Answer to Question #143877 in Statistics and Probability for Vladimyr Lubin

Question

(3.2.9) Listed below are the numbers of hurricanes that occurred in each year in a certain region. The data are listed in order by year. Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results. What important feature of the data is not revealed by any of the measures of​ variation? (include whether its in year, years^2,hurricanes,hurricane^2)
16,1,12,1,20,3,5
18,19,7,18,12,4,20

Answer 1

Solution

Range:

$$Range = Maximum - Minimum$$ $$= 20 -1 = 19 \space hurricanes$$

Variance:

$$var = {\sum {(x-\bar{x})}^2 \over n-1 }$$ $$={715.7143 \over 13} = 55. 0549 \space {hurricanes}^2$$

Standard Deviation:

$$sd = \sqrt{var}$$ $$=\sqrt{55. 0549} = 7.4199 \space hurricanes$$

The measures of variation reveal nothing about the pattern over time