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Question

If the sum of the deviations of a set of values x1,x2,x3,,xn measured from 50 is -10 and the sum of deviations of the values from 46 is 70, then the mean is _____.


A

49

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B

49.5

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C

49.75

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D

50

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Solution

The correct option is B

49.5


Given:
x150+x250++xn50=10
(x1+x2++xn)50n=10
(x1+x2++xn)=10+50n(i)
Also given that,
x146+x246++xn46=70
(x1+x2++xn)46n=70
x1+x2++xn=70+46n(ii)
From Eqs. (i) and (ii)
10+50n=70+46n4n=80n=20
From Eq. (i)
x1+x2++xn=990Mean=x1+x2++xnn=99020=49.5


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