The mean and standard deviation of six observ | vedclass

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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 $12.$

Class Interval	Frequency
$0 - 6$	$10$
$6 - 12$	$8$
$12 - 18$	$6$
$18 - 24$	$4$
$24 - 30$	$2$

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.

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