AP Statistics 1.7 B Calculate Measures of Variability for Quantitative Data Questions

Practise calculating and interpreting range, interquartile range and standard deviation from raw values, summary statistics and common data displays.

Exam points

calculate or estimate range from minimum and maximum values, including combined graphical data
calculate or estimate IQR from quartiles, ordered values, stemplots, histograms or boxplots
interpret and compare standard deviation from graphical spread, homogeneity and the effect of outliers

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 the range of the combined data set? Justify your answer.

Model Solution
The maximum is 40 mpg and the minimum is 14 mpg, so the range is $40-14=26\text{ mpg}$ . The boxplots show that all Country A mileages are below 40 mpg and all Country B mileages are above 14 mpg.

Scoring components
1. Correctly calculates 26 mpg as the range.
2. Justifies the range using 40 mpg as the maximum and 14 mpg as the minimum.

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AP Statistics 1.7 B Calculate Measures of Variability for Quantitative Data Questions question 1