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 |
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 |