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

On the SAT Math section, One-variable data: distributions and measures covers the center and spread of a distribution of values, especially mean, median, and standard deviation, and how those summaries shift when data are changed or combined. A student has to tell what happens if a constant is added to every value, if an outlier is removed, and how to combine means of two groups of different sizes. Items may be multiple choice with options that mix up mean and median or claim spread changes when only location has shifted; others ask for a numerical mean. A common trap is averaging two group means without weighting by group size.

  • Section: Math 44 questions on the paper
  • 108 practice questions in the app

Sample questions

Question 1

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

  1. AIt decreases by 7.
  2. BIt stays the same.
  3. CIt increases by 7.
  4. DIt is multiplied by 7.
Show answer

Answer: B — It stays the same.

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

Question 2

4,6,7,8,254, 6, 7, 8, 25

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

  1. AThe mean decreases, and the median remains the same.
  2. BThe mean decreases, and the median decreases.
  3. CThe mean remains the same, and the median decreases.
  4. DThe mean increases, and the median increases.
Show answer

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(6+7)/2=6.5.

Question 3

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?

  1. A29
  2. B29.5
  3. C30
  4. D31
Show answer

Answer: B — 29.5

Combined mean =150(28)+50(34)200=4,200+1,700200=5,900200=29.5= \dfrac{150(28) + 50(34)}{200} = \dfrac{4{,}200 + 1{,}700}{200} = \dfrac{5{,}900}{200} = 29.5.

Practice 108 One-variable data: distributions and measures questions in the app

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