AP Statistics Unit 1: Exploring One-Variable Data

A data set of 12 exam scores has a mean of 78 and a median of 82. Which of the following best describes the shape of the distribution?

A researcher says a score at the 90th percentile in a normal distribution with mean 50 and SD 6 corresponds to a score of about 57.7. Another student says the 90th percentile score is about 42.3. Who is correct, and why?

A boxplot shows the following five-number summary for a data set: Min = 10, Q1 = 22, Median = 30, Q3 = 45, Max = 70. What is the interquartile range (IQR)?

Which of the following correctly identifies an outlier using the 1.5 × IQR rule? A data set has Q1 = 20, Q3 = 50, and contains the value 95.

A cumulative relative frequency plot (ogive) shows that the 60th percentile of commute times is 35 minutes. Which of the following statements is correct?

A histogram of household incomes in a neighborhood is strongly right-skewed. Which measure of center and spread is most appropriate to report?

A distribution of test scores is approximately normal with mean $\mu =72$ and standard deviation $\sigma =8$. Approximately what percentage of scores fall between 64 and 88?

A dot plot shows the ages (in years) of 9 trees: 3, 5, 5, 7, 8, 9, 10, 12, 40. Which measure of center best represents the typical age, and why?

A set of exam scores has mean 70 and standard deviation 10. Each score is multiplied by 1.05 (a 5% curve), then 3 points are added. What are the new mean and standard deviation?

A biology class recorded the number of seeds that germinated out of 20 seeds for each of 30 students. The data are roughly bell-shaped with mean $\bar{x}=14.2$ and $s=2.1$. Using the normal model, approximately what proportion of students had fewer than 10 seeds germinate?

A stemplot of hourly wages (in dollars) for 10 part-time workers is shown below. What is the median wage?

A student scored 85 on a test where the class mean was 78 and the standard deviation was 7. What is the student's standardized score ($z$-score)?