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Question

The algebraic sum of the deviations of 20 observations measured from 30 is 2. What would be the mean of the observations?

A
30
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B
32
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C
30.2
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D
30.1
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Solution

The correct option is B 30.1
Let the 20 deviations be a1,a2,...,a20

Therefore the observations are (30+a1),(30+a2),...,(30+a20)

Given that sum of the deviations is 2

Therefore, a1+a2+...+a20=2 ------(1)

Hence, mean=(30+a1)+(30+a2)+...+(30+a20)20

mean=a1+a2+...+a20+20(30)20

mean=2+20(30)20 (from (1))

mean=60220=30.1

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