Statistics

1. Xuan sold 9 used books for $9.80 each. With the money from these sales, she bought 4 new books and had $37.80 left over. What was the average amount Xuan paid for each new book?

2019 June(A11) Math Question 1

1. A car was purchased 4 years ago for $26,200. The current value of the car is $17,500. What was the car’s average decrease in value per year?

2013 June(71C) Math Question 1

1. The monthly fees for single rooms at 5 colleges are $370, $310, $380, $340, and $310, respectively. What is the mean of these monthly fees?

2014 June(72C) Math Question 1

2012 June(70C) Math Question 1

A retail sales associate's daily commission during 1 week was $20 on Monday and Tuesday and $60 on Wednesday, Thursday, and Friday. What was the associate's average daily commission for these 5 days?

2024 April(Z13) Math Question 1

2020 July(C01) Math Question 2

2. The age, in years, of each of the first 6 presidents of the United States at his first inauguration was 57, 61, 57, 57, 58, and 57, respectively. Which of the following values is closest to the mean age, in years, of the first 6 presidents at their respective first inaugurations?

2015 December(72E) Math Question 2

Dawn randomly selected 6 books from the teen library, read them, and then rated them as follows: 40, 60, 10, 80, 30, and 40. Based on the sample data, what is the best estimate of Dawn's average rating of all the books in the library?

2024 September(H11) Math Question 3

2009 June(67C) Math Question 4

A ball was dropped from a table, and the maximum rebound height, in inches, after each of the first 4 bounces was measured and recorded in the bar graph below. One of the following values is the mean of the 4 recorded heights. Which one?

2023 September(G01) Math Question 4

A retail sales associate's daily commission during 1 week was $30 on Monday and Tuesday and $60 on Wednesday, Thursday, and Friday. What was the associate's average daily commission for these 5 days?

2024 June(G20) Math Question 4

To determine a student's overall test score for the semester, Mr. Weintraub omits the lowest test score and calculates the average of the remaining test scores. Holly took all 5 tests and earned the following test scores in Mr. Weintraub's class this semester: 71, 76, 81, 84, and 95. What overall test score did Holly earn in Mr. Weintraub's class this semester?

2024 December(H31) Math Question 4

2020 June(C02) Math Question 6

2011 June(69F) Math Question 6

7. A certain group consists of 5 children, 3 of whom are age 10 and 2 of whom are age 5. What is the mean age of the children in the group?

2018 June(A11) Math Question 7

7. What is the sum of 3 consecutive odd integers whose
mean is 27?

2019 June(B02) Math Question 7

7. In Summit City, the daily low temperatures, in degrees Fahrenheit (°F), during the first week in December were —7, —11, 15, 23, 45, 23, and 2. To the nearest 1°F, what was the mean daily low temperature for that week?

2014 December(72G) Math Question 7

2020 June(C02) Math Question 7

8. The table below shows the number of cars Jing sold each month last year. What is the median of the data in the table?

2014 June(72C) Math Question 8

2010 April(68G) Math Question 9

9. The principal of Lowe High School (LHS) authorized a study to estimate the percent of the LHS student population that will attend a 4-year college after graduation. LHS students in honors courses were asked about their postgraduation plans, and their responses were recorded. Students in other courses were NOT included in the study. Which of the following phrases best describes the principal’s study?

Survey Design and Interpreting Results

2020 December(D03) Math Question 9

10. Adina plays in a bowling league. Her bowling scores for last week are listed below. What is the median of Adina's bowling scores for last week? 142,186,201,191,116,201,175

2014 April(71H) Math Question 10

2010 December(69A) Math Question 10

The graph below shows the average daily consumption, in thousands of barrels, of oil for Uzbekistan for the years 2003 through 2013. From what year to the following year did the average daily consumption decrease the most?

2024 June(G20) Math Question 10

11. The table below shows Shannon’s height, in inches, on her birthday from the day she was born (birth) to age 5. What was the average rate of change in Shannon’s height, in inches per year, from birth to age 5 ?

