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Cumulative Frequency Tables

In this worksheet, students calculate cumulative frequencies from data shown in a table.

'Cumulative Frequency Tables' worksheet

Key stage:  KS 4

Curriculum topic:  Statistics

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

Difficulty level:  

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Worksheet Overview

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  

 

 

 

 

 

 

 

Answer

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  

 

CORRECT ANSWER
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  

 

CORRECT ANSWER
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  

 

CORRECT ANSWER
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  

 

CORRECT ANSWER
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  

 

CORRECT ANSWER
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  

 

CORRECT ANSWER
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  

 

CORRECT ANSWER
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  

 

CORRECT ANSWER
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  

 

CORRECT ANSWER
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  

 

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