This practice test covers key concepts from Chapter 2 of a typical AP Statistics textbook, focusing on describing distributions of data. Remember to show your work where applicable and justify your answers. This isn't just about getting the right answer; it's about demonstrating your understanding of statistical principles.
Section 1: Multiple Choice
1. Which of the following is NOT a way to describe the shape of a distribution?
(a) Symmetric (b) Skewed left (c) Uniform (d) Mean
2. A distribution is skewed right. Which of the following is true?
(a) The mean is less than the median. (b) The mean is equal to the median. (c) The mean is greater than the median. (d) The relationship between the mean and median cannot be determined.
3. A histogram shows data that is roughly symmetric and bell-shaped. Which of the following is the BEST description of the distribution?
(a) Skewed left (b) Skewed right (c) Approximately normal (d) Uniform
4. The median is a better measure of center than the mean when:
(a) The data is symmetric. (b) The data is skewed. (c) The data is normally distributed. (d) The data has no outliers.
5. The interquartile range (IQR) is a measure of:
(a) Center (b) Spread (c) Shape (d) Outliers
Section 2: Free Response
1. The following data represents the number of hours students spent studying for an exam:
2, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10
(a) Create a histogram of the data. Remember to label your axes clearly. (b) Describe the shape, center, and spread of the distribution. Use appropriate measures of center and spread to support your description. Consider using the median and IQR. Are there any outliers? Explain your reasoning. (c) Suppose a student studied for 20 hours. How would this outlier affect the mean and median? Explain.
2. Two datasets are shown below. Dataset A has a mean of 50 and a standard deviation of 5. Dataset B has a mean of 50 and a standard deviation of 10.
(a) Which dataset has more variability? Explain your reasoning. (b) Draw a rough sketch of what the distributions might look like if both datasets are approximately normal.
3. Explain the difference between a histogram and a stemplot. When might you choose one over the other?
Answer Key (Section 1):
- (d) Mean - The mean is a measure of center, not shape.
- (c) The mean is greater than the median. - In a right-skewed distribution, the tail pulls the mean to the right.
- (c) Approximately normal - A bell-shaped, symmetric distribution is characteristic of a normal distribution.
- (b) The data is skewed. - The median is less sensitive to outliers than the mean, making it a better measure of center for skewed data.
- (b) Spread - The IQR measures the spread of the middle 50% of the data.
This practice test provides a solid foundation for your AP Statistics Chapter 2 review. Remember to consult your textbook and class notes for further clarification on any concepts you find challenging. Good luck!
