Question

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? 13 19 11 4 2 2 14 11 6 7 7 13 19 11 7 7 7 1 The range of the sample data is 18 hurricanes. (Round to one decimal place as needed) 4 The standard deviation of the sample data is 5.3 |huricanes (Round to one decimal place as needed) The variance of the sample data is 27:6 hurricanes (Round to one decimal place as needed)

Answer 1

1. Range of the data = Highest value - lowest value = 19-1 = 18

2. Mean of the data = Sum of data / Number of data = 108/14 =7.71

Mean	7.71
No of hurricane (X)	X-Mean	(X-Mean)^2
4.00	-3.71	13.80
2.00	-5.71	32.65
2.00	-5.71	32.65
14.00	6.29	39.51
11.00	3.29	10.80
6.00	-1.71	2.94
7.00	-0.71	0.51
13.00	5.29	27.94
19.00	11.29	127.37
11.00	3.29	10.80
7.00	-0.71	0.51
7.00	-0.71	0.51
1.00	-6.71	45.08
4.00	-3.71	13.80
Total		358.86
Standard Deviation=	√Sum of (X-Mean)^2/n-1
	√358.86/(14-1)
	5.25
Variance=	Standard Deviation ^ 2
	5.25 x 5.25
	27.6043956

The Measure of Variation reveal nothing about the pattern over time because standard deviation and range shows at how spread out a group of numbers is from the mean and range shows the largest and smallest number of hurricane.