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Question

The mean of a set of observation is a. If each observation is multiplied by b and each product is decreased by c then the mean of new set of observation is

A
ab+c
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B
abc
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C
abc
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D
ab+c
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Solution

The correct option is D abc
Mean is the sum of the data values divided by the total number of data values.
Given that mean of a set of observations is a
Let the number of observations be n
Let the observations be x1,x2,x3,...,xn

Therefore, a=x1+x2+...+xnn

x1+x2+...+xn=an -------(1)

Given that each observation is multiplied by b and the product is decreased by c

Therefore the new observations are bx1c,bx2c,bx3c,...,bxnc

Therefore, the new mean is bx1c+bx2c+...+bxncn

new mean=bx1+bx2+...+bxnncn

new mean=b(x1+x2+...+xn)ncn

new mean=b(an)ncn (from (1))

new mean=n(abc)n

new mean=abc

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