Let the mean and the variance of 20 observati | vedclass

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

Question

(D) Given that the mean $\bar{x} = 15$ and variance $\sigma^{2} = 9$ for $n = 20$ observations.$\sum x_{i} = 15 	imes 20 = 300$$\sigma^{2} = \frac{\s

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Given that the mean $\bar{x} = 15$ and variance $\sigma^{2} = 9$ for $n = 20$ observations.$\sum x_{i} = 15 	imes 20 = 300$$\sigma^{2} = \frac{\sum x_{i}^{2}}{n} - (\bar{x})^{2} \Rightarrow 9 = \frac{\sum x_{i}^{2}}{20} - 225$$\frac{\sum x_{i}^{2}}{20} = 234 \Rightarrow \sum x_{i}^{2} = 4680$Now,the mean of $(x_{i} + \alpha)^{2}$ is $178$:$\frac{1}{20} \sum (x_{i} + \alpha)^{2} = 178$$\sum (x_{i}^{2} + 2\alpha x_{i} + \alpha^{2}) = 178 	imes 20 = 3560$$\sum x_{i}^{2} + 2\alpha \sum x_{i} + 20\alpha^{2} = 3560$$4680 + 2\alpha(300) + 20\alpha^{2} = 3560$$20\alpha^{2} + 600\alpha + 1120 = 0$Dividing by $20$:$\alpha^{2} + 30\alpha + 56 = 0$$(\alpha + 28)(\alpha + 2) = 0$So,$\alpha = -28$ or $\alpha = -2$.The maximum value of $\alpha$ is $-2$.The square of the maximum value is $(-2)^{2} = 4$.

Class	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Frequency	$2$	$k$	$28$	$54$	$k + 1$	$5$

$x_i$	$1$	$2$	$3$	$4$	$5$
$f_i$	$5$	$4$	$f$	$2$	$3$

Let the mean and the variance of $20$ observations $x_{1}, x_{2}, \ldots, x_{20}$ be $15$ and $9$,respectively. For $\alpha \in R$,if the mean of $(x_{1}+\alpha)^{2}, (x_{2}+\alpha)^{2}, \ldots, (x_{20}+\alpha)^{2}$ is $178$,then the square of the maximum value of $\alpha$ is equal to $...........$

Similar Questions

Let the mean and variance of $8$ numbers $-10, -7, -1, x, y, 9, 2, 16$ be $\frac{7}{2}$ and $\frac{293}{4}$ respectively. Then the mean of $4$ numbers $x, y, x + y + 1, |x - y|$ is:

If the mean of the data:
Class $5 - 10$ $10 - 15$ $15 - 20$ $20 - 25$ $25 - 30$ $30 - 35$
Frequency $2$ $k$ $28$ $54$ $k + 1$ $5$

is $21$, then $k$ is one of the roots of the equation:

If both mean and variance of $50$ observations $x_1, x_2, \ldots, x_{50}$ are equal to $16$ and $256$ respectively,then the mean of $(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2$ is

If the mean of the following frequency distribution is $2.6$,find the value of $f$.

$x_i$ $1$ $2$ $3$ $4$ $5$

$f_i$ $5$ $4$ $f$ $2$ $3$

If $G_1$ and $G_2$ are the geometric means of two series of sizes $n_1$ and $n_2$ respectively,and $G$ is the geometric mean of their combined series,then what is $\log G$ equal to?

Vedclass Test Series

Exam Paper Generator

Online Exam Module