Question

Find the standard deviation of this sample of numbers. ROUND yOUR ANSWER TO TWO DECIMAL POINT

Answer 1

`10.68`

1) Let's write this dataset in ascending order:

`42,52,58,63,70`

2) Now, let's calculate the standard deviation from the mean of that sample:

`s\left(x\right)=\sqrt{\frac{\sum_(i=1)^n\left(x_i-\bar{x}\right)^2}{n-1}}`

But before that, let's find the mean and the variance:

`\begin{gathered} \\ \bar{x}=(1)/(n)\sum_(i=1)^na_i=(285)/(5)=57 \\ \\ Var\left(X\right)=\sum_(i=1)^n\frac{\left(x_i-\bar{x}\right)^2}{n-1}= \\ \\ (\left(42-57\right)^2+\left(52-57\right)^2+\left(58-57\right)^2+\left(63-57\right)^2+\left(70-57\right)^2)/(5-1) \\ \\ Var\left(X\right)=(456)/(4)=114 \\ \\ \end{gathered}`

3) Finally, we can take the square root of the variance:

`s(x)=\sqrt{\sum_(i=1)^n\frac{\left(x_i-\bar{x}\right)^2}{n-1}}=\sqrt{(114)/(4)}=10.67707\approx10.68`