The mean and standard deviation of six observ | vedclass

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

Question

(A) Let the original observations be $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}$ with mean $\bar{x} = 8$ and standard deviation $\sigma = 4.$When each

Vedclass · Accepted Answer

Mean = $24,$ Standard Deviation = $12$

Vedclass · Answer

(A) Let the original observations be $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}$ with mean $\bar{x} = 8$ and standard deviation $\sigma = 4.$When each observation is multiplied by a constant $k = 3,$ the new observations are $y_{i} = 3x_{i}.$The new mean $\bar{y}$ is given by $\bar{y} = k \bar{x} = 3 	imes 8 = 24.$The new standard deviation $\sigma_{y}$ is given by $\sigma_{y} = |k| \sigma = |3| 	imes 4 = 12.$Thus,the new mean is $24$ and the new standard deviation is $12.$

$x_i$	$60$	$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$
$f_i$	$2$	$1$	$12$	$29$	$25$	$12$	$10$	$4$	$5$

The mean and standard deviation of six observations are $8$ and $4,$ respectively. If each observation is multiplied by $3,$ find the new mean and new standard deviation of the resulting observations.

Similar Questions

If $M.D.$ is $12$,the value of $S.D.$ will be

If the variance of $6, 7, 8, 9, 10, 11$ is $\sigma^2$,then the variance of $12, 14, 16, 18, 20, 22$ is

The data is obtained in tabular form as follows:
$x_i$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$
$f_i$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$

Find the standard deviation of the given data. (in $.69$)

If the standard deviation of the numbers $2, 3, 2x$,and $11$ is $3.5$,find the possible values of $x$.

The variance of $50$ observations is $7$. Suppose that each observation in this data is multiplied by $6$ and then $5$ is subtracted from it. Then the variance of that new data is

Vedclass Test Series

Exam Paper Generator

Online Exam Module