Question

The following are distances (in miles) traveled to the workplace by 6 employees of a certain university.13, 7, 34, 25, 14, 27Send data to calculatorFind the standard deviation of this sample of distances. Round your answer to two decimal places i need help with this math problem.

Answer 1

The standard derivation of the sample (s) is:

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

Where:

s = standard derivation of sample

n = number of data provided

xi = each of the values of the sample

x = the mean of xi

So, first, let's find the mean.

Given:

n = 6

The mean is:

`\begin{gathered} x=\frac{\sum_{i\mathop{=}1}^nx_i}{n} \\ x=(13+7+34+25+14+27)/(6) \\ x=(120)/(6) \\ x=20 \end{gathered}`

And the standard derivation:

`\begin{gathered} s=\sqrt{((13-20)^2+(7-20)^2+(34-20)^2+(25-20)^2+(14-20)^2+(27-20)^2)/(6-1)} \\ s=\sqrt{((-7)^2+(-13)^2+(14)^2+(5)^2+(6)^2+(7)^2)/(5)} \\ s=\sqrt{(524)/(5)} \\ s=10.24 \end{gathered}`

Answer: 10.24.