The formula to calculate the standard deviation is given to be:
[tex]\sigma=\sqrt{\frac{\sum(x_i-\mu)^2}{N-1}}[/tex]
where
σ = population standard deviation
N = the size of the population
xi = each value from the population
μ = the population mean
The mean of the data set is calculated as follows:
[tex]\begin{gathered} \mu=\frac{sum\text{ }of\text{ }numbers}{number\text{ }of\text{ }numbers} \\ \therefore \\ \mu=\frac{28.9+17.7+2.6+13.1+3.2+11+15+4}{8}=\frac{95.5}{8} \\ \mu=11.9375 \end{gathered}[/tex]
Using a calculator, we have the sum of squares to be:
[tex]\sum(x_i-\mu)^2=559.07875[/tex]
There are 8 data. Therefore, the standard deviation is calculated to be:
[tex]\begin{gathered} \sigma=\sqrt{\frac{559.07875}{8-1}} \\ \sigma=8.94 \end{gathered}[/tex]
The standard deviation is 8.94.
