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Lesson: The Mean of a Data Set

In this lesson, we will learn how to find the mean of a set of data and how to use it to find missing data.

Sample Question Videos

01:48

Worksheet • 25 Questions • 1 Video

Q1:

Before the last soccer game of the season, Karim scored a total of 23 goals. He scored 5 goals in the final game, with an average of 4 goals per game this season. To calculate the total number of games Karim played, we first find the sum of 23 and 5. What would be the next step?

  • Adivide the sum by 4
  • Bdivide the sum by 5
  • Cadd the sum to 4
  • Dmultiply the sum by 4
  • Esubtract 4 from 230

Q2:

Given the mean of the values 8, 22, 4, 12, and 𝑋 is 15, find the value of 𝑋 .

Q3:

A student’s mean score in four tests is 35 marks. After he takes a fifth test, his mean score increases to 37 marks. What was his score on the fifth test?

  • A45 marks
  • B2 marks
  • C36 marks
  • D7 marks
  • E50 marks

Q4:

The table shows the total precipitation in Arches National Park in January of each year. Calculate the mean January precipitation over the entire period shown in the table.

Year 1,997 1,998 1,999 2,000 2,001 2,002 2,003 2,004
Precipitation (in) 1.09 0.013 0.54 0.80 0.89 0.24 0.11 0.16

Q5:

The mean of the given data set is 7. Find the missing value π‘₯ .

9 6 3 8 5 π‘₯

Q6:

Given that the mean of the marks of 9 students is 45, determine the sum of their marks.

Q7:

A student takes five tests: A, B, C, D, and E. Their mean score for tests A, B, and C is 48. Their mean score for tests D and E is 38. Calculate the mean score of all 5 tests.

Q8:

The table shows how much Bassem saved each day. Describe how the mean would be affected if the savings for Monday were not included.

Day Saturday Sunday Monday Tuesday Wednesday Thursday
Amount Saved $11.90 $6.00 $3.70 $3.10 $6.10 $8.10
  • AThe mean would increase from $6.48 to $7.04.
  • BThe mean would increase from $6.48 to $11.90.
  • CThe mean would decrease from $7.04 to $6.48.
  • DThe mean would remain unchaged at $6.48.
  • EThe mean would decrease from $11.90 to $6.48.

Q9:

If the mean age of two people is 50 and one of the people is 54 years old, how old is the other person?

Q10:

The table shows the hours trained per month for two athletes. Find the mean number of hour trained for athlete (B).

Athlete (A) 64 54 53 75 54 56 73 46 75 47 53 70
Athlete (B) 52 67 73 74 70 69 57 64 48 73 68 65

Q11:

Adam has the following data: 18, , 11, 15.

If the mean is 13, find the value of .

Q12:

The 6 most recent customers at a bookshop bought the following numbers of books: 3 books, 2 books, 2 books, 2 books, 4 books, and 5 books. What is the mean number of books bought?

  • A3 books
  • B6 books
  • C4 books
  • D5 books
  • E2 books

Q13:

Find the mean of the following data set: π‘₯ + 3 , 5 π‘₯ , 3 π‘₯ + 3 .

  • A 3 π‘₯ + 2
  • B 9 π‘₯ + 6
  • C 6 π‘₯ + 9
  • D 2 π‘₯ + 3

Q14:

Given that the mean of the values π‘š , 2 π‘š , 3 π‘š , and 8 is 56, find the value π‘š .

Q15:

Find, to the nearest cent, the mean of the set of costs in the table.

Cost Tally Frequency
$12.64 11
$18.06 15
$10.50 10

Q16:

Determine the mean of three numbers which sum to 42.

Q17:

In order to get a C in maths, Nabil must have an average score of 70 or more. His test scores so far are 63.3, 85, 79.73, and 70.57. Calculate the minimum score Nabil needs to get on his final test to earn a C.

  • A51.4
  • B50
  • C53.4
  • D46
  • E41.4

Q18:

Find, to two decimal places, the mean of the test scores in the table. Then determine which group’s score is closest to the mean.

Class Group Group A Group B Group C Group D Group E Group F Group G Group H
Test Score 78 86 72 93 92 84 87 70
  • A The mean is 82.75, and Group F is the closest to the mean.
  • B The mean is 94.57, and Group D is the closest to the mean.
  • C The mean is 82.75, and Group E is the closest to the mean.
  • D The mean is 84.57, and Group F is the closest to the mean.
  • E The mean is 82.75, and Group G is the closest to the mean.

Q19:

The table shows the greatest distances thrown by the finalists in the discus competition of the 2016 Rio Olympics for both men and women.

Distance (m)
Men Women
Gold 68.37 69.21
Silver 67.55 66.73
Bronze 67.05 65.34
4 66.58 64.90
5 65.10 64.37
6 64.95 63.13
7 64.50 63.11
8 63.72 63.06

Calculate, to the nearest hundredth of a meter, the mean distance thrown by men and the mean distance thrown by women.

  • Amen: 65.98 m, women: 64.98 m
  • Bmen: 65.01 m , women: 64.98 m
  • Cmen: 64.98 m, women: 65.98 m
  • Dmen: 64.73 m, women: 65.60 m
  • Emen: 66.12 m, women: 65.25 m

What is the correct interpretation of these mean distances?

  • AOn average, men threw farther than women.
  • BOn average, women threw farther than men.
  • CThe longest throw by a man was farther than the longest throw by a woman.
  • DThere was a greater variability in the distances thrown by women.
  • EThere was a greater variability in the distances thrown by men.

Q20:

Bassem studied a daily average of 52 minutes Sunday through Thursday. If he studied 39 minutes on Sunday, 66 minutes on Monday, 51 minutes on Tuesday, and 59 minutes on Wednesday, how many minutes did he study on Thursday?

Q21:

Over a period of fifteen days, temperatures were measured and subsequently recorded in the table shown. Determine whether the following statement is true or false: If the total of these temperatures was equally distributed among the days, each day would have a temperature of 8 degrees Celsius.

3 3 14 13 7
1 0 11 6 3
8 13 13 11 14
  • Afalse
  • Btrue

Q22:

Find the mean of the following set of data: 9.2, 2.5, 1.7, 2.2, 6.4, 9.1, 2.2, 5.9. If necessary, round your answer to the nearest tenth.

Q23:

The table shows the number of subscribers of several internet providers. What is the mean number of subscribers for these internet providers?

Internet Provider Company A Company B Company C
Subscribers (millions) 1.65 1.16 1.9

Q24:

What is the mean of the following numbers: 6, 4, 5, 3, 5, 1?

Q25:

Find the mean of the set of data in the line plot. If necessary, write your answer to the nearest tenth.

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