Measures of center and spread sample question 3

The mean increases by about 2.5 hours and the median increases by 0.5 hour.

ACT · Math · Preparing for Higher Math: Statistics and Probability

Measures of center and spread

Measures of center and spread is part of Preparing for Higher Math: Statistics and Probability in the ACT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.

Question types you will see here include mean of a data set, median, mode, or range, find the value that gives a target mean, effect of adding, removing and or changing a value.

Common traps: dividing by the number of distinct values instead of the count; ignoring the frequency column; an addition error in a long list.

Sample questions

Question 1
A drone delivery service recorded these flight times, in minutes, for five deliveries: 12, 18, 24, 30, 46. What is the mean flight time, in minutes?
- A.
  18.6
- B.
  21
- C.
  24
- D.
  26
Answer: D. 26
The sum is 130, and 130 ÷ 5 = 26 minutes. A divides by 7 instead of the number of deliveries. B leaves out the longest flight, 46. C is the median, the middle value, rather than the mean.
Question 2
Aisha's scores on the first 5 quizzes were 89, 72, 79, 97, 66. What score does Aisha need on the next quiz so that the mean of all 6 scores is exactly 75?
- A.
  47
- B.
  50
- C.
  75
- D.
  403/5
Answer: A. 47
The total needed is 75 × 6 = 450. The current total is 403. The needed score is 450 - 403 = 47.
Question 3
Six students recorded these hours spent painting a school mural: 6, 7, 7, 8, 9, 10. A seventh student, who painted for 25 hours, joins the list. Which statement is true?
- A.
  The mean increases by about 2.5 hours and the median increases by 0.5 hour.
- B.
  The mean and the median increase by the same amount.
- C.
  The median increases by more than the mean does.
- D.
  The range stays the same because 25 is only one value.
Answer: A. The mean increases by about 2.5 hours and the median increases by 0.5 hour.
Mean: 47/6 ≈ 7.83 to 72/7 ≈ 10.29, up about 2.46. Median: 7.5 to 8, up 0.5. Choice B (The mean and the median increase by the same amount.) ignores that the large new value pulls the mean much more. Choice C (The median increases by more than the mean does.) reverses which measure an outlier affects more. Choice D (The range stays the same because 25 is only one value.) the range goes from 4 to 19.
Question 4
The mean area of five quilt patches is 18 square centimeters. When one patch is removed, the mean area of the remaining four patches is 16 square centimeters. What is the area, in square centimeters, of the patch that was removed?
- A.
  2
- B.
  18
- C.
  26
- D.
  64
Answer: C. 26
The five patches total 5 × 18 = 90 and the remaining four total 4 × 16 = 64, so the removed patch is 90 − 64 = 26 cm². Choice A (2) subtracts the two means; Choice B (18) repeats the original mean; Choice D (64) gives the total area of the remaining four.
Question 5
A school lab logged how long each of its 20 print jobs ran on a 3D printer.
Hours per job Number of jobs
1 8
3 6
5 4
12 2
What is the mean number of hours per job?
- A.
  1
- B.
  3
- C.
  3.5
- D.
  5.25
Answer: C. 3.5
Total hours = 1(8) + 3(6) + 5(4) + 12(2) = 8 + 18 + 20 + 24 = 70 over 20 jobs, so the mean is 3.5 hours. Choice A (1) is the mode, the most common value. Choice B (3) is the median, not the mean. Choice D (5.25) averages the four listed values without using the job counts.

Hours per job	Number of jobs
1	8
3	6
5	4
12	2

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