2014 April(71H) Math Question 11

2013 April(71G) Math Question 11

13. At Tamika's Treat Shop, what is the average price per candy in a box of 20, to the nearest $0.01 ?

2015 June(73C) Math Question 13

This table lists the engine size, x liters, and the weight, w kilograms, of each of 5 vehicles. A linear model for the data in the table is w = 375x + 370. The actual weight of the vehicle with the smallest engine size differs from the linear model's predicted weight of this vehicle by how many kilograms?

2025 October(J08) Math Question 13

What is the median of the data set below? 4, 8, 14, 4, 20

2024 June(G20) Math Question 13

14. The average of 5 distinct scores has the same value as

2017 April(74F) Math Question 14

What is the mean, in seconds, of the times listed in the table for the 200-meter dash?

35 February(Z14) Math Question 14

2011 April(67F) Math Question 15

16. What is the value of tan A in right triangle AABC below?

2017 December(A10) Math Question 16

16. What is the difference between the median and the mean number of tickets sold at the 5 schools?

2018 April(A09) Math Question 16

2010 June(68C) Math Question 16

2020 July(C01) Math Question 16

16. Jamal earned scores of 70, 75, 85, and 94 points on the first 4 history projects, and he has 1 more project to complete. What is the minimum score Jamal needs to earn on the 5th project so that the mean of his scores on all 5 projects is at least 2 points more than the mean of the scores he earned on the first 4 projects?

2016 April(73E) Math Question 16

2012 December(71A) Math Question 17

2020 July(C01) Math Question 17

2018 December(B05) Math Question 17

18. A function f(x) is defined as f(x) = —6x^2. What is f(-3) ?

2017 December(A10) Math Question 18

18. The mean of a list of 7 numbers is 85. The first 6 numbers on the list are 82, 93, 68, 93, 70, and 98. What is the 7th number on the list?

2018 April(A09) Math Question 18

2020 June(C02) Math Question 18

18. What is the median of the list of numbers below? 6, 3, 5, 7, 12, 9, 5, 5, 11

2016 April(73E) Math Question 18

On each of 8 tests, Gustav scored 2 points higher than Russ. When their average test scores on these 8 tests are compared, how many points higher is Gustav's average than Russ's average?

2023 April(F11) Math Question 18

2019 June(72F) Math Question 19

2012 April(70G) Math Question 19

2020 July(C01) Math Question 19

19. A team of biologists tagged and released 90 deer in a forest. From the same forest 2 weeks later, the biologists collected a random sample of 30 deer, 5 of which were tagged. Let p be the proportion of deer in this forest that are tagged. What is pˆ, the sample proportion, for this sample?

2021 June(D06) Math Question 19

2019 December(C03) Math Question 19

Each of 5 different data sets is summarized with its own boxplot below. Which of these data sets has the greatest interquartile range?

2023 April(F11) Math Question 19

2012 December(71A) Math Question 20

23. The scores given below were earned by 10 students on a recent biology test. What is the median score?

2017 June(74C) Math Question 23

The mean of 3 consecutive whole numbers is 30. What are the 3 numbers?

2023 April(F11) Math Question 23

24. The histogram below shows the results of a survey of 100 people. Each person identified the number of hours per week that they watch TV. How many people surveyed watch TV at least 4 hours per week?

Frequency Tables, Histograms, and Standard Deviation

2020 December(D03) Math Question 24

A normal distribution for random variable X is given. Each percentage shown is the percentage of the area under that portion of the curve. One of the following values is the value of P(1,100 < X < 1,200) to the nearest 1%. Which one?

2025 October(J08) Math Question 24

Biologists tagged and released 50 fish in a lake. From the same lake 3 weeks later, the biologists collected a random sample of 15 fish, 5 of which were tagged. Let p be the proportion of the fish in the lake that are tagged. What is p̂, the sample proportion, for this sample?

2024 April(Z13) Math Question 24

25. The average weight of Juan, Jim, and Malik is exactly 160 pounds. The average weight of Juan, Jim, Malik, and Harry is exactly 150 pounds. How many pounds does Harry weigh?

