If the mean of the series x_1, x_2, ......., | vedclass

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(B) Given that the mean of $x_1, x_2, ......., x_n$ is $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$.Let the new series be $y_i = x_i + 2i$ for $i = 1, 2,

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$\bar{x} + n + 1$

Vedclass · Answer

(B) Given that the mean of $x_1, x_2, ......., x_n$ is $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$.Let the new series be $y_i = x_i + 2i$ for $i = 1, 2, ......., n$.The mean of the new series is $\bar{y} = \frac{1}{n} \sum_{i=1}^{n} (x_i + 2i)$.$\bar{y} = \frac{1}{n} (\sum_{i=1}^{n} x_i + 2 \sum_{i=1}^{n} i)$.Using the sum of first $n$ natural numbers formula $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$:$\bar{y} = \frac{\sum x_i}{n} + \frac{2}{n} 	imes \frac{n(n+1)}{2}$.$\bar{y} = \bar{x} + (n+1)$.

$x_i$	$3$	$6$	$10$	$12$	$7$	$15$
$f_i$	$3$	$4$	$2$	$8$	$13$	$10$

If the mean of the series $x_1, x_2, ......., x_n$ is $\bar{x}$,then what will be the mean of the series $x_i + 2i, (i = 1, 2, ......., n)$?

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