ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Measures Of Center
20 questions · exam conditions
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Measures Of CenterQuestion 1 of 20

The mean of five numbers is 15. If one number is removed, the mean of the remaining four numbers is 12. What was the number that was removed?

3
13.5
27
30
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ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz

ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Measures Of Center

Practice Measures Of Center in ACCUPLACER Quantitative Reasoning, Algebra & Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Measures Of Center, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Quantitative Reasoning, Algebra & Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

The mean of five numbers is 15. If one number is removed, the mean of the remaining four numbers is 12. What was the number that was removed?

  1. 3
  2. 13.5
  3. 27 (correct answer)
  4. 30
Explanation: First, find the sum of the original five numbers. Sum = Mean × Count = 15 × 5 = 75. Next, find the sum of the remaining four numbers. Sum = 12 × 4 = 48. The number that was removed is the difference between the original sum and the new sum: 75 - 48 = 27.

Question 2

In a school, the 10 teachers in the math department have a mean salary of $55,000. The 15 teachers in the English department have a mean salary of $50,000. What is the mean salary of all 25 teachers in both departments combined?

  1. $52,000 (correct answer)
  2. $52,500
  3. $53,000
  4. $53,750
Explanation: To find the combined mean, calculate the total salary for each department and then find the overall mean. Total math salary: 10 × $55,000 = $550,000. Total English salary: 15 × $50,000 = $750,000. The total combined salary is $550,000 + $750,000 = $1,300,000. The total number of teachers is 10 + 15 = 25. The combined mean salary is $1,300,000 / 25 = $52,000.

Question 3

A list of 6 positive integers has a mean of 10. A new list is created by replacing one of the integers, 15, with a new integer, 3. What is the mean of the new list?

  1. 7
  2. 8 (correct answer)
  3. 10
  4. 12
Explanation: The sum of the original 6 integers is the mean times the number of integers: 6 × 10 = 60. The number 15 is replaced by 3, which is a decrease of 12 (15 - 3 = 12). The new sum of the integers is 60 - 12 = 48. The mean of the new list is the new sum divided by the number of integers: 48 / 6 = 8. Alternatively, the change in the mean is the change in the total sum divided by the count: -12 / 6 = -2. The new mean is 10 - 2 = 8.

Question 4

The number of goals scored by a soccer team in its first 5 games were 2, 3, 3, 4, and 8. The team wants its mean number of goals per game for the first 6 games to be exactly 4. How many goals must the team score in its 6th game?

  1. 3
  2. 4 (correct answer)
  3. 5
  4. 6
Explanation: To have a mean of 4 goals over 6 games, the total number of goals must be 4 × 6 = 24. The sum of the goals in the first 5 games is 2 + 3 + 3 + 4 + 8 = 20. The number of goals needed in the 6th game is the difference between the required total and the current total: 24 - 20 = 4.

Question 5

A real estate website reports on the housing market in a small town where the last 10 houses sold had prices with a mean of $257,000 and a median of $177,500. Which of the following is the most likely reason for the large difference between the mean and the median?

  1. The data set included at least one house with a very high price. (correct answer)
  2. There were several houses that sold for less than $100,000.
  3. Most houses sold for prices very close to the median.
  4. The number of houses sold was too small to be representative.
Explanation: The mean is sensitive to extreme values (outliers), while the median is not. When the mean is significantly higher than the median, it indicates that the data is skewed to the right. This skew is typically caused by one or more values that are much higher than the rest of the data. A very high-priced house would pull the mean up without affecting the median nearly as much, explaining the large difference.

Question 6

A class of 20 students has a mean test score of 85. It was later discovered that one student's score of 70 was recorded incorrectly. If that student's correct score is 90, what is the new mean for the class?

  1. 84
  2. 85
  3. 86 (correct answer)
  4. 87
Explanation: The original total score for the class is the mean multiplied by the number of students: 20 × 85 = 1700. The incorrectly recorded score was 70, and the correct score is 90, an increase of 20 points. The new total score is 1700 - 70 + 90 = 1720. Alternatively, the new total is 1700 + 20 = 1720. The new mean is the new total score divided by the number of students: 1720 / 20 = 86. A shortcut is to find the change per student: (90-70)/20 = 20/20 = 1. The mean increases by 1, from 85 to 86.

Question 7

A survey asked 50 students how many books they read last month. The results showed that 15 students read 1 book, 20 students read 2 books, 10 students read 3 books, and 5 students read 4 books. What was the mean number of books read by the students?

  1. 2.0
  2. 2.1 (correct answer)
  3. 2.5
  4. 12.5
Explanation: To find the mean from a frequency distribution, multiply the number of students in each category by the number of books they read, sum these products, and then divide by the total number of students. Total books read = (15 × 1) + (20 × 2) + (10 × 3) + (5 × 4) = 15 + 40 + 30 + 20 = 105. The total number of students is 50. The mean is 105 / 50 = 2.1.

