Answer:
5.75
Explanation:
Given the data set below:
[tex]7.8,-3.9,7.8,-3.5,1.7[/tex]
The formula for the standard deviation of a sample is given as:
[tex]s=\sqrt{\sum\frac{(x_i-\mu)^2}{N-1}}[/tex]
First, find the mean of the data set.
[tex]\begin{gathered} Mean=\frac{7.8+(-3.9)+7.8+(-3.5)+1.7}{5} \\ =\frac{9.9}{5} \\ =1.98 \end{gathered}[/tex]
Next, the deviation and squares are calculated below:
Therefore:
[tex]\begin{gathered} s=\sqrt{\sum\frac{(x_i-\mu)^2}{N-1}}=\sqrt{\frac{132.428}{5-1}} \\ =\sqrt{\frac{132.428}{4}} \\ s\approx5.75 \end{gathered}[/tex]
The standard deviation of the data set is 5.75 (rounded to the nearest hundredth).
