Answer to Question #319875 in Statistics and Probability for Sohan

Question

Calculate the standard deviation and CV for the age distribution presented below:

Age: 09.5-12.5 12.5-15.5 15.5-18.5 18.5-21.5 21.5-24.5 24.5-27.5 27.5-30.5

Frequency: 3 14 23 12 8 4 1

Explain your results

Answer 1

Class Class midpoint (x) Frequency(F) F$\cdot x$ F$\cdot(x-\mu)^2$

09.5 -12.5 11 3 33 151.57

12.5- 15.5 14 14 196 236.26

15.5-18.5 17 23 391 28.24

18.5-21.5 20 12 240 42.96

21.5-24.5 23 8 184 191.45

24.5-27.5 26 4 104 249.13

27.5-30.5 29 1 29 118.64

Total 65 1177 1018.25

$mean =\frac{\sum f\cdot x}{\sum f}$

mean =$\frac{1177}{65}$ =18.108

standard deviation= $\sqrt{\frac{\sum f\cdot( x-\mu)}{\sum f-1}}$

standard deviation =$\sqrt{\frac{1018.25}{64}}$

standard deviation =1.997

CV=$\frac{s}{mean }$ $\cdot 100$

CV=$\frac{1.997}{18.108}$ $\cdot 100$

CV=11.03%

Since the coefficient of variation is low the the level of dispersion around the mean is low.