Respuesta :
The given data are
2, 9, 8, 7, 9, 7
To find the standard deviation we will find the mean at first
[tex]Mean=\frac{sum}{no.}[/tex]The sum = 2 + 9 + 8 + 7 + 9 + 7 = 42
The no. = 6, then
[tex]\begin{gathered} Mean=\frac{42}{6} \\ \\ Mean=7 \end{gathered}[/tex]Then we will square the difference between each number and the mean
[tex]\begin{gathered} (2-7)^2=25 \\ (9-7)^2=4 \\ (8-7)^2=1 \\ (7-7)^2=0 \\ (9-7)^2=4 \\ (7-7)^2=0 \end{gathered}[/tex]Add all the answers
[tex]\sum_^(x-M)^2=25+4+1+0+4+0=34[/tex]Divide it by the no. and find the square root
[tex]\begin{gathered} \sigma=\sqrt{\frac{\sum_^(x-M)^2}{N}} \\ \\ \sigma=\sqrt{\frac{34}{6}} \\ \\ \sigma=2.380476143 \end{gathered}[/tex]The standard deviation is about 2.38 to the nearest hundredth
