Mean of four observation is 12 . If first , second, third and fouth observation are decreased by 1,2,3 and 4 respectively , then find the new mean

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Solution

Let the four observations be $x_{1}, x_{2}, x_{3}, x_{4}$
given that mean of $4$ observations $= 12$
$\frac{x_{1}, x_{2}, x_{3}, x_{4}}{4} = 12$ ------------------- $(1)$
given that if $1^{s t}, 2^{n d}, 3^{r d}$ and $4^{t h}$ observations are decreased by $1, 2, 3, 4$
$= \frac{x_{1} - 1 + x_{2} - 2 + x_{3} - 3 + x_{4} - 4}{4}$
$= x_{1} + x_{2} + x_{3} + x_{4} - \frac{10}{4}$
$= \frac{x_{1} + x_{2} + x_{3} + x_{4}}{4} - \frac{10}{4}$
$= 12 - \frac{10}{4}$
$= \frac{48 - 10}{4} = \frac{38}{4} = 9.5$
We get, new mean $= 9.5$

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Mean of four observation is 12 . If first , second, third and fouth observation are decreased by 1,2,3 and 4 respectively , then find the new mean

Let the four observations be x1,x2,x3,x4given that mean of 4 observations =12x1,x2,x3,x44=12-------------------(1)given that if 1st,2nd,3rd and 4th observations are decreased by 1,2,3,4=x1−1+x2−2+x3−3+x4−44=x1+x2+x3+x4−104=x1+x2+x3+x44−104=12−104=48−104=384=9.5We get, new mean=9.5