# 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

#### 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 ofC.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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