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

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