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Q.
The mean of the series $x _1, x _2, \ldots ., x _{ n }$ is $\overline{ X }$. If $x _2$ is replaced by $\lambda$, then the new mean is-
Statistics
Solution:
$\because \frac{ x _1+ x _2+ x _3+---+ x _{ n }}{ n }=\overline{ x }$...(i)
When $x_2$ is replaced by $\lambda$ then
$\text { New Mean }=\frac{ x _1+\lambda+ x _3+---+ x _{ n }}{ n } $
$=\frac{\left( x _1+ x _2+ x _3+---+ x _{ n }\right)+\lambda- x _2}{ n }=\frac{ n \overline{ x }+\lambda- x _2}{ n }$ by(i)