# Lesson Worksheet: The Mean of a Data Set Mathematics • 6th Grade

In this worksheet, we will practice calculating the mean of a set of whole numbers or decimals.

Q1:

Which of the following data sets has a mean of 59?

• A52, 76, 23, 50, 15
• B81, 34, 85, 21, 76
• C74, 79, 27, 59, 56
• D90, 64, 49, 13, 50
• E11, 50, 21, 72, 48

Q2:

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

If the mean is 13, find the value of .

Q3:

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

Q4:

Find the mean of the values 15, 20, 37, 43, 13, 34, 41, and 39.

Q5:

Find the mean of the set of data in the line plot. If necessary, write your answer to the nearest tenth. Q6:

The mean of the given data set is 7. Find the missing value .

 9 6 3 8 5 𝑥

Q7:

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

Q8:

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

Q9:

The 6 most recent customers at a bookstore 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?

Q10:

Table shows the distribution of the wages of 250 factory workers. Find the mean wage received.

 Wages in Pounds Number of Workers 10–19 20–29 30–39 40–49 50–59 60–69 49 32 𝑘 𝑘+5 50 34

Q11:

The table shows the marks that four students received in their end of year exams. Calculate the mean mark of student (C).

StudentsMathematicsChemistryPhysicsBiologyHistory
(A)1011121314
(B)910876
(C)8137512
(D)14139118

Q12:

The table shows the total number of votes that each act received in a local talent show.

SingerDancerComedianAcrobatMagicianMusician
14293672311

Find the mean number of votes.

Describe what the mean represents.

• AThe difference between the largest value and the smallest value in the list
• BThe average between the third and fourth terms

Q13:

David took samples of students from each grade in his school to investigate the average height of a student. The results are summarized as shown:

 Grade Number of Students Mean Height K 1 2 3 4 5 14 16 15 19 17 18 116 cm 122 cm 127 cm 132 cm 137 cm 143 cm

Use his data to find the mean height of a student in the school. Give your answer to the nearest centimeter.

Q14:

In the soccer world cup, a team scored 32 total goals with a mean of 2 goals per game. How many games did they play in total?

Q15:

In a recent skating championship, a skater’s scores for speed were , 3, 3, , , and . Determine his average score for speed in the championship.

Q16:

The table shows the number of hours that two students spent studying on each day of a week. Calculate the mean number of hours spent studying by student (B).

 Student (A) Student (B) 5 7 7 7 6 7 3 7 6 4 8 3 4 3

Q17:

Calculate the mean of the values .

Q18:

Given that the mean of the values and 18 is 10, find the value of .

Q19:

The table shows the marks that four students received in their end of year exams. Calculate the mean mark for mathematics.

StudentMathematicsChemistryPhysicsBiologyHistory
(A)12515148
(B)121114810
(C)13109127
(D)111014615

Q20:

Given that the sum of five values is 165, find the mean of the values.

Q21:

Anthony would like to estimate how many books he reads per week on average. For six weeks, he has been producing a list of the books he had just read. His results are given in the table.

 Week Numbers of Books 1 2 3 4 5 6 2 3 1 2 0 1

Assuming that these six weeks are representative of his reading habits, what is the average number of books does Anthony read per week?

Q22:

At a school, every student belongs to one of four houses, and the houses compete throughout the year to earn points.

The graph shows how many points each house had scored at the end of the year. Calculate the mean number of points earned.

Describe what the mean represents.

• AThe difference between the largest value in the list and the smallest value in the list.
• BThe average between the third and fourth terms.
• CThe number of points that each house would have earned if they had all earned the same number of points.

Q23:

Ethan’s test scores in chemistry were 69.4, 78, 81.1, 69.1, and 76.4. Determine his average test score, and using the table, determine his grade.

 Grade Average Score A B C D F 90–100 80–89 70–79 60–69 50–59
• A69.8, B
• B74.8, C
• C69, D
• D74.4, A
• E74, C

Q24:

If the average of two numbers is 65, where one of them is 60, find the other number.

Q25:

In a given month, the price of a bag of sugar increased by in the first week, increased by another in each of the next 2 weeks, and then decreased by in the fourth week. Determine the average change in the price of sugar over these 4 weeks.

• A per week
• B per week
• C per week
• D per week
• E per week