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Question

Mean of n observations x1,x2,,xn is ¯¯¯x. If an observation xq is replaced by xq then the mean is

A
¯¯¯xxq+xq
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B
(n1)¯¯¯x+xqn
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C
(n1)¯¯¯xxqn
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D
n¯¯¯xxq+xqn
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Solution

The correct option is D n¯¯¯xxq+xqn
x1+x2+...+xq+...+xnn=¯¯¯x
x1+x2+...+xq+...+xn=n¯¯¯x

As per question, replace xq with xq
x1+x2+...+xq+...+xn =x1+x2+...+xq+...+xn+xqxq
x1+x2+...+xq+...+xn=n¯¯¯x+xqxq

Hence, new mean is
x1+x2+...+xq+...+xnn=n¯¯¯xxq+xqn

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