# What is the standard deviation of {11, 23, 3, 1, 500, 27, 18, 14, 2}?

Dec 4, 2015

$\sigma = \sqrt{\frac{251 , 913}{9} - 27990.3 \dot{3}} \approx 0.1826$ to 4dp

#### Explanation:

The 500 is spurious data (Does not look like it is meant to be part of the data set). This will drastically effect the mean value. The standard deviation equations (There is a set of them) are derived from $s = \frac{1}{n - 1} {\sum}_{i = 1 \to n} {\left({x}_{i} - \overline{x}\right)}^{2}$ (the varience) where n is the count of the whole sample. In your case $n = 9$ and

$\overline{x} = \frac{11 + 23 + 3 + 1 + \textcolor{b l u e}{500} + 27 + 18 + 14 + 2}{9} \approx 66.56$ to 2 decimal places (2 dp).

Sometimes $\mu$ is used instead of $\overline{x}$

They will be expecting you to include the 500. By the way, if you are testing the whole population you use $\frac{1}{n}$ and not $\frac{1}{n - 1}$

Using sigma = sqrt(s)=sqrt((sum(x_i^2))/9 -(barx)^2

$\sigma = \sqrt{\frac{251 , 913}{9} - 27990.3 \dot{3}} \approx 0.1826$ to 4dp