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

 

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