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Cumulative Frequency Table

The cumulative frequency of a set of data or class intervals of a frequency table is the sum of the frequencies of the data up to a required level. It can be used to determine the number of items that have values below a particular level.

 

 

Example : (Ungrouped data)

The following table gives the frequency distribution of marks obtained by 28 students in a particular test.

Marks

30

31

32

33

Frequency

5

7

10

6

Construct a cumulative frequency table for the given data.

Solution:

Marks

Frequency

Marks less than

Cumulative Frequency

30

5

30

5

31

7

31

5 + 7 =12

32

10

32

12 + 10 =22

33

6

33

22 + 6 =28

 

 

Example : (Grouped data)

The following table gives the frequency distribution of mass of 40 objects.

Mass (g)

10–14

15–19

20–24

25–29

30–34

35–39

40–44

Frequency

3

4

10

12

6

3

2

Construct a cumulative frequency table for the given data.

Solution:

Mass

Upper class boundaries

Frequency

Mass less than

Cumulative Frequency

10 – 14

14.5

3

14.5

3

15 – 19

19.5

4

19.5

3 + 4 = 7

20 – 24

24.5

10

24.5

7 + 10 = 17

25 – 29

29.5

12

29.5

17 + 12 = 29

30 – 34

34.5

6

34.5

29 + 6 = 35

35 – 39

39.5

3

39.5

35 + 3 = 38

40 – 44

44.5

2

44.5

38 + 2 = 40

 

 

The following video how to construct the cumulative frequency table and cumulative frequency graph.

 

 

 

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