2021 June(D06) Math Question 25

2019 April(B04) Math Question 26

26. An outlier is added to the data set below. Which of the following pairs of statistics has no change in value as a result of the addition of the outlier? {60, 63, 66, 70, 72, 72, 73, 73, 73, 75}

Statistics (Mean, Median, Mode, Standard Deviation)

2020 December(D03) Math Question 26

27. In a chemistry course, a student scored 99 on one test, 98 on another test, and 88 on each of the other tests. The student's test average for the course, where each test is weighted equally, is exactly 91. What is the total number of tests that the student has taken in the course?

2015 December(72E) Math Question 27

27. Sophia's goal this past summer was to save an average of $5.00 per week for 10 weeks. She saved an average of $4.00 per week for the first 9 weeks and saved $12.00 for the 10th week. On average, how much more should Sophia have saved each week to reach her goal?

2015 April(73G) Math Question 27

27. On the first 7 statistics tests of the semester, Jamal scored 61, 76, 79, 80, 80, 84, and 91. The mean, median, and mode of his scores were 79, 80, and 80, respectively. On the 8th statistics test, Jamal scored 90. How do the mean, median, and mode of all 8  of his scores compare to the mean, median, and mode of his first 7 scores?

2021 April(Z04) Math Question 27

2018 December(B05) Math Question 28

28. The average of a list of 4 numbers is 90.0. A new list of 4 numbers has the same first 3 numbers as the original list. but the fourth number in the original list is 80, and the fourth number in the new list is 96. What is the average of this new list of numbers?

2017 April(74F) Math Question 28

2009 April(66F) Math Question 29

29. For one school week, Hannah recorded the following temperatures, in degrees Fahrenheit, so she could investigate the difference between the high and low temperature each day.

Day
Monday Tuesday Wednesday Thursday Friday
Low High
−3° 26° −5° 32° −7° 22° 03° 40° 02° 40°

To the nearest degree, what was the mean of the differences in daily high and low temperatures for these 5 days?

2021 June(D06) Math Question 29

29. To increase the mean of 7 numbers by 4, by how much would the sum of the 7 numbers have to increase?

2021 December(E23) Math Question 29

2010 June(68C) Math Question 30

30. The average of a list of 4 numbers is 92.0. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40, and the fourth number in the new list is 48. What is the average of this new list of numbers?

Averages

2021 April(Z04) Math Question 30

2020 July(C01) Math Question 31

31. All 25 students in a chemistry class took a test. Each student earned a test score that was an integer number of points, and no 2 students earned the same test score. The median test score was 80 points. How many students earned a test score that was greater than 80 points?

2021 December(E23) Math Question 31

32. Over a 7-day period at Phil's Fitness, the average attendance of the slowest day and the busiest day was 247 members. The average of the other 5 days was also 247 members. The total attendance for the 7-day period at Phil's Fitness was how many members?

2013 June(71C) Math Question 32

32. Four identical glasses are shown below. One glass is empty, and the other 3 glasses are 1/4 full, 1/2 full, and 4/5 full of water, respectively. If the water were redistributed equally among the 4 glasses, what fractional part of each glass would be filled?

2021 April(Z04) Math Question 32

34. To increase the mean of 4 numbers by 3, by how much would the sum of the 4 numbers have to increase?

2018 June(A11) Math Question 34

2019 April(Z15) Math Question 34

A Chinese language proficiency test was given to 60 university students. The students' scores were recorded as integers. The table below shows the frequency and cumulative frequency of test scores in certain ranges. To be classified as proficient, a student must score 70 or higher on the test. What is the ratio of the number of students who were classified as proficient to the number who were NOT classified as proficient?

35 February(Z14) Math Question 34

2019 December(C03) Math Question 35

2009 April(66F) Math Question 35

The average of a list of 4 numbers is 88.0. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 50, and the fourth number in the new list is 70. What is the average of this new list of numbers?

2024 April(Z13) Math Question 35

35. The price of the doll was how much greater than the mean of the 4 prices shown on the partial receipt?

2021 December(E23) Math Question 35

37. Andre's Floral Shop asked each of 20 customers to
give a rating of the shop's service. The table below
, summarizes the 20 customer ratings.
Which of the following values is closest to the mean of
the 20 customer ratings?

