If bar{x} is the mean of x_{1}, x_{2}, ldots, | vedclass

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(B) Given that $\bar{x}$ is the mean of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$.Therefore,the sum of these observations is $\sum_{i=1}^{n} x_{i

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$\frac{\bar{x}+\bar{y}}{2}$

Vedclass · Answer

(B) Given that $\bar{x}$ is the mean of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$.Therefore,the sum of these observations is $\sum_{i=1}^{n} x_{i} = n \bar{x}$.Similarly,$\bar{y}$ is the mean of $n$ observations $y_{1}, y_{2}, \ldots, y_{n}$.Therefore,the sum of these observations is $\sum_{i=1}^{n} y_{i} = n \bar{y}$.Now,$\bar{z}$ is the mean of all $2n$ observations $(x_{1}, \ldots, x_{n}, y_{1}, \ldots, y_{n})$.Thus,$\bar{z} = \frac{\sum x_{i} + \sum y_{i}}{n + n}$.Substituting the sums,we get $\bar{z} = \frac{n \bar{x} + n \bar{y}}{2n}$.Simplifying this,$\bar{z} = \frac{n(\bar{x} + \bar{y})}{2n} = \frac{\bar{x} + \bar{y}}{2}$.

Length (in mm)	Number of leaves
$118-126$	$8$
$127-135$	$10$
$136-144$	$12$
$145-153$	$17$
$154-162$	$7$
$163-171$	$5$
$172-180$	$3$

Score $(x)$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Frequency $(f)$	$5$	$9$	$12$	$17$	$14$	$10$	$6$

Number of hours	$0-5$	$5-10$	$10-15$	$15-20$
Frequency	$8$	$16$	$4$	$2$

Frequency $(f_i)$	Variable $(x_i)$
$4$	$4$
$8$	$6$
$14$	$8$
$11$	$10$
$3$	$12$

If $\bar{x}$ is the mean of $x_{1}, x_{2}, \ldots, x_{n}$ and $\bar{y}$ is the mean of $y_{1}, y_{2}, \ldots, y_{n}$. If $\bar{z}$ is the mean of $x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}$,then $\bar{z}$ is equal to

Similar Questions

Find the mean of the following frequency distribution:

Score $(x)$ $1$ $2$ $3$ $4$ $5$ $6$ $7$

Frequency $(f)$ $5$ $9$ $12$ $17$ $14$ $10$ $6$

....... is a branch of Mathematics in which the extraction of meaningful information is studied.

Obtain the mean of the following distribution:

Frequency $(f_i)$ Variable $(x_i)$

$4$ $4$

$8$ $6$

$14$ $8$

$11$ $10$

$3$ $12$

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