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Calculate the Mean of the Distribution Given Below Using the Shortcut Method. - Mathematics

Calculate the mean of the distribution given below using the shortcut method.

Marks 11-20 21-30 31-40 41-50 51-60 61-70 71-80
No. of students 2 6 10 12 9 7 4
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Solution

Let A be the assumed mean and d be the deviation of x from the assumed mean.

Let A = 45.5.

d = x – A

Marks (C.I.) No. of students
(Frequency f)
Mid-point of
C.I. (x)
d = x – A f × d
11-20 2 15.5 -30 -60
21-30 6 25.5 -20 -120
31-40 10 35.5 -10 -100
41-50 12 45.5 0 0
51-60 9 55.5 10 90
61-70 7 65.5 20 140
71-80 4 75.5 30 120
        `sumfd = 70`

Mean  = `A + (sumfd)/(sum f)`

`=> Mean = 45.5 + 70/50`

`=> Mean  = 45.5 + 1.4`

`:. Mean = 45.9`

 

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