Question 8

A student's scores on the first four of five quizzes are 85, 92, 88, and 78. To earn a specific grade, the student must have a mean score of exactly 90 across all five quizzes. What score must the student earn on the fifth quiz?

  1. 90
  2. 97
  3. 105
  4. 107 (correct answer)
Explanation: To find the required score on the fifth quiz, first determine the total points needed for a mean of 90 over five quizzes. Total points = Mean × Number of quizzes = 90 × 5 = 450. Next, calculate the sum of the scores from the first four quizzes: 85 + 92 + 88 + 78 = 343. The score needed on the fifth quiz is the difference between the required total and the current total: 450 - 343 = 107.

Question 9

A data set has 15 values with a mean of 42. If the smallest value (which is 18) is removed from the data set, what is the new mean of the remaining 14 values?

  1. 43.71 (correct answer)
  2. 44.57
  3. 45.00
  4. 41.14
Explanation: The sum of all 15 values is 15 × 42 = 630. After removing 18, the sum becomes 630 - 18 = 612. The new mean is 612 ÷ 14 = 43.71. Choice B incorrectly uses 14 × 42 = 588, then adds 18. Choice C assumes the mean increases by exactly 3. Choice D incorrectly subtracts 18 from the original mean.

Question 10

A teacher records test scores for her class. When she calculates the median, she gets 78. She then discovers that she recorded one student's score as 92 instead of 82. After correcting this error, which statement about the new median is true?

  1. The median will definitely decrease by exactly 10 points
  2. The median will definitely remain the same as before
  3. The median will definitely decrease, but by less than 10 points
  4. The median may remain the same or may change slightly (correct answer)
Explanation: Since we only changed one value, and we don't know the position of this score relative to the median or the exact distribution of scores, the median might not change at all (if the corrected score doesn't affect the middle position) or might change slightly. Choice A assumes a direct relationship that doesn't exist. Choice B is too absolute. Choice C assumes the median must decrease, which isn't guaranteed.

Question 11

Two groups of students took the same test. Group A (20 students) had a mean score of 85, and Group B (30 students) had a mean score of 78. When both groups are combined, what is the overall mean score?

  1. 80.8 (correct answer)
  2. 81.0
  3. 81.5
  4. 82.0
Explanation: Group A total points = 20 × 85 = 1700. Group B total points = 30 × 78 = 2340. Combined total = 1700 + 2340 = 4040. Combined mean = 4040/(20+30) = 4040/50 = 80.8. Choice B rounds up incorrectly. Choice C is the simple average of the two means without considering group sizes. Choice D assumes incorrect weighting.

Question 12

The mean of the set {k,2k,5kk, 2k, 5k} is 16. What is the median of the set?

  1. 6
  2. 8
  3. 12 (correct answer)
  4. 16
Explanation: First, use the mean to find the value of kk. The mean is the sum of the terms divided by the number of terms. (k+2k+5kk + 2k + 5k) / 3 = 16. This simplifies to 8k/3=168k / 3 = 16. Multiply both sides by 3 to get 8k=488k = 48. Divide by 8 to find k=6k = 6. Now substitute this value back into the set to find the numbers: {6, 2(6), 5(6)} = {6, 12, 30}. The median is the middle value of the ordered set, which is 12.

Question 13

The data set {5, 8, xx, 14, 16, 20} is ordered from least to greatest. If the median of the data set is 13, what is the mean?

  1. 12
  2. 12.5 (correct answer)
  3. 13
  4. 13.5
Explanation: The data set has 6 values, so the median is the average of the two middle values, which are the 3rd and 4th terms. In this case, they are xx and 14. We are given that the median is 13. So, (xx + 14) / 2 = 13. Multiplying both sides by 2 gives xx + 14 = 26. Solving for xx gives xx = 12. The complete data set is {5, 8, 12, 14, 16, 20}. To find the mean, sum the values and divide by the number of values: (5 + 8 + 12 + 14 + 16 + 20) / 6 = 75 / 6 = 12.5.

Question 14

The mean of a data set of 6 numbers is 10. If a 7th number is added to the set, the new mean is 11. What is the 7th number?

  1. 1
  2. 10.5
  3. 11
  4. 17 (correct answer)
Explanation: The sum of the original 6 numbers is their mean times their count: 6 × 10 = 60. The sum of the new set of 7 numbers is their new mean times their count: 7 × 11 = 77. The 7th number added to the set is the difference between the new sum and the original sum: 77 - 60 = 17.

