Question

If the standard deviation of a data set was originally 5, and if each value in the data set was multiplied by 3.6, what would be the standard deviation of the resulting data?

Answer 1

You would take 5 and multiply it by 3.6 which gives you 18. I believe that is how you would do that problem. Hope it helped.

Answer 2

New Standard Deviation = 18

Explanation:

`\text{Standard Deviation for sample is given by : }s=\sqrt{(\sum_(i=1) ^(n) (x_i-\bar x))/(n-1)`

When each value is multiplied by 3.6 then there would be no effect on n as the number of terms will be same.

But the mean will be effected.

`\implies \bar{x}=(\sum_(i=1)^(n) x_i)/(n)\\\\\implies \text{New mean = }\frac {\sum_(i=1) ^(n) 3.6* x_i}{n}\\\\\text{Also, each term }x_i\text{ is multiplied by 3.6}\\\\\implies\text{New terms = }3.6* x_i`

So, the New standard deviation now becomes :

`s'=\sqrt{(\sum_(i=1) ^(n) (3.6* x_i-3.6* \bar x))/(n-1)}\\\\\implies s'= 3.6* \sqrt{(\sum_(i=1) ^(n) (x_i-\bar x))/(n-1)}\\\\\implies s'=3.6* s\\\\ \implies s'=3.6* 5\\\\\implies\textbf{New Standard Deviation = }\bf 18`