**1. Which of the following boxplots correctly represents the data set shown below? **

7, 8, 8, 11, 13, 14, 15, 15, 16, 17, 21, 23, 23, 24, 31, 35, 35, 35, 38, 38, 40, 45, 49, 50, 50

7, 8, 8, 11, 13, 14, 15, 15, 16, 17, 21, 23, 23, 24, 31, 35, 35, 35, 38, 38, 40, 45, 49, 50, 50

**2. Given the parallel boxplots shown below, which of the following statements is true?**

- The boxplot for data set A has a larger interquartile range and a larger median.
- The boxplot for data set B has a larger interquartile range and a larger median.
- The boxplot for data set A has a larger interquartile range and a smaller median.
- The boxplot for data set B has a larger interquartile range and a smaller median.

**3. Given the double bar graph shown below, which of the following statements is true?**

- Group A is negatively skewed, while Group B is approximately normal.
- Group A is positively skewed, while Group B is approximately normal.
- Group A is approximately normal, while Group B is negatively skewed.
- Group A is approximately normal, while Group B is positively skewed.

**4. Which of the following data sets is represented by the histogram shown below?**

- 6,7, 7, 8, 12, 13, 18, 22, 26, 27, 28, 31, 36, 36, 36,

36, 37, 38, 38, 38, 39, 41, 41, 41, 42, 42, 43, 43, 48, 49 - 2, 3, 4, 4, 8, 9, 10, 10, 11, 15, 19, 21, 21, 21, 21,

22, 24, 24, 25, 29, 31, 33, 40, 43, 45, 46, 48, 48, 49, 50 - 1, 2, 8, 8, 9, 9, 12, 13, 15, 15, 16, 17, 18, 19, 19,

21, 29, 31, 31, 35, 36, 38, 41, 42, 42, 45, 46, 47, 47, 49 - 1, 4, 4, 5, 10, 10, 10, 12, 12, 16, 20, 22, 23, 23, 25,

27, 31, 31, 37, 39, 40, 41, 41, 43, 45, 46, 48, 49, 49, 50

**5. The statistics scores for Sections 101 and 102 are shown below. Which of the following statements accurately compare the center and variability of the sets of scores?**

- The statistics scores for Section 101 show a greater center and variability.
- he statistics scores for Section 101 show a greater center but smaller variability.
- he statistics scores for Section 101 show a smaller center but greater variability.
- The statistics scores for Section 101 show a smaller center and variability.

**6. Given the histograms shown below, which of the following statements is true?**

- Group A is negatively skewed and has a mean that is less than the mean of Group B.
- Group A is positively skewed and has a mean that is more than the mean of Group B.
- Group B is negatively skewed and has a mean that is more than the mean of Group A.
- Group B is positively skewed and has a mean that is less than the mean of Group A.

**7. Given a normal distribution, which of the following best represents the area under the curve to the right of a z-score of 1.38?**

- 0.03
- 0.08
- 0.12
- 0.15

**8. Given ? = 18 and ? = 2, which of the following best represents the proportion of scores falling above 19?**

- 31%
- 18%
- 41%
- 22%

**9. Which of the following best represents the area under the curve of a normal distribution, falling between the z-scores of ?0.8 and 1.2?**

- 62%
- 67%
- 72%

d. - 77%

**10. Given the table below, which of the following best represents the probability that a student is enrolled at TAMU or prefers lattes?**

- 55%
- 60%
- 65%
- 70%

## Answers and Explanations

**1. A: **The minimum and maximum values are 7 and 50, respectively. The median is 23, while the first and third quartiles are 15 and 38. The boxplot for Choice A correctly represents these five values.

**2. B: **The boxplot for data set B shows a larger range between the first and third quartiles. In addition, its median is approximately 25, which is higher than the median of data set A.

**3. B:** Data is said to be positively skewed when there are a higher number of lower values, indicating data that is skewed right. An approximately normal distribution shows an increase in frequency, followed by a decrease in frequency, of approximately the same rate.

**4. A: **The data set, shown in Choice A, correctly represents a frequency of 4 for the interval 1 – 10, a frequency of 3 for 11 – 20, a frequency of 4 for 21 – 30, a frequency of 10 for 31 – 40, and a frequency of 9 for 41 – 50.

**5. A: **The scores for Section 101 have a mean of approximately 81.1, with a standard deviation of approximately 13.2. The scores for Section 102 have a mean of approximately 78.5, with a standard deviation of approximately 12.0. Thus, the center and variability of scores for Section 101 are greater.

**6. C:** Group B is negatively skewed since there are more high scores. With more high scores, the mean for Group B will be higher.

**7. B:** Using a standard z-table, the area from the mean to z is shown to be 0.4162. This area should be subtracted from 0.5 in order to show the area to the right of a z-score of 1.38. Thus, the area to the right of the z-score is 0.0838, or approximately 0.08. A z-table, including the smaller portion of area under a curve may also be used. This area is reported as 0.0838.

**8. A:** The z-score may be represented as z=^{19-18}/_{2} or z=^{1}/_{2}. Using a standard z-table, the area from the mean to z is shown to be 0.1915. Subtraction of this area from 0.5 gives 0.3085. Thus, the proportion of scores falling above 19 is approximately 31%. A z-table, including the smaller portion of area under a curve may also be used. This area is reported as 0.3085.

**9. B:** A standard z-table shows an area of 0.2881 between a z-score of ?0.8 and the mean. It also shows an area of 0.3849 between the mean and a z-score of 1.2. The sum of the two areas is 0.673. Thus, the area between the two z-scores is approximately 67%. Using a table that reports the mean to z, the two mean-to-z areas may be extracted and summed. You may also add the smaller portions and subtract the sum from 1.

**10. C: **The probability may be written as P(A or B)= ^{750} /_{ 1650} + ^{675} / _{1650} – ^{350}/_{1650}, which simplifies to P(A or B)=^{1075} / _{1650} or approximately 65%.

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by Enoch Morrison | Last Updated: January 9, 2019