Question

Find the standard deviation & variance for the given sample data. Round your answer to one more decimalplace than the original data.7, 2, 5, 1

Answer 1

The data is given to be:

`7,2,5,1`

Standard Deviation

The formula used to calculate the standard deviation of a sample data is given to be:

`\sigma={\sqrt{\frac{\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 sample mean is calculated as shown below:

`\mu=(7+2+5+1)/(4)=3.75`

Therefore, we can calculate the standard deviation to be:

`\begin{gathered} \sigma=\sqrt{((7-3.75)^2+(2-3.75)^2+(5-3.75)^2+(1-3.75)^2)/(4-1)} \\ \sigma=2.8 \end{gathered}`

Variance

The variance is the square of the standard deviation. Therefore, we can calculate the variance as follows:

`Variance=2.8^2=7.8`

ANSWERS

`\begin{gathered} Standard\text{ }Deviation=2.8 \\ Variance=7.8 \end{gathered}`