Question

Find the standard deviation of the following data set. Round to the nearest hundredth.(7.8, -3.9, 7.8, -3.5, 1.7)

Answer 1

5.75

Explanation:

Given the data set below:

`7.8,-3.9,7.8,-3.5,1.7`

The formula for the standard deviation of a sample is given as:

`s=\sqrt{\sum((x_i-\mu)^2)/(N-1)}`

First, find the mean of the data set.

`\begin{gathered} Mean=(7.8+(-3.9)+7.8+(-3.5)+1.7)/(5) \\ =(9.9)/(5) \\ =1.98 \end{gathered}`

Next, the deviation and squares are calculated below:

Therefore:

`\begin{gathered} s=\sqrt{\sum((x_i-\mu)^2)/(N-1)}=\sqrt{(132.428)/(5-1)} \\ =\sqrt{(132.428)/(4)} \\ s\approx5.75 \end{gathered}`

The standard deviation of the data set is 5.75 (rounded to the nearest hundredth).