ANSWER:
Average age 10
Standard deviation 4.9
STEP-BY-STEP EXPLANATION:
To calculate average age of the gorillas:
[tex]average=\frac{\sum^n_i}{n}[/tex]Replacing:
[tex]\begin{gathered} average=\frac{8+4+14+16+8}{5} \\ average=\frac{50}{5} \\ average=10 \end{gathered}[/tex]The average age of the gorillas is 10
The formula for standard deviation is:
[tex]s^2=\frac{1}{n-1}\cdot\sum ^n_i(x_i-\bar{x})^2[/tex]Replacing:
[tex]\begin{gathered} s^2=\frac{1}{5-1}\cdot\mleft\lbrace(8-10)^2+(4-10)^2+(14-10)^2+(16-10)^2+(8-10)^2\mright\rbrace^{} \\ s^2=\frac{1}{4}\cdot(4+36+16+36+4) \\ s^2=\frac{96}{4} \\ s=\sqrt[]{24} \\ s=4.9 \end{gathered}[/tex]The standard deviation of gorillas is 4.9
