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?
15 18 18 1 20 14 3
6 7 6 2 7 6 17
the range of the sample data is 19.0 hurricanes.
(round to one decimal place as needed.)
the standard deviation of the sample data is 6.7 hurricanes.
(round to one decimal place as needed.)
the variance of the sample data is 44.5 hurricanes²
(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 no information about the scale of the data.
c. the measures of variation reveal nothing about the pattern over time.
d. the measures of variation reveal nothing about how the numbers of hurricanes are spread

Explanation:

• Option A: The range is a measure of variation that specifically shows the difference between the largest and smallest values. So this option is incorrect.
• Option B: The measures of variation (range, variance, standard deviation) do give some indication about the scale of the data (e.g., range gives an idea of the spread from the smallest to the largest value). So this option is incorrect.
• Option C: Range, variance, and standard deviation are all measures that describe the spread of the data values. They do not take into account the order of the data (i.e., the time - order of the years). So they do not reveal the pattern over time.
• Option D: Variance and standard deviation are measures that specifically describe how the data values are spread out from the mean. So this option is incorrect.

Answer:

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