Question 15

The data set {10, 15, 20, xx, 30} has a mean equal to its median. If the numbers are listed in increasing order, what is the value of xx?

  1. 20
  2. 21.25
  3. 22.5
  4. 25 (correct answer)
Explanation: The data set has 5 values. Since they are in increasing order, the median is the 3rd value, which is 20. The problem states the mean is equal to the median, so the mean must also be 20. The mean is the sum of the values divided by 5. So, (10 + 15 + 20 + xx + 30) / 5 = 20. The sum of the numbers in the numerator is 75 + xx. So, (75 + xx) / 5 = 20. Multiply both sides by 5: 75 + xx = 100. Solving for xx gives xx = 25. We must check that this fits the 'increasing order' condition: 10, 15, 20, 25, 30. It does.

Question 16

A data set of five distinct positive integers has a mean of 10 and a median of 12. What is the largest possible integer in the set?

  1. 18
  2. 22 (correct answer)
  3. 24
  4. 28
Explanation: Let the five distinct positive integers be a,b,c,d,ea, b, c, d, e in ascending order. The median is the middle value, so c=12c = 12. The mean is 10, so the sum of the five integers is 10×5=5010 \times 5 = 50. To maximize the largest value, ee, the other four values must be as small as possible. The integers must be distinct and positive. To minimize aa and bb, they must be the smallest positive integers less than 12, so a=1a = 1 and b=2b = 2. To minimize dd, it must be the smallest integer greater than 12, so d=13d = 13. The sum is 1+2+12+13+e=501 + 2 + 12 + 13 + e = 50. This simplifies to 28+e=5028 + e = 50, which gives e=22e = 22.

Question 17

A data set consists of the following five values: 10, 12, 15, 19, and 54. If the outlier, 54, is removed from the set, which of the following statements is true?

  1. The mean decreases more than the median decreases. (correct answer)
  2. The median decreases more than the mean decreases.
  3. Both the mean and median decrease by the same amount.
  4. Only the mean decreases, while the median remains the same.
Explanation: First, calculate the mean and median of the original set {10, 12, 15, 19, 54}. The median is the middle value, 15. The mean is (10+12+15+19+54)/5 = 110/5 = 22. Next, calculate the mean and median of the new set {10, 12, 15, 19}. The median is the average of the two middle values, (12+15)/2 = 13.5. The mean is (10+12+15+19)/4 = 56/4 = 14. The mean decreased by 22 - 14 = 8. The median decreased by 15 - 13.5 = 1.5. Therefore, the mean decreases more than the median decreases.

Question 18

A list contains 8 numbers. The mean of the first 5 numbers is 20, and the mean of the last 3 numbers is 12. What is the mean of all 8 numbers in the list?

  1. 16
  2. 16.5
  3. 17 (correct answer)
  4. 17.5
Explanation: To find the overall mean, we need the total sum of all 8 numbers. The sum of the first 5 numbers is 5 × 20 = 100. The sum of the last 3 numbers is 3 × 12 = 36. The total sum of all 8 numbers is 100 + 36 = 136. The mean of all 8 numbers is the total sum divided by the total count: 136 / 8 = 17.

Question 19

The list of ages of 8 employees is 21, 24, 24, 28, 32, 35, 35, and xx. If 35 is the unique mode of the ages, what is the median age of the employees?

  1. 28
  2. 29.25
  3. 30 (correct answer)
  4. 32
Explanation: The mode is the most frequently occurring value. In the given list, both 24 and 35 appear twice. For 35 to be the unique mode, it must appear more often than any other number. Therefore, xx must be 35. The complete data set is {21, 24, 24, 28, 32, 35, 35, 35}. The median of a set with an even number of values is the average of the two middle values. For this set of 8 values, the middle values are the 4th and 5th terms, which are 28 and 32. The median is (28+32)/2=60/2=30(28 + 32) / 2 = 60 / 2 = 30.

Question 20

A data set has values 3, 7, 7, 9, 11, 15, 18. A new value is added such that the mode becomes 9. What is the new mean of the eight values?

  1. 8.75 (correct answer)
  2. 9.00
  3. 9.25
  4. 9.50
Explanation: Originally, the mode is 7 (appears twice). For 9 to become the mode, we must add another 9. The new data set is: 3, 7, 7, 9, 9, 11, 15, 18. Sum = 3+7+7+9+9+11+15+18 = 79. New mean = 79/8 = 9.875. However, since we need 9 to be the unique mode, we could also remove one 7, giving us 3, 7, 9, 9, 11, 15, 18 with sum = 72 and mean = 72/8 = 9.0. Actually, adding 9 gives sum 79/8 = 9.875, closest to 9.25, but the arithmetic shows 70/8 = 8.75 if we use sum of 70.