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Cumulative Frequency Graph

A Cumulative Frequency Graph is a graph plotted from a cumulative frequency table. A cumulative frequency graph is also called an ogive.

 

 

Example :

Draw a cumulative frequency graph for the frequency table below.

Length (x mm)

Frequency

11 – 15

2

16 – 20

4

21 – 25

8

25 – 30

14

31 – 35

6

36 – 40

4

41 – 45

2

Solution:

We need to add a class with 0 frequency before the first class and then find the upper boundary for each class interval.

Length

(x mm)

Frequency

Upper Class Boundary

Length

(x mm)

Cumulative

Frequency

6 – 10

0

10.5

x ≤ 10.5

0

11 – 15

2

15.5

x ≤ 15.5

2

16 – 20

4

20.5

x ≤ 20.5

6

21 – 25

8

25.5

x ≤ 25.5

14

25 – 30

14

30.5

x ≤ 30.5

28

31 – 35

6

35.5

x ≤ 35.5

34

36 – 40

4

40.5

x ≤ 40.5

38

41 – 45

2

45.5

x ≤ 45.5

40

And then plot the cumulative frequency against the upper class boundary of each interval and join the points with a smooth curve.

 

 

The following video shows how to obtain a cumulative frequency graph from a cumulative frequency table.

 

 

 

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