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?

8 9 8 7 9 15 5 6 8 4 12 7 8 2

Answer 1

Range = 13

Variance = 10.22

Standard deviation = 3.20

Since this data is time-series therefore, the measures of variation do not reveal anything about the pattern of hurricanes over time.

Explanation:

We are given the number of hurricanes that occurred in each year in a certain region.

8 9 8 7 9 15 5 6 8 4 12 7 8 2

Range:

The range of the data set is found by

Range = Maximum value - minimum value

The maximum value in the data set is 15

The minimum value in the data set is 2

Range = 15 - 2

Range = 13

Variance:

To find the variance, first compute the mean of the data set.

Mean = Sum/n

Mean = (8+9+8+7+9+15+5+6+8+4+12+7+8+2)/14

Mean = 108/14

Mean = 7.714

The variance is given by

σ² = (x - mean)²/(n - 1)

σ² = (8 - 7.714)² + (9 - 7.714)²+ (8 - 7.714)² + (7 - 7.714)² + (9 - 7.714)² + (15 - 7.714)² + (5 - 7.714)² + (6 - 7.714)² + (8 - 7.714)² + (4 - 7.714)² + (12 - 7.714)² + (7 - 7.714)² + (8 - 7.714)² + (2 - 7.714)²/(14 - 1)

σ² = 10.22

Standard deviation:

The standard deviation of the data set is given by

σ² = √σ

σ² = √10.22

σ² = 3.20

Since this data is time-series therefore, the measures of variation do not reveal anything about the pattern of hurricanes over time.