AP Statistics 1.7 Summary Statistics for One Quantitative Variable Questions

Practise calculating, transforming and comparing summary statistics for quantitative data, then choose measures that fit the distribution and support the conclusion.

Exam points

calculate means, medians, quartiles and percentiles from raw, grouped or graphical data
calculate and compare range, IQR and standard deviation, choosing resistant measures when needed
transform location and spread under linear unit changes, including variance and invariant z-scores
identify potential outliers with IQR fences or mean ± 2SD and compare the rules under skewness
compare independent samples using centre and spread while accounting for context and group sizes

Covered syllabus points

1.7.A—Calculate measures of center and position for quantitative data 1.7.B—Calculate measures of variability for quantitative data 1.7.C—Calculate different units of measurement for summary statistics 1.7.D—Calculate outliers for quantitative data 1.7.E—Compare multiple quantitative one-variable summary statistics 1.7.F—Justify the selection of a summary statistic for describing quantitative data

[Maximum number: 4]

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

Scoring for Question 1	Score
Complete Response<br>Three parts essentially correct	4
Substantial Response<br>Two parts essentially correct and one part partially correct	3
Developing Response<br>Two parts essentially correct and no part partially correct OR<br>One part essentially correct and one or two parts partially correct OR<br>Three parts partially correct	2
Minimal Response<br>One part essentially correct and no parts partially correct OR<br>No part essentially correct and two parts partially correct	1

(a)

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.

(i)

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.

(ii)

What is a possible value of the median of the combined data set? Justify your answer by referencing the boxplots shown.

[Maximum number: 1]

The kelvin is a unit of measurement for temperature; 0 K is absolute zero, the temperature at which all thermal motion ceases. Conversion from Fahrenheit to Kelvin is given by $\mathrm{K}=\frac{5}{9} \times(\mathrm{F}-32)+273$ . The average daily temperature in Monrovia, Liberia, is 78.35°F with a standard deviation of 6.3°F. If a scientist converts Monrovia daily temperatures to the Kelvin scale, what will be the new mean and standard deviation?

Mean, 231.75 K; standard deviation, 3.5 K

Mean, 298.75 K; standard deviation, 3.5 K

Mean, 298.75 K; standard deviation, 258.72 K

Mean, 298.75 K; standard deviation, 276.5 K

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Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question 2