Answer:
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.
Step-by-step 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.
