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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 
  1. ¯¯¯xxq+xq
  2. (n1)¯¯¯xxqn
  3. (n1)¯¯¯x+xqn
  4. n¯¯¯xxq+xqn


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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