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?

22	66	1414	44	55	88	44
1919	1515	99	11	99	1717	77

The range of the sample data is

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​(Round to one decimal place as​ needed.)

The standard deviation of the sample data is

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​(Round to one decimal place as​ needed.)

The variance of the sample data is

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​(Round to one decimal place as​ needed.)

What important feature of the data is not revealed through the different measures of​ variation?

A.

The measures of variation do not reveal the difference between the largest number of hurricanes and the smallest number of hurricanes in the data.

B.

The measures of variation reveal nothing about how the numbers of hurricanes are spread.

C.

The measures of variation reveal nothing about the pattern over time.

D.

The measures of variation reveal no information about the scale of the data.

Answer 1

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

11   14   15   17   19   22   44   44   55   66   77   88   99   99   

The lowest value is 11.

The highest value is 99.

The range = 99 - 11 = 88.

s² = Sample Variance = Σ(x_i - x̄)²/(n - 1) = 14139.714=/13 = 1087.67

s = Sample Standard Deviation = √ Sample Variance = √1087.67 = 32.979

The correct option is C

The measures of variation reveal nothing about the pattern over time.