 # Cumulative Frequency Tables

In this worksheet, students calculate cumulative frequencies from data shown in a table. Key stage:  KS 4

Curriculum topic:  Statistics

Curriculum subtopic:  Interpret and Construct Tables and Line Graphs for Time Series Data

Difficulty level:   ### QUESTION 1 of 10

Frequency tells you how often a result happens.

Cumulative frequency tells you how often a result happens that is less than or equal to the given value.

To find cumulative frequency, we add together the frequencies up to and including the given result.

Example

The marks of 30 children in a maths exam were recorded in a table as shown below.

Calculate the cumulative frequencies for each class.

Marks frequency (f) Cumulative frequency
0 ≤ m ≤ 20 2
20 < m ≤ 40 5
40 < m ≤ 60 11
60 < m ≤ 80 8
80 < m ≤ 100 4
Total  30

To work out the cumulative frequency for each class interval, add the previous cumulative frequency to the frequency for that class.

Alternatively, add up all the frequencies up to and including that class.

Marks frequency (f) Cumulative frequency
0 ≤ m ≤ 20 2 2
20 < m ≤ 40 5 2 + 5 = 7
40 < m ≤ 60 11 7 + 11 = 18
60 < m ≤ 80 8 18 + 8 = 26
80 < m ≤ 100 4 26 + 4 = 30
Total  30

The marks of 30 children in a maths exam were recorded in a table as shown below.

Calculate the value of A.

Marks frequency (f) Cumulative frequency
0 ≤ m ≤ 20 2  2
20 < m ≤ 40 4 6
40 < m ≤ 60 11  A
60 < m ≤ 80 9  B
80 < m ≤ 100 4  C
Total  30

The marks of 30 children in a maths exam were recorded in a table as shown below.

Calculate the value of B.

Marks frequency (f) Cumulative frequency
0 ≤ m ≤ 20 2  2
20 < m ≤ 40 4 6
40 < m ≤ 60 11  A
60 < m ≤ 80 9  B
80 < m ≤ 100 4  C
Total  30

The marks of 30 children in a maths exam were recorded in a table as shown below.

Calculate the value of C.

Marks frequency (f) Cumulative frequency
0 ≤ m ≤ 20 2  2
20 < m ≤ 40 4 6
40 < m ≤ 60 11  A
60 < m ≤ 80 9  B
80 < m ≤ 100 4  C
Total  30

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of A.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 6 6
2 < t ≤ 4 14 20
4 < t ≤ 6 11  A
6 < t ≤ 8 15  B
8 < t ≤ 10 4  C
Total  50

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of B.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 6 6
2 < t ≤ 4 14 20
4 < t ≤ 6 11  A
6 < t ≤ 8 15  B
8 < t ≤ 10 4  C
Total  50

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of A in this table.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 6 6
2 < t ≤ 4 12 18
4 < t ≤ 6 13
6 < t ≤ 8 15
8 < t ≤ 10 A
Total  50

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of B in this table.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 6 6
2 < t ≤ 4 12 18
4 < t ≤ 6 B 33
6 < t ≤ 8 15
8 < t ≤ 10 A
Total  50

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of B in this table.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 A 6
2 < t ≤ 4 B 17
4 < t ≤ 6 C 33
6 < t ≤ 8 15
8 < t ≤ 10 D
Total  50

A survey of 1000 people was carried out to see how many times they checked their email at the weekend.

Calculate the value of B in this table.

Times (n) frequency (f) Cumulative frequency
0 ≤ n ≤ 5 A 8
5 < n ≤ 10 9
10 < n ≤ 15 B 53
15 < n ≤ 20 35
20 < n ≤ 25 C
Total  100

A survey of 100 people was carried out to see how many times they checked their email at the weekend.

Calculate the value of C in this table.

