The standard deviation of n observations a_{1 | vedclass

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

Question

(C) Let the observations be $x_{i} = a_{i}$ for $i = 1, 2, \ldots, n$. The standard deviation $\sigma$ is given by $\sigma = \sqrt{\frac{1}{n} \sum_{i

Vedclass · Accepted Answer

$|\lambda| \sigma$

Vedclass · Answer

(C) Let the observations be $x_{i} = a_{i}$ for $i = 1, 2, \ldots, n$. The standard deviation $\sigma$ is given by $\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_{i} - \bar{x})^2}$.Let the new observations be $y_{i} = \lambda a_{i} = \lambda x_{i}$.The mean of the new observations is $\bar{y} = \frac{1}{n} \sum_{i=1}^{n} \lambda x_{i} = \lambda \left( \frac{1}{n} \sum_{i=1}^{n} x_{i} \right) = \lambda \bar{x}$.The standard deviation of the new observations $\sigma_{y}$ is:$\sigma_{y} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_{i} - \bar{y})^2}$$= \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\lambda x_{i} - \lambda \bar{x})^2}$$= \sqrt{\frac{1}{n} \sum_{i=1}^{n} \lambda^2 (x_{i} - \bar{x})^2}$$= \sqrt{\lambda^2 \cdot \frac{1}{n} \sum_{i=1}^{n} (x_{i} - \bar{x})^2}$$= \sqrt{\lambda^2} \cdot \sigma$$= |\lambda| \sigma$.

\text{Parameter}	\text{Plant } $A$ \text{ and } $B$ \text{ Data}
\text{No. of workers}	$A: 500, B: 6000$
\text{Average monthly wages}	$A: Rs. 2500, B: Rs. 2500$
\text{Variance of distribution of wages}	$A: 81, B: 100$

$x_i$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

The standard deviation of $n$ observations $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ is $\sigma$. Then, the standard deviation of the observations $\lambda a_{1}, \lambda a_{2}, \ldots, \lambda a_{n}$ is

Similar Questions

For a set of $50$ observations,the sum of their squares is $3050$ and their arithmetic mean is $6$. Find the standard deviation of these observations.

The $S.D.$ of $5$ scores $1, 2, 3, 4, 5$ is

If the standard deviation of data is $12$ and mean is $72$,then the coefficient of variation is: (in $\%$)

Find the variance and standard deviation for the following data:

$x_i$ $4$ $8$ $11$ $17$ $20$ $24$ $32$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

Vedclass Test Series

Exam Paper Generator

Online Exam Module