Question

the data sets give the number of platinum albums for the five male artists and the five female artists in a country with the most platinum albums through a recent year. (platinum albums sell one million units or more.) complete parts (a) through (d) below. d. male artists have the greater mean number of platinum albums because all of the data items for the men are greater than the greatest data item for the women. b. verify your conjecture from part (a) by calculating the mean number of platinum albums for each data set. mean (male artists) = 96.40 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. a. female artists have the greater standard deviation because there is a lower spread in the data for women. b. female artists have the greater standard deviation because there is a greater spread in the data for women. c. male artists have the greater standard deviation because there is a greater spread in the data for men. d. male artists have the greater standard deviation because there is a lower spread in the data for men.

Explanation:

Step1: Recall the concept of standard deviation

Standard deviation measures the spread of data. A greater spread means a greater standard deviation.

Step2: Analyze the spread of data for male and female artists

Looking at the data for male artists: \(145, 110, 86, 75, 66\). The values range from \(66\) to \(145\).
For female artists: \(64, 60, 56, 52, 48\). The values range from \(48\) to \(64\).
The range of male - artist data (\(145 - 66=79\)) is much larger than the range of female - artist data (\(64 - 48 = 16\)). A larger range (in general, when considering spread) implies a greater spread in the data.

Answer:

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