2019 June(B02) Math Question 37

2011 April(67F) Math Question 37

The probability distribution for both values of a random variable X is given in the table below. Given that the expected value of X is 20, what is the value of k?

2023 September(G01) Math Question 37

39. There are exactly 5 people in a bookstore at 12:00 p.m. Each person earns an annual income that is between $30,000 and $35,000. No one enters or leaves the bookstore until 12:15 p.m., when a professional athlete with an annual income of more than $1,000,000 enters the bookstore and joins the other 5 people. The mean, median, range, and standard deviation of the annual incomes of the 5 people in the bookstore at 12:00 p.m. are calculated and compared to, the same 4 statistics of the annual incomes of the 6 people in the bookstore at 12:15 p.m. If it can be determined, which of the 4 statistics changed the least?

2017 December(A10) Math Question 39

39. For which of the following data sets is the difference between the mean and the median the greatest?

2018 April(A09) Math Question 39

2018 December(B05) Math Question 39

2020 June(C02) Math Question 39

41. Set A and Set B each consist of 5 distinct numbers. The 2 sets contain identical numbers with the exception of the number with the least value in each set. The number with the least value in Set B is greater than the number with the least value in Set A. The value of which of the following measures must be greater for Set B than- for Set A?

2017 June(74C) Math Question 41

41. For 20 quiz scores in a typing class, the table below gives the frequency of the scores in each score interval. Which score interval contains the median of the scores?

2015 June(73C) Math Question 41

2019 December(C03) Math Question 41

Thomas wanted to test whether his coin was unfair. To do this, he flipped the coin 6 times and counted the number of heads and tails. Four of the flips resulted in heads, and two resulted in tails. One of the following statements is a correct conclusion based on Thomas's test. Which one?

2024 September(H11) Math Question 41

42. Jin's Office Supply sells different styles of notebooks. The sale price and number of sheets per notebook for 3 styles of notebooks are given in the table below. The sale price is the amount a customer pays for that notebook. Which of the following amounts is closest to the average sale price per sheet for a Style B notebook?

2014 April(71H) Math Question 42

43. From June 17 through June 21, the average of the “Hours away” was 5.50 hours. To the nearest 0.01, what is the value of “Hours away” when Ben was driving the truck?

2021 April(D05) Math Question 43

43. Mario plays basketball on a town league team. The table below gives Nlario’s scoring statistics for last season. flow many points did Mario score playing basketball last season!

2017 April(74F) Math Question 43

2009 December(68A) Math Question 43

44. Ling asked 11 people how many text messages each of them sent last week. Each of the 11 responses was in one of the intervals given in the table below. Which interval contains the median of the data?

2016 December(74H) Math Question 44

44. The table below gives experimental data values for variables x and y. Theory predicts that y varies directly with x. Based on the experimental data, which of the following values is closest to the constant of variation? (Note: The variable y varies directly with the variable x provided that y = kx for some nonzero constant k, called the constant of variation.)

2015 June(73C) Math Question 44

44. The mean of 10 numbers entered into a computer statistics program was 75.0. One number was incorrectly entered as 73 instead of 78. When the 73 is replaced by 78, by how much will the mean increase?

Percentage Increase / Decrease

Ratios

2020 December(D03) Math Question 44

Sumiko, who works at a restaurant, recorded the amounts of her customers' checks and the corresponding amounts of her tips, both in dollars, for 25 consecutive customers she served. She plotted the data in the standard (x,y) coordinate plane below with the amount of the check on the x-axis and the amount of the tip on the y-axis. Sumiko then performed a linear regression on the data, finding the regression equation to be y = 0.16x − 0.44 with a correlation coefficient, r, of 0.81. From her statistical analysis, Sumiko can correctly conclude that every $1 increase in the total amount of the check will result in approximately:

StatisticsThere are 137 ACT math questions under Statistics

Sub-topics

2019 June(A11) Math Question 1

2013 June(71C) Math Question 1