Question

In a study of speed​ dating, female subjects were asked to rate the attractiveness of their male​ dates, and a sample of the results is listed below ​(1equalsnot ​attractive; 10equalsextremely ​attractive). Find the​ range, variance, and standard deviation for the given sample data. Can the results be used to describe the variation among attractiveness ratings for the population of adult​ males? 9 6 2 1 2 5 5 1 2 6 8 10 6 6 1 5 1 3 4 4 4 5 10 9 1 6 The range of the sample data is 2 . ​(Round to one decimal place as​ needed.) The standard deviation of the sample data is 2.88 . ​(Round to one decimal place as​ needed.) The variance of the sample data is . ​(Round to one decimal place as​ needed.) Can the results be used to describe the variation among attractiveness ratings for the population of adult​ males? A. It is unlikely that a random sample of adult males can be representative of all adult males.​ Therefore, the results cannot be used to describe the population. B. Since it is likely that the male subjects volunteered to participate in speed​ dating, they may not be representative of all adult males.​ Therefore, the results cannot be used to describe the population. C. The results cannot be used to describe the population because a smaller sample would be needed. D. The results can be used to describe the population because the sample is random. Click to select your answer(s).

Answer 1

Solution:

9, 6, 2, 1, 2, 5, 5, 1, 2, 6, 8, 10, 6, 6, 1, 5, 1, 3, 4, 4, 4, 5, 10, 9, 1, 6

The range is the difference between the largest and smallest values in a set of values.
This implies that
Range = 10-1
Range = 9
-------------------------------------------------------------------------------------------------
variance = ∑(xi − x̅)^2/n-1
= 207.5385/26−1
≈ 8.3015
--------------------------------------------------------------------------------------------------
Standard deviation = sqrt(variance)
= sqrt(8.3015)
= 2.8812
----------------------------------------------------------------------------------------------
B. Since it is likely that the male subjects volunteered to participate in speed​ dating, they may not be representative of all adult males.​