CUMULATIVE FREQUENCY
Statistics of Class 9
(i) Discrete frequency distribution : From the table of discrete frequency distribution, it can be identified that number of employees whose monthly income is 4000 or how many employees of monthly income 1100 are there. But if we want to know how many employees whose monthly income is upto 11000, then we should add 10 + 8 + 5 7 i.e., number of employees whose monthly income is upto 11000 is 30. Here we add all previous frequency and get cumulative frequency. If will be more clear from the following table
Class |
Frequency (f) |
Cumulative frequency (cf) |
Explanation |
4000 |
10 |
10 |
10 = 1 0 |
6000 |
8 |
18 |
10 + 8 |
8000 |
5 |
23 |
18 + 5 |
11000 |
7 |
30 |
23 + 7 |
20000 |
2 |
32 |
30 + 2 |
25000 |
1 |
33 |
32 + 1 |
(ii) Continuous frequency distribution: In the previous page we obtained cumulative frequency for discrete series. Similarly cumulative frequency table can be made from continuous frequency distribution also. For example, for table:
Monthly income |
No. of employee |
Cumulative |
Explanation |
Variate (x) |
Frequency (f) |
Frequency (cf) |
|
0 – 5 |
72 |
72 |
72 = 72 |
5 – 10 |
103 |
175 |
72 + 103 = 175 |
10 – 15 |
50 |
225 |
175 + 50 = 225 |
15 - 20 |
25 |
250 |
225 + 25 = 250 |
Above table can also be written as follows :
Class |
Cumulative Frequency |
Less than 5 |
72 |
Less than 10 |
175 |
Less than 15 |
225 |
Less than 20 |
250 |
From this table the number of students of age less than the upper limit of a class, i.e., number of student whose age is less than 5, 10, 15, 20 year can determined by merely seeing the table but if we need the number students whose age is more than zero, more than 5, more than 10 or more than 15, then table should be constructed as follows:
Class |
Frequency |
Age Cumulative frequency |
Explanation |
0 – 5 |
72 |
0 and more 50 |
250 = 250 |
5 – 10 |
103 |
5 and more 78 |
250 – 72 = 178 |
10 - 15 |
50 |
10 and more 75 |
178 – 103 = 75 |
15 - 20 |
25 |
15 and more 25 |
75 – 50 = 25 |