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

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

Let $r$ be the range and ${S^2} = \frac{1}{{n - 1}}\sum\limits_{i = 1}^n {{{({x_i} - \bar x)}^2}} $ be the $S.D.$ of a set of observations ${x_1},\,{x_2},\,.....{x_n}$, then

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking, it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

If it is replaced by $12$

Find the mean and variance for the first $10$ multiples of $3$

The mean and $S.D.$ of the marks of $200$ candidates were found to be $40$ and $15$ respectively. Later, it was discovered that a score of $40$ was wrongly read as $50$. The correct mean and $S.D.$ respectively are...