Question

The second moment about arithmetic mean is 16, the standard deviation will be?​

Answer 1

Answer: 4

Step-by-step explanation:

Answer 2

SOLUTION

GIVEN

The second moment about arithmetic mean is 16

TO DETERMINE

The standard deviation

EVALUATION

Let arithmetic mean

$\sf{ = \bar{x}}$

Now

Second moment about arithmetic mean

$\displaystyle\sf{ = \sum \: \frac{ {( x_i - \bar{x} )}^{2} }{n} }$

Now it is given that thr second moment about arithmetic mean is 16

So by the given condition

$\displaystyle\sf{ \sum \: \frac{ {( x_i - \bar{x} )}^{2} }{n} = 16}$

Hence the required standard deviation

$\displaystyle\sf{ = \sqrt{\sum \: \frac{ {( x_i - \bar{x} )}^{2} }{n} }}$

$\displaystyle\sf{ = \sqrt{16}}$

$= 4$

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