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Question

​The following table shows the marks scored by 80 students in an examination:
Marks Less than 5 Less than 10 Less than 15 Less than 20 Less than 25 Less than 30 Less than 35 Less than 40
Number of students 3 10 25 49 65 73 78 80

Calculate the mean marks correct to 2 decimal places.

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Solution

Let us choose a = 17.5, h = 5, then di = xi − 17.5 and ui = xi-17.55.

Using Step-deviation method, the given data is shown as follows:
Marks Number of students (cf) Frequency (fi) Class mark (xi) di = xi − 17.5 ui = xi-17.55 fiui
0−5 3 3 2.5 −15 −3 −9
5−10 10 7 7.5 −10 −2 −14
10−15 25 15 12.5 −5 −1 −15
15−20 49 24 17.5 0 0 0
20−25 65 16 22.5 5 1 16
25−30 73 8 27.5 10 2 16
30−35 78 5 32.5 15 3 15
35−40 80 2 37.5 20 4 8
Total fi = 80 ∑ fiui = 17

The mean of given data is given by

x¯=a+ifiuiifi×h =17.5+1780×5 =17.5+1.06 =18.56

​Thus, the mean marks correct to 2 decimal places is 18.56.

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