Given: The data below
[tex]9,10,11,12,13,14,15,16,17,18[/tex]To Determine: The range, population variance and population standard deviation
Solution
The range of a data set is the difference between the largest number and the smallest number in the data set. Therefore
[tex]\begin{gathered} Range=18-9 \\ Range=9 \end{gathered}[/tex]The population variance of a data set can be calculated using the formula below
[tex]\begin{gathered} Variance(s^2)=\frac{1}{n}\Sigma(x-\bar{x})^2 \\ n=Total-number \\ \bar{x}=mean \end{gathered}[/tex][tex]\bar{x}=\frac{9+10+11+...+18}{10}=\frac{135}{10}=13.5[/tex][tex]Variance(s^2)=\frac{(9-13.5)^2+(10-13.5)^2+...+(18-13.5)^2}{10}[/tex][tex]Variance(s^2)=\frac{82.5}{10}=8.25[/tex]The population standard deviation is
[tex]\begin{gathered} Population-standard-devation(s)=\sqrt{Population-variance} \\ s=\sqrt{8.25} \\ s=2.872 \\ s\approx2.9 \end{gathered}[/tex]Hence:
Range = 9
Population variance = 8.25
Population standard deviation = 2.9