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If $\sum\left(x_{i}-2\right)=110, \quad \sum^{n}\left(x_{i}-5\right)=20$, then what is the
mean?
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mean?
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The correct answer is:
$17 / 3$
$\begin{aligned} & \sum_{t=1}^{n}\left(x_{i}-2\right)=110 \\ & \therefore x_{1}+x_{2}+\ldots+x_{n}-2 n=110 \\ & \Rightarrow x_{1}+x_{2}+\ldots+x_{n}=2 n+110 \\ & \text { and } \sum_{i=1}^{n}\left(x_{i}-5\right)=20 \\ & \Rightarrow x_{1}+x_{2}+\ldots+x_{n}-5 n=20 \\ & \Rightarrow x_{1}+x_{2}+\ldots+x_{n}=5 n+20 \end{aligned}$
From equations (i) and (ii), we get $5 n+20=2 n+110$
$\Rightarrow 3 n=90 \Rightarrow n=30$
Now, mean $=\frac{x_{1}+x_{2}+\ldots x_{n}}{n}$
$=\frac{5 \times 30+20}{30}=\frac{170}{30}=\frac{17}{3}$
From equations (i) and (ii), we get $5 n+20=2 n+110$
$\Rightarrow 3 n=90 \Rightarrow n=30$
Now, mean $=\frac{x_{1}+x_{2}+\ldots x_{n}}{n}$
$=\frac{5 \times 30+20}{30}=\frac{170}{30}=\frac{17}{3}$
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