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Calculate the Mean of the Following Distribution Using Step Deviation Method. - Mathematics

Calculate the mean of the following distribution using step deviation method.

Marks 0-10 10-20 20-30 30-40 40-50 50-60
Number of
students
10 9 25 0 16 10
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Solution

Let the assumed mean A = 25

Marks

Mid-value

x

f d = x - A `t= (x-A)/i = (x-25)/10` ft
0 - 10 5 10 -20 -2 -20
10 - 20 15 9 -10 -1 -9
20 - 30 25 25 0 0 0
30 - 40 35 30 10 1 30
40 - 50 45 16 20 2 32
50 - 60 55 10 30 3 30
    `sumf= 100`     `sumft = 63`

`:. Mean = A+ (sumft)/(sumf) xx i = 25 + 63/100 xx 10 = 25 + 63/10 = 25 + 6.3 = 31.3`

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