One-variable data: distributions and measures — SAT practice questions

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Practice 110 One-variable data: distributions and measures questions in the app

What this topic is

One-variable data: distributions and measures covers mean, median, mode, range and standard deviation, shown in lists, dot plots, histograms or frequency tables.

Conceptual questions are frequent here. Adding the same number to every value shifts the mean and median but leaves the standard deviation and range unchanged, since the spread stays the same. Removing an outlier far above the rest lowers the mean noticeably while barely moving the median.

Combining two groups of different sizes calls for a weighted mean, where each group's average counts in proportion to how many members it has, rather than a simple average of the two means.

Sample questions

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Question 1Mid

Seven is added to every value in a data set. Which of the following is true about the standard deviation of the data set?

It decreases by 7.✗ Not this oneIt stays the same.✓ CorrectIt increases by 7.✗ Not this oneIt is multiplied by 7.✗ Not this one

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Answer: B — It stays the same.

Adding the same constant to every value shifts the data without changing its spread.

Question 2Mid

4, 6, 7, 8, 25

If 25 is removed from the data shown, what happens to the mean and median?

The mean decreases, and the median remains the same.✗ Not this oneThe mean decreases, and the median decreases.✓ CorrectThe mean remains the same, and the median decreases.✗ Not this oneThe mean increases, and the median increases.✗ Not this one

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Answer: B — The mean decreases, and the median decreases.

Removing the high outlier lowers the mean; the median changes from 7 to $(6 + 7) / 2 = 6.5$ .

Question 3Mid

A researcher measured the wingspans of 150 bats from Cave R and 50 bats from Cave S. The mean wingspan of the 150 bats from Cave R was 28 centimeters, and the mean wingspan of the 50 bats from Cave S was 34 centimeters. What was the mean wingspan, in centimeters, of all 200 bats the researcher measured?

29✗ Not this one29.5✓ Correct30✗ Not this one31✗ Not this one

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Answer: B — 29.5

Combined mean $= \frac{150 (28) + 50 (34)}{200} = \frac{4, 200 + 1, 700}{200} = \frac{5, 900}{200} = 29.5$ .

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Practice 110 One-variable data: distributions and measures questions in the app

One-variable data: distributions and measures — SAT practice questions

What this topic is

Sample questions

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Math