Question

Hello I'm confused on this question and need help thank you

Answer 1

Given the data:

36, 14, 18, 18, 34

Let's find the standard deviation of the sample distances.

To find the standard deviation, apply the formula:

`S=\sum_{i\mathop{=}1}^n\sqrt{((x_i-x_(avg))^2)/(n-1)}`

Where:

n = 5

Let's first find the average/,mean:

`\begin{gathered} avg=(36+14+18+18+34)/(5) \\ \\ avg=(120)/(5) \\ \\ avg=24 \end{gathered}`

The mean of the sample is 24.

Now, to find the standard deviation, we have:

`\begin{gathered} S=\sqrt{((36-24)^2+(14-24)^2+(18-24)^2+(18-24)^2+(34-24)^2)/(5-1)} \\ \\ S=\sqrt{((12)^2+(-10)^2+(-6)^2+(-6)^2+(10)^2)/(4)} \\ \\ S=\sqrt{(144+100+36+36+100)/(4)} \\ \\ S=\sqrt{(416)/(4)} \\ \\ S=√(104) \\ \\ S=10.20 \end{gathered}`

Therefore, the standard deviation of the given sample distances is 10.20

ANSWER:

10.20