If each observation of the data is increased by 8, then their mean

Question:

If each observation of the data is increased by 8, then their mean
(a) remains the same
(b) is decreased by 8
(c) is increased by 5
(d) becomes 8 times the original mean

Solution:

(b) is decreased by 8

Let the numbers be $x_{1}, x_{2} \ldots x_{n} .$

Hence, mean $=\frac{x_{1}+x_{2}+\ldots+x_{n}}{n}$

Now the new numbers after decreasing every number by $8:\left(x_{1}-8\right),\left(x_{2}-8\right) \ldots,\left(x_{n}-8\right)$

New Mean $=\frac{\left(x_{1}-8\right)+\left(x_{2}-8\right)+\ldots+\left(x_{n}-8\right)}{n}$

$=\frac{x_{1}+x_{2}+\ldots .+x_{n}-8 n}{n}$

$=\frac{x_{1}+x_{2}+\ldots .+x_{n}}{n}-8$

$\therefore$ New mean $=$ mean $-8$

Hence, mean is decreased by 8.

 

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