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. a. without calculating, which data set has the greater mean number of platinum albums? explain your answer. a. male artists have the greater mean number of platinum albums because all of the data items for the men are less than the greatest data item for the women. b. female artists have the greater mean number of platinum albums because all of the data items for the women are greater than the greatest data item for the men. c. female artists have the greater mean number of platinum albums because all of the data items for the women are less than the greatest data item for the men. 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.

Explanation:

The mean is the average of a data set. If all data items in one set are greater than all data items in another set, then the first set will have a greater mean. Looking at the data:

• The male artists' platinum album counts are \(145\), \(110\), \(80\), \(75\), \(66\).
• The female artists' platinum album counts are \(64\), \(60\), \(56\), \(52\), \(48\).

We can see that each value for male artists (\(145>64\), \(110 > 60\), \(80>56\), \(75>52\), \(66>48\)) is greater than the corresponding (and all) values for female artists.

Answer:

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.