Question

Calculate the standard deviation of the sample data to shown. to decimal places

Answer 1

The formula to calculate the standard deviation is given to be:

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

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:

`\begin{gathered} \mu=\frac{sum\text{ }of\text{ }numbers}{number\text{ }of\text{ }numbers} \\ \therefore \\ \mu=(28.9+17.7+2.6+13.1+3.2+11+15+4)/(8)=(95.5)/(8) \\ \mu=11.9375 \end{gathered}`

Using a calculator, we have the sum of squares to be:

`\sum(x_i-\mu)^2=559.07875`

There are 8 data. Therefore, the standard deviation is calculated to be:

`\begin{gathered} \sigma=\sqrt{(559.07875)/(8-1)} \\ \sigma=8.94 \end{gathered}`

The standard deviation is 8.94.