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

Answer:  

New Standard Deviation = 18

Step-by-step explanation:

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

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.

$\implies \bar{x}=\frac{\sum_{i=1}^{n} x_i}{n}\\\\\implies \text{New mean = }\frac {\sum_{i=1} ^{n} 3.6\times x_i}{n}\\\\\text{Also, each term }x_i\text{ is multiplied by 3.6}\\\\\implies\text{New terms = }3.6\times x_i$

So, the New standard deviation now becomes :

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