AP Statistics 1.7: Measures of Center and Position
Calculate and interpret measures of center and position, including mean, median, percentiles, quartiles, and related summaries.
- Syllabus
- Effective Fall 2025
- Course
- AP Statistics
Calculate and interpret measures of center and position, including mean, median, percentiles, quartiles, and related summaries.
The manager of an automotive company is interested in comparing the gas mileages for cars
manufactured in Country A and cars manufactured in Country B. The manager selected a
random sample of 100 cars manufactured in Country A and a random sample of 100 cars
manufactured in Country B. The gas mileages for each sample, in miles per gallon (mpg), are
summarized in the boxplots.

Boxplots of Gas Mileage for Each Country
The manager will create a new boxplot with the combined data from the sample of cars
manufactured in Country A and the sample of cars manufactured in Country B.
What is a possible value of the median of the combined data set? Justify your answer by
referencing the boxplots shown.
Model Solution
One possible median is 24 mpg. There are 200 observations. Country A's third quartile is 24 mpg, so at least 75 Country A observations are at or below 24; Country B's first quartile is 24 mpg, so at least 25 Country B observations are at or below 24. Similarly, at least 100 combined observations are at or above 24. Thus 24 mpg can be the combined median.
Scoring components
3. Correctly identifies 24 mpg as a possible median.
4. Justifies 24 mpg by correctly using information in the boxplots.