Question

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largestnumber of decimal places given in the data.9, 10, 11, 12, 13, 14, 15, 16, 17, 18Copy DataAnswerHow to enter your answer (opens in new window)Range:Population Variance:Population Standard Deviation:KeypacKeyboard ShortcuTables

Answer 1

Given: The data below

`9,10,11,12,13,14,15,16,17,18`

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

`\begin{gathered} Range=18-9 \\ Range=9 \end{gathered}`

The population variance of a data set can be calculated using the formula below

`\begin{gathered} Variance(s^2)=(1)/(n)\Sigma(x-\bar{x})^2 \\ n=Total-number \\ \bar{x}=mean \end{gathered}`
`\bar{x}=(9+10+11+...+18)/(10)=(135)/(10)=13.5`
`Variance(s^2)=((9-13.5)^2+(10-13.5)^2+...+(18-13.5)^2)/(10)`
`Variance(s^2)=(82.5)/(10)=8.25`

The population standard deviation is

`\begin{gathered} Population-standard-devation(s)=√(Population-variance) \\ s=√(8.25) \\ s=2.872 \\ s\approx2.9 \end{gathered}`

Hence:

Range = 9

Population variance = 8.25

Population standard deviation = 2.9