The mean of two samples of size 200 and 300 w | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\mathrm{x}_{1}=200 \quad \mathrm{x}_{2}=300$

$\overline{\mathrm{x}}_{1}=25 \quad \overline{\mathrm{x}}_{2}=10$

$\sigma_{1}=3 \quad \sigma_{2}=4

Vedclass · Accepted Answer

$67.2$

Vedclass · Answer

$\mathrm{x}_{1}=200 \quad \mathrm{x}_{2}=300$

$\overline{\mathrm{x}}_{1}=25 \quad \overline{\mathrm{x}}_{2}=10$

$\sigma_{1}=3 \quad \sigma_{2}=4$

combined mean $=\frac{25 	imes 200+10 	imes 300}{500}=16$

$\sigma_{1}^{2}=9=\frac{1}{200}\left(\sum x_{i}^{2}ight)-625$

$126800=\sum x_{i}^{2}$

$\sigma_{2}^{2}=16=\frac{1}{300} \sum y_{1}^{2}-100$

$34800=\sum y_{1}^{2}$

$\sigma^{2}=\frac{1}{500}(126800+34800)-(16)^{2}$

$=323.2-256=67.2$

$\mathrm{x}$	$-2$	$-1$	$3$	$4$	$6$
$\mathrm{P}(\mathrm{X}=\mathrm{x})$	$\frac{1}{5}$	$\mathrm{a}$	$\frac{1}{3}$	$\frac{1}{5}$	$\mathrm{~b}$

Classes	$0-30$	$30-60$	$60-90$	$90-120$	$120-150$	$50-180$	$180-210$
$f_i$	$2$	$3$	$5$	$10$	$3$	$5$	$2$

The mean of two samples of size $200$ and $300$ were found to be $25, 10$ respectively their $S.D.$ is $3$ and $4$ respectively then variance of combined sample of size $500$ is :-

Similar Questions

If the mean and variance of the following data:

$6,10,7,13, a, 12, b, 12$ are 9 and $\frac{37}{4}$ respectively, then $(a-b)^{2}$ is equal to:

Let $\mathrm{X}$ be a random variable with distribution.

$\mathrm{x}$ $-2$ $-1$ $3$ $4$ $6$

$\mathrm{P}(\mathrm{X}=\mathrm{x})$ $\frac{1}{5}$ $\mathrm{a}$ $\frac{1}{3}$ $\frac{1}{5}$ $\mathrm{~b}$

If the mean of $X$ is $2.3$ and variance of $X$ is $\sigma^{2}$, then $100 \sigma^{2}$ is equal to :

Find the mean and variance for the following frequency distribution.

Classes $0-30$ $30-60$ $60-90$ $90-120$ $120-150$ $50-180$ $180-210$

$f_i$ $2$ $3$ $5$ $10$ $3$ $5$ $2$

The mean and variance of $7$ observations are $8$ and $16,$ respectively. If five observations are $2, 4, 10,12,14,$ then the absolute difference of the remaining two observations is

The frequency distribution:

$\begin{array}{|l|l|l|l|l|l|l|} \hline X & A & 2 A & 3 A & 4 A & 5 A & 6 A \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$

where $A$ is a positive integer, has a variance of $160 .$ Determine the value of $A$.

The mean of two samples of size $200$ and $300$ were found to be $25, 10$ respectively their $S.D.$ is $3$ and $4$ respectively then variance of combined sample of size $500$ is :-

Similar Questions

If the mean and variance of the following data: $6,10,7,13, a, 12, b, 12$ are 9 and $\frac{37}{4}$ respectively, then $(a-b)^{2}$ is equal to:

Let $\mathrm{X}$ be a random variable with distribution. $\mathrm{x}$ $-2$ $-1$ $3$ $4$ $6$ $\mathrm{P}(\mathrm{X}=\mathrm{x})$ $\frac{1}{5}$ $\mathrm{a}$ $\frac{1}{3}$ $\frac{1}{5}$ $\mathrm{~b}$ If the mean of $X$ is $2.3$ and variance of $X$ is $\sigma^{2}$, then $100 \sigma^{2}$ is equal to :

Find the mean and variance for the following frequency distribution. Classes $0-30$ $30-60$ $60-90$ $90-120$ $120-150$ $50-180$ $180-210$ $f_i$ $2$ $3$ $5$ $10$ $3$ $5$ $2$

The mean and variance of $7$ observations are $8$ and $16,$ respectively. If five observations are $2, 4, 10,12,14,$ then the absolute difference of the remaining two observations is

The frequency distribution: $\begin{array}{|l|l|l|l|l|l|l|} \hline X & A & 2 A & 3 A & 4 A & 5 A & 6 A \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$ where $A$ is a positive integer, has a variance of $160 .$ Determine the value of $A$.

If the mean and variance of the following data:

$6,10,7,13, a, 12, b, 12$ are 9 and $\frac{37}{4}$ respectively, then $(a-b)^{2}$ is equal to:

Find the mean and variance for the following frequency distribution.

Classes $0-30$ $30-60$ $60-90$ $90-120$ $120-150$ $50-180$ $180-210$

$f_i$ $2$ $3$ $5$ $10$ $3$ $5$ $2$

The frequency distribution:

$\begin{array}{|l|l|l|l|l|l|l|} \hline X & A & 2 A & 3 A & 4 A & 5 A & 6 A \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$

where $A$ is a positive integer, has a variance of $160 .$ Determine the value of $A$.