If each observation of a raw data whose variance is σ2 ismultiplied by h, then the variance of the new set is

A
$σ^{2}$
B
$h^{2} σ^{2}$
C
$h σ^{2}$
D
$h + σ^{2}$

Solution:

Let $x_{1}, x_{2}, \dots, x_{n}$ be a raw data. Then,

$σ^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{X})}^{2}$ ,

If each value is multiplied by $h$ , then the values are

$h x_{1}, h x_{2}, \dots, h x_{n}$ .The AM of the new values is

$\frac{h x_{1} + h x_{2} + \dots + h x_{n}}{n} = h \bar{X} .$

The variance $σ^{2}$ of the new set of values is given by

$σ_{1}^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(h x_{i} - h \bar{X})}^{2} = h^{2} \{\frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{X})}^{2}\} = h^{2} σ^{2}$ .

If each observation of a raw data whose variance is $σ^{2}$ is
multiplied by $h,$ then the variance of the new set is

Solution:

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