If bar{x}_{1}, bar{x}_{2}, bar{x}_{3}, ldots, | vedclass

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Question

(D) The mean of a group is defined as the sum of observations divided by the number of observations. For group $i$,the sum of observations is $S_{i} =

Vedclass · Accepted Answer

$\frac{\sum_{i=1}^{n} n_{i} \bar{x}_{i}}{\sum_{i=1}^{n} n_{i}}$

Vedclass · Answer

(D) The mean of a group is defined as the sum of observations divided by the number of observations. For group $i$,the sum of observations is $S_{i} = n_{i} \bar{x}_{i}$.To find the combined mean $\bar{x}$ of all $n$ groups,we divide the total sum of all observations by the total number of observations.Total sum of observations = $\sum_{i=1}^{n} n_{i} \bar{x}_{i}$Total number of observations = $\sum_{i=1}^{n} n_{i}$Therefore,the combined mean is $\bar{x} = \frac{\sum_{i=1}^{n} n_{i} \bar{x}_{i}}{\sum_{i=1}^{n} n_{i}}$.

Name of student	Kavya	Ariv	Ahaan	Arya	Arushi
Marks scored	$90$	$80$	$50$	$60$	$40$

Score	Frequency
$1$	$15$
$2$	$13$
$3$	$20$
$4$	$17$
$5$	$20$
$6$	$15$

Class interval	Frequency
$150-153$	$7$
$154-157$	$7$
$158-161$	$15$
$162-165$	$10$
$166-169$	$5$
$170-173$	$6$

If $\bar{x}_{1}, \bar{x}_{2}, \bar{x}_{3}, \ldots, \bar{x}_{n}$ are the means of $n$ groups with $n_{1}, n_{2}, \ldots, n_{n}$ number of observations respectively,then the combined mean $\bar{x}$ of all the groups taken together is given by:

Similar Questions

Represent the following data by a bar graph:

Name of student Kavya Ariv Ahaan Arya Arushi

Marks scored $90$ $80$ $50$ $60$ $40$

If the sum of $25$ observations is $900$, find the mean of those observations.

Represent the following data by a bar graph:

Score Frequency

$1$ $15$

$2$ $13$

$3$ $20$

$4$ $17$

$5$ $20$

$6$ $15$

Convert the given frequency distribution into a continuous grouped frequency distribution:

Class interval Frequency

$150-153$ $7$

$154-157$ $7$

$158-161$ $15$

$162-165$ $10$

$166-169$ $5$

$170-173$ $6$

In which intervals would $153.5$ and $157.5$ be included?

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

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