AP Statistics 1.8 Graphical Representations of Summary Statistics Questions

Practise constructing and interpreting graphical summaries for quantitative data, from five-number boxplots to mean-median evidence about symmetry and skewness.

Exam points

construct a boxplot from a five-number summary after applying IQR fences to potential outliers
read a boxplot to compare median, quartiles, IQR, range, proportions and isolated values
use mean-median order and tail direction to justify symmetry or skewness, including transformed data

Covered syllabus points

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

The sizes, in square feet, of the 20 rooms in a student residence hall at a certain university are summarized in the following histogram.

Summary statistics for the sizes are given in the following table.

Determine whether there are potential outliers in the data. Then use the following grid to sketch a boxplot of room size.

Part (b):
The interquartile range is IQR =292-174=118 square feet. There are no potential outliers because the minimum room size of 134 square feet does not fall below $\mathrm{Q}_{1}-1.5(\mathrm{IQR})=-3$ square feet, and the maximum room size of 315 square feet does not exceed $\mathrm{Q}_{3}+1.5(\mathrm{IQR})=469$ square feet.

DISTRIBUTION OF ROOM SIZES

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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Covered syllabus points

Question 1

Question 2