The mean of the 10 observations is 68. If eac | vedclass

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(C) Let the $10$ observations be $x_1, x_2, \dots, x_{10}$.The mean is given by $\bar{x} = \frac{\sum_{i=1}^{10} x_i}{10} = 68$.This implies $\sum_{i=

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(C) Let the $10$ observations be $x_1, x_2, \dots, x_{10}$.The mean is given by $\bar{x} = \frac{\sum_{i=1}^{10} x_i}{10} = 68$.This implies $\sum_{i=1}^{10} x_i = 680$.According to the problem, each observation is divided by $2$ and then $6$ is added. Let the new observations be $y_i = \frac{x_i}{2} + 6$.The mean of the new observations is $\bar{y} = \frac{\sum_{i=1}^{10} y_i}{10}$.Substituting $y_i$, we get $\bar{y} = \frac{\sum_{i=1}^{10} (\frac{x_i}{2} + 6)}{10} = \frac{\frac{1}{2} \sum x_i + 10 	imes 6}{10}$.$\bar{y} = \frac{1}{2} \bar{x} + 6$.Substituting $\bar{x} = 68$, we get $\bar{y} = \frac{68}{2} + 6 = 34 + 6 = 40$.

Marks $(x_{i})$	$15$	$22$	$28$	$31$	$35$	$40$	$44$	$46$
Number of students $(f_{i})$	$2$	$3$	$5$	$6$	$6$	$4$	$3$	$1$

The mean of the $10$ observations is $68$. If each observation is divided by $2$ and then $6$ is added to each result, find the mean of the new observations so obtained.

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