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ACT Measures of center & spread practice questions

Measures of center & spread sits in the Statistics & Probability reporting category on the ACT Math section. Prep36 has 13 questions tagged to this skill, every one with a worked explanation. Three of them are below in full, with the reasoning, so you can see what the skill actually looks like before you practise it.

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What Measures of center & spread covers on the ACT

Within this skill the Prep36 bank covers weighted mean of two groups, median of an even-sized data set, minimum score for a target mean, score needed to reach a target average, median of an even-sized list and effect of removing a value on the mean.

Math is 45 questions in 50 minutes, which is about 66 seconds each, and it is one of the three sections that average into your composite. The difficulty split across the 13 questions tagged here is 4 easier, 6 medium and 3 harder.

Questions are original, written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.

3 measures of center & spread questions, with the reasoning

Question 1 easy

The values below are listed from least to greatest.2, 6, 7, 9, 14, 18, 28What is the median of this data set?

  1. A. 8
  2. B. 9 correct
  3. C. 12
  4. D. 26
Why: There are 7 values already in order, so the median is the 4th one, the value with three numbers on each side, which is 9. The distractors are the other summary statistics: 12 is the mean (84 ÷ 7), pulled upward by the outlier 28; 26 is the range (28 − 2); and 8 is the midpoint of 7 and 9 rather than a value in the list. Tip: For an odd number of ordered values, the median sits in position (n + 1)/2, so count to that slot instead of averaging anything.
Question 2 medium

A class of 12 students has a test average of 78. A second class of 18 students has a test average of 88. What is the average score of all 30 students?

  1. A. 83
  2. B. 84 correct
  3. C. 85
  4. D. 86
Why: The total points are 12(78) + 18(88) = 936 + 1,584 = 2,520, and dividing by the 30 students gives an average of 84. The choice 83 is the plain average of 78 and 88, which ignores that the classes differ in size. The choices 85 and 86 overweight the larger class without doing the actual computation. Tip: when group sizes differ, add up total points and divide by total people rather than averaging the averages.
Question 3 hard

A data set of 20 values has a mean of 46. One of the values, 8, is removed from the data set. What is the mean of the remaining 19 values?

  1. A. 38.0
  2. B. 46.0
  3. C. 48.0 correct
  4. D. 48.4
Why: The original total is 20 × 46 = 920. Take out the value 8 and the sum becomes 912 across 19 values, so the new mean is 912/19 = 48.0. The choice 48.4 is 920/19, which shrinks the count but forgets to remove 8 from the sum. The choice 38.0 subtracts 8 from the mean itself, and 46.0 assumes nothing changed, but pulling out a value far below the mean has to pull the average up. Tip: mean questions are really sum questions. Convert mean × count into a total, adjust the total, then divide by the new count.

The explanation is the point. Getting a question wrong tells you nothing you did not already suspect; knowing which step you missed is what changes the next one.

Practise the rest of the 13

The other 10 questions on this skill are in the free question bank, filterable by difficulty, each with the same worked explanation. No account and no card.

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Frequently asked questions

How many ACT measures of center & spread questions does Prep36 have?
13, each tagged to this skill and each with a worked explanation.
Are these real ACT questions?
No. They are original questions written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.
Is the Math section part of the composite?
Yes. On the Enhanced ACT the composite is the average of English, Math and Reading. Science is optional and reported separately.
Keep readingACT Math practiceEvery Math skill in one place.How many questions can you miss?The miss budget for every score.ACT Score CalculatorTurn raw scores into a composite.
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