Question

verify your conjecture from part (a) by calculating the mean number of platinum albums for each data set
mean (male artists) = 96.80
mean (female artists) = 56.00
(round to two decimal places as needed.)
c. without calculating, which data set has the greater standard deviation? explain your answer.
o a. male artists have the greater standard deviation because there is a greater spread in the data for men.
o b. male artists have the greater standard deviation because there is a lower spread in the data for men.
o c. female artists have the greater standard deviation because there is a lower spread in the data for women.
o d. female artists have the greater standard deviation because there is a greater spread in the data for women.

Explanation:

To determine which data set (male or female artists) has a greater standard deviation, we use the concept that a greater spread in data values leads to a greater standard deviation. The mean for male artists (96.80) is higher than that for female artists (56.00). If the data for male artists has a greater spread (more variation from the mean), their standard deviation would be greater. Option A states male artists have a greater standard deviation because of a greater spread in their data, which aligns with the relationship between data spread and standard deviation. Options B and C incorrectly link lower spread to greater standard deviation, and Option D incorrectly attributes greater spread to female artists.

Answer:

A. Male artists have the greater standard deviation because there is a greater spread in the data for men.