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Let $y_1$ , $y_2$ , $y_3$ ,..... $y_n$ be $n$ observations. Let ${w_i} = l{y_i} + k\,\,\forall \,\,i = 1,2,3.....,n,$ where $l$ , $k$ are constants. If the mean of $y_i's$ is is $48$ and their standard deviation is $12$ , then mean of $w_i's$ is $55$ and standard deviation of $w_i's$ is $15$ , then values of $l$ and $k$ should be
$l = 2.5, k = 5$
$l = 1.25, k = 5$
$l = 1.25, k = -5$
$l = 2.5, k = -5$
Solution
Mean of ${\omega _i} = l$ (mean of ${{y_i}}$) $+k$
$55 = l.48 + {\rm{k}}$ ………$(i)$
standard deviation of
${\omega _i} = l$ (standard deviation of ${{{\rm{y}}_i}}$)
$15 = l.12$ ………..$(ii)$
$l = 1.25$ and $\mathrm{k}=-5$
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