Respuesta :
Let's begin by listing out the information given to us:
[tex]\mleft\{35,27,31,29,28,32,28\mright\}[/tex]The mean is calculated thus:
[tex]\begin{gathered} \mu=\frac{35+27+31+29+28+32+28}{7}=\frac{210}{7}=30 \\ \mu=30 \end{gathered}[/tex]Subtract the Mean and square the result is given:
[tex]\begin{gathered} (35-30)^2=5^2=25 \\ (27-30)^2=(-3^{})^2=9 \\ (31-30)^2=1^2=1 \\ (29-30)^2=(-1)^2=1 \\ (28-30)^2=(-2)^2=4 \\ (32-30)^2=2^2=4 \\ (28-30)^2=(-2)^2=4 \end{gathered}[/tex]The mean of those squared differences. is given by:
[tex]\begin{gathered} 25+9+1+1+4+4+4=48 \\ \text{divide by (n-1); n = 7}\Rightarrow n-1=7-1=6 \\ variance=\frac{48}{6}=8 \\ variance=8 \\ sd=\sqrt[]{variance}=\sqrt[]{8}=2.828 \\ sd=2.828 \end{gathered}[/tex]