In this lesson, we will learn how to construct Cumulative Frequency Tables for Ungrouped data and Grouped data.
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.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 |
Statistics - How to make a cumulative frequency chart (Ungrouped data)
This example shows how to make a cumulative frequency chart. Remember that in these charts, we simply want to keep track of the grand total of the 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.
Completing a cumulative frequency table from a grouped frequency table.