The mean and variance of a set of 15 numbers | vedclass

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

Question

(D) Let the two sets be $S_1$ and $S_2$ with $n_1 = 15, n_2 = 15$. Given: $\bar{x}_1 = 12, \sigma_1^2 = 14$ and $\bar{x}_2 = 14, \sigma_2^2 = \sigma^2

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(D) Let the two sets be $S_1$ and $S_2$ with $n_1 = 15, n_2 = 15$. Given: $\bar{x}_1 = 12, \sigma_1^2 = 14$ and $\bar{x}_2 = 14, \sigma_2^2 = \sigma^2$. The combined variance $\sigma^2_{comb}$ of $n_1 + n_2$ observations is given by: $\sigma^2_{comb} = \frac{n_1 \sigma_1^2 + n_2 \sigma_2^2}{n_1 + n_2} + \frac{n_1 n_2 (\bar{x}_1 - \bar{x}_2)^2}{(n_1 + n_2)^2}$ Substituting the given values: $13 = \frac{15(14) + 15(\sigma^2)}{15 + 15} + \frac{15 	imes 15 (12 - 14)^2}{(15 + 15)^2}$ $13 = \frac{15(14 + \sigma^2)}{30} + \frac{225(-2)^2}{900}$ $13 = \frac{14 + \sigma^2}{2} + \frac{900}{900}$ $13 = \frac{14 + \sigma^2}{2} + 1$ $12 = \frac{14 + \sigma^2}{2}$ $24 = 14 + \sigma^2$ $\sigma^2 = 10$

$x_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$f_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$

The mean and variance of a set of $15$ numbers are $12$ and $14$ respectively. The mean and variance of another set of $15$ numbers are $14$ and $\sigma^2$ respectively. If the variance of all the $30$ numbers in the two sets is $13$,then $\sigma^2$ is equal to $.........$.

Similar Questions

The raw data $x_1, x_2, \ldots, x_{n}$ is an $A$.$P$. with common difference $d$ and first term $0$. If $\bar{x}$ and $\sigma^2$ are the mean and variance of $x_{i}, i=1, 2, \ldots, n$,then $\sigma^2$ is:

Consider three observations $a, b,$ and $c$ such that $b = a + c$. If the standard deviation of $a + 2, b + 2, c + 2$ is $d$,then which of the following holds true?

The variance of the following data is
$x_{i}$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$f_{i}$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$

If for a distribution,$\Sigma(x-5)=3$ and $\Sigma(x-5)^2=43$ and the total number of observations is $18$,then the variance of the distribution is

Two teams $A$ and $B$ have the same mean and their coefficients of variation are $4$ and $2$,respectively. If $\sigma_A$ and $\sigma_B$ are the standard deviations of teams $A$ and $B$ respectively,then the relation between them is

Vedclass Test Series

Exam Paper Generator

Online Exam Module