Question

Find the standard deviation for the following group of data items. Round your answer to the nearest tenth (or one decimal place). 8, 9, 12, 15, 18, 21, 22

Answer 1

we must use the formula

`\sqrt[]{(\sum^N_i(x_i-X)^2)/(N)}`

where N is the total of numbers xi each value and X the average

CALCULATIONS

X

`X=(8+9+12+15+18+21+22)/(7)=15`

Sum of (xi-X)

`\begin{gathered} x1=8-15=-7 \\ x2=9-15=-6 \\ x3=12-15=-3 \\ x4=15-15=0 \\ x5=18-15=3 \\ x6=21-15=6 \\ x7=22-15=7 \end{gathered}`
`x1+x2+x3+x4+x5+x6+x7=0`

STANDARD DEVIATION

`\sqrt[]{(0)/(7)}=0`

THE STANDARD DEVIATION IS 0