Given:
Total doctor = 6
Age of doctor
[tex]32,40,37,50,30,33[/tex]Find-:
The standard deviation of the population
Explanation-:
The formula of standard deviation is
[tex]\sigma_x=\sqrt{\frac{1}{N}\sum^.X^2-(X\~)^2})^2}[/tex]Where,
[tex]\begin{gathered} N=6 \\ \\ X^{\prime}=\frac{1}{N}\sum^.X \end{gathered}[/tex]The value is:
[tex]\begin{gathered} X^{\prime}=\frac{1}{N}\sum^.X \\ \\ X^{\prime}=\frac{1}{6}(32+40+37+50+30+33) \\ \\ X^{\prime}=\frac{1}{6}(222) \\ \\ X^{\prime}=37 \end{gathered}[/tex]So, standard deviation is:
[tex]\sigma_x=\sqrt{\frac{1}{6}(32^2+40^2+37^2+50^2+30^2+33^2)-(37)^2}[/tex]The value is:
[tex]\begin{gathered} \sigma_x=\sqrt{\frac{1}{6}(1024+1600+1369+2500+900+1089)-1369} \\ \\ \sigma_x=\sqrt{\frac{1}{6}(8482)-1369} \\ \\ \sigma_x=\sqrt{1413.667-1369} \\ \\ \sigma_x=\sqrt{44.667} \\ \\ \sigma x=6.68 \end{gathered}[/tex]The standard deviation of the population 6.68
