Two-Variable Data Analysis Review Problems for AP Statistics

Review the following concepts if necessary:

• Scatterplots for AP Statistics
• Correlation for AP Statistics
• Lines of Best Fit for AP Statistics
• Residuals for AP Statistics
• Coefficient of Determination for AP Statistics
• Outliers and Influential Observations for AP Statistics
• Transformations to Achieve Linearity for AP Statistics

Problems

1. Explain the difference between a statistic and a parameter.
2. TRUE–FALSE. The area under a normal curve between z = 0.1 and z = 0.5 is the same as the area between z = 0.3 and z = 0.7.
3. The following scores were achieved by students on a statistics test: 82, 93, 26, 56, 75, 73, 80, 61, 79, 90, 94, 93, 100, 71, 100, 60. Compute the mean and median for these data and explain why they are different.
4. Is it possible for the standard deviation of a set of data to be negative? Zero? Explain.
5. For the test scores of problem #3, compute the five-number summary and draw a boxplot of the data.

Solutions

1. A statistic is a measurement that describes a sample. A parameter is a value that describes a population.
2. FALSE. For an interval of fixed length, there will be a greater proportion of the area under the normal curve if the interval is closer to the center than if it is removed from the center. This is because the normal distribution is mound shaped, which implies that the terms tend to group more in the center of the distribution than away from the center.
3. The mean is 77.1, and the median is 79.5. The mean is lower than the median because it is not resistant to extreme values—it is pulled down by the 26, but that value does not affect the median.
4. By definition, s = , which is a positive square root. Since n >1 and ∑(x – )² ≥ 0, s cannot be negative. It can be zero, but only if x = for all values of x.
5. The 5-number summary is: [26, 66, 79.5, 93, 100].