Times (n) frequency (f) Cumulative frequency
0 ≤ n ≤ 5 A 7
5 < n ≤ 10 9
10 < n ≤ 15 B 55
15 < n ≤ 20 35
20 < n ≤ 25 C
Total  100

• Question 1

The marks of 30 children in a maths exam were recorded in a table as shown below.

Calculate the value of A.

Marks frequency (f) Cumulative frequency
0 ≤ m ≤ 20 2  2
20 < m ≤ 40 4 6
40 < m ≤ 60 11  A
60 < m ≤ 80 9  B
80 < m ≤ 100 4  C
Total  30

17
EDDIE SAYS
A = 2 + 4 + 11
• Question 2

The marks of 30 children in a maths exam were recorded in a table as shown below.

Calculate the value of B.

Marks frequency (f) Cumulative frequency
0 ≤ m ≤ 20 2  2
20 < m ≤ 40 4 6
40 < m ≤ 60 11  A
60 < m ≤ 80 9  B
80 < m ≤ 100 4  C
Total  30

26
EDDIE SAYS
B = 2 + 4 + 11 + 9
• Question 3

The marks of 30 children in a maths exam were recorded in a table as shown below.

Calculate the value of C.

Marks frequency (f) Cumulative frequency
0 ≤ m ≤ 20 2  2
20 < m ≤ 40 4 6
40 < m ≤ 60 11  A
60 < m ≤ 80 9  B
80 < m ≤ 100 4  C
Total  30

30
EDDIE SAYS
C = 2 + 4 + 11 + 9 + 4
• Question 4

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of A.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 6 6
2 < t ≤ 4 14 20
4 < t ≤ 6 11  A
6 < t ≤ 8 15  B
8 < t ≤ 10 4  C
Total  50

31
EDDIE SAYS
A = 6 + 14 + 11
• Question 5

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of B.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 6 6
2 < t ≤ 4 14 20
4 < t ≤ 6 11  A
6 < t ≤ 8 15  B
8 < t ≤ 10 4  C
Total  50

46
EDDIE SAYS
B = 6 + 14 + 11 + 15
• Question 6

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of A in this table.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 6 6
2 < t ≤ 4 12 18
4 < t ≤ 6 13
6 < t ≤ 8 15
8 < t ≤ 10 A
Total  50

4
EDDIE SAYS
A = 50 - (6 + 12 + 13 + 15) = 50 - 46
• Question 7

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of B in this table.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 6 6
2 < t ≤ 4 12 18
4 < t ≤ 6 B 33
6 < t ≤ 8 15
8 < t ≤ 10 A
Total  50

15
EDDIE SAYS
18 + B = 33
• Question 8

A survey of 50 children was carried out to see how long they spent watching television per week.

Calculate the value of B in this table.

Time (t hours) frequency (f) Cumulative frequency
0 ≤ t ≤ 2 A 6
2 < t ≤ 4 B 17
4 < t ≤ 6 C 33
6 < t ≤ 8 15
8 < t ≤ 10 D
Total  50

11
EDDIE SAYS
B = 17 - 6
• Question 9

A survey of 1000 people was carried out to see how many times they checked their email at the weekend.

Calculate the value of B in this table.

Times (n) frequency (f) Cumulative frequency
0 ≤ n ≤ 5 A 8
5 < n ≤ 10 9
10 < n ≤ 15 B 53
15 < n ≤ 20 35
20 < n ≤ 25 C
Total  100

36
EDDIE SAYS
A = 8
B = 53 - 9 - 8 = 36
• Question 10

A survey of 100 people was carried out to see how many times they checked their email at the weekend.

Calculate the value of C in this table.

Times (n) frequency (f) Cumulative frequency
0 ≤ n ≤ 5 A 7
5 < n ≤ 10 9
10 < n ≤ 15 B 55
15 < n ≤ 20 35
20 < n ≤ 25 C
Total  100

10
EDDIE SAYS
A = 7
B = 55 - 9 - 7 = 39
C = 100 - 35 - 39 - 9 - 7 = 10
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.