The data is given to be:
[tex]7,2,5,1[/tex]Standard Deviation
The formula used to calculate the standard deviation of a sample data 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 sample mean is calculated as shown below:
[tex]\mu=\frac{7+2+5+1}{4}=3.75[/tex]Therefore, we can calculate the standard deviation to be:
[tex]\begin{gathered} \sigma=\sqrt{\frac{(7-3.75)^2+(2-3.75)^2+(5-3.75)^2+(1-3.75)^2}{4-1}} \\ \sigma=2.8 \end{gathered}[/tex]Variance
The variance is the square of the standard deviation. Therefore, we can calculate the variance as follows:
[tex]Variance=2.8^2=7.8[/tex]ANSWERS
[tex]\begin{gathered} Standard\text{ }Deviation=2.8 \\ Variance=7.8 \end{gathered}[/tex]