Statistics

Mean, Median

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

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

2009 June(67C) 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

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

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

2011 April(67F) Math Question 15

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. 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

2019 June(72F) Math Question 19

2012 April(70G) Math Question 19

2019 December(C03) 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

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

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

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?

Statistics (Mean, Median, Mode, Standard Deviation)

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

2019 December(C03) Math Question 35

2009 April(66F) 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

2018 December(B05) Math Question 39

2020 June(C02) Math Question 39

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

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 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

46. The difference (larger minus smaller) between 2 numbers is 15. If n represents the larger number, which expression below represents the average (arithmetic mean) of the 2 numbers?

2014 June(72C) Math Question 46

47. For those in the sample who are 26 to 45 years old, which of the following values is closest to the average number of car owners per company?

2020 December(D03) Math Question 47

2011 June(69F) Math Question 48

49. Each of 20 students in a class took a test and received a whole number score. The median of the scores was 87. None of the students received a score of 87, and 30% of the students received scores of 90 or above. How many students received scores of 88 or 89 ?

2014 December(72G) Math Question 49

2019 April(B04) Math Question 51

2009 April(66F) Math Question 51

2013 April(71G) Math Question 52

2020 July(C01) Math Question 52

56. The mean of the set of 5 numbers {42, 3, 11, 27, x} is 24, and the median of the set of 4 numbers {53, 8, 29, y) is 38. If it can be determined, which of the following values is equal to x-y?

2017 December(A10) Math Question 56

58. The frequency histogram below shows the distribution '
of the heights, in inches, of 11 basketball players.

Using the data from the frequency histogram, what is
the sum of the mean the median of this distribution?

2019 June(B02) Math Question 58

59. 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 ?

Mean, MedianStatisticsACT math questions

2019 June(A11) Math Question 1

2013 June(71C) Math Question 1