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.

male artists with the most platinum albums

artist	platinum albums
artist 2	110
artist 3	86
artist 4	75
artist 5	66

female artists with the most platinum albums

artist	platinum albums
artist 2	60
artist 3	56
artist 4	52
artist 5	48

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.

b. verify your conjecture from part (a) by calculating the mean number of platinum albums for each data set.

mean (male artists) =
mean (female artists) =
(round to two decimal places as needed.)

Explanation:

Step1: Calculate the sum of male artists' platinum albums

The number of platinum albums for male artists are \(145\), \(110\), \(86\), \(75\), \(66\).
The sum \(S_{m}=145 + 110+86 + 75+66\)

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Step2: Calculate the mean of male artists' platinum albums

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 5\) (the number of male artists).
\(\bar{x}_{m}=\frac{482}{5}=96.4\)

Step3: Calculate the sum of female artists' platinum albums

The number of platinum albums for female artists are \(64\), \(60\), \(56\), \(52\), \(48\).
The sum \(S_{f}=64 + 60+56 + 52+48\)

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Step4: Calculate the mean of female artists' platinum albums

Using the mean formula \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), with \(n = 5\) (the number of female artists)
\(\bar{x}_{f}=\frac{280}{5}=56\)

Answer:

Mean (Male artists) \(=96.40\)
Mean (Female artists) \(=56.00\)