AP Statistics 1.8: Mean, Median, and Skewness

Describe skewness in a quantitative distribution by using the relative positions of its mean and median and the shape shown in a summary graph.

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

For the distribution of gas mileage for the sample of cars manufactured in Country A, would

you expect the mean to be greater than 18 mpg, less than 18 mpg, or equal to 18 mpg ? Justify

your answer.

	Model Solution	Scoring
B	The mean of the distribution of gas mileage for the sample of cars manufactured in Country A is expected to be greater than 18 mpg, the median of the distribution. Because the distribution of gas mileage for the sample of cars manufactured in Country A has an outlier to the right (or is skewed to the right), the mean of the distribution (which is not resistant) is expected to be pulled above the median (which is resistant) toward the higher values of gas mileage.	Essentially correct (E) if the response satisfies the following three components: 1. Indicates that the mean of the distribution of gas mileage for the sample of cars manufactured in Country A is expected to be greater than 18 mpg 3. Provides a reasonable justification for the relationship between the mean and the median based on a right-skewed distribution or the expectation that an outlier in the right tail will pull the mean above the median Partially correct (P) if the response satisfies component 1 AND either component 2 or component 3. Incorrect (I) if the response does not meet the criteria for E or P.

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1.8.B—Describe quantitative one-variable graphical representations of summary statistics based on the relationship of… question 1