Question

Standard deviation of a collection of data is $2\sqrt{2}$. If each value in a data set is multipled by $3$, then the standard deviation of the new data is.

• A. $\sqrt{12}$
• B. $4\sqrt{2}$
• C. $6\sqrt{2}$
• D. $9\sqrt{2}$

Answer 1

The correct option is C $6\sqrt{2}$

The standard deviation would also be multiplied by $3$.

Because the mean would also be $3x$ larger, the differences from the mean would be $3x$ larger too.

It is the same idea as if you were looking at your data set through an enlarging lens- everything would be $3x$ bigger, not only the data values, but also the mean, the differences from the mean, but just everything!

$\therefore$ the standard deviation becomes $2\sqrt{2}\times 3=6\sqrt{2}$