1. It's the square root of the average squared deviation from the mean.
2. It's resistant to extreme values.
3. It's independent of the number of terms in the distribution.
4. If you added 25 to every value in the dataset, the standard deviation wouldn't change.
5. The interval ± 2s contains 50% of the data in the distribution.
18. Look again at the salaries of the Golden State Warriors in question 11 (in millions, 6.2, 5.4, 5.4, 4.9, 4.4, 4.4, 3.4, 3.3, 3.0, 2.4, 2.3, 1.3, .3, .3). Erick Dampier was the highest paid player at \$6.2 million. What sort of raise would he need so that his salary would be an outlier among these salaries?
19. Given the histogram below, draw, as best you can, the boxplot for the same data.
20. On the first test of the semester, the class average was 72 with a standard deviation of 6. On the second test, the class average was 65 with a standard deviation of 8. Nathan scored 80 on the first test and 76 on the second. Compared to the rest of the class, on which test did Nathan do better?
21. What is the mean of a set of data where s = 20, Σ x = 245, and Σ (x)2 = 13 600?

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