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	58
artist 4	52
artist 5	48

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.
d. verify your conjecture from part (c) by calculating the standard deviation for each data set.
standard deviation (male artists)=
standard deviation (female artists)=
(round to two decimal places as needed )

Explanation:

Step1: Calculate the standard deviation for male artists

The formula for the standard deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}\)
For male artists: \(\bar{x}=96.4\), \(n = 5\)
\((145 - 96.4)^{2}=(48.6)^{2}=2361.96\)
\((110 - 96.4)^{2}=(13.6)^{2}=184.96\)
\((86 - 96.4)^{2}=(- 10.4)^{2}=108.16\)
\((75 - 96.4)^{2}=(-21.4)^{2}=457.96\)
\((66 - 96.4)^{2}=(-30.4)^{2}=924.16\)
\(\sum_{i = 1}^{5}(x_{i}-\bar{x})^{2}=2361.96+184.96 + 108.16+457.96+924.16=4037.2\)
\(s_{male}=\sqrt{\frac{4037.2}{5 - 1}}=\sqrt{\frac{4037.2}{4}}=\sqrt{1009.3}\approx31.77\)

Step2: Calculate the standard deviation for female artists

For female artists: \(\bar{x}=56\), \(n = 5\)
\((64 - 56)^{2}=8^{2}=64\)
\((60 - 56)^{2}=4^{2}=16\)
\((58 - 56)^{2}=2^{2}=4\)
\((52 - 56)^{2}=(-4)^{2}=16\)
\((48 - 56)^{2}=(-8)^{2}=64\)
\(\sum_{i = 1}^{5}(x_{i}-\bar{x})^{2}=64 + 16+4+16+64=164\)
\(s_{female}=\sqrt{\frac{164}{5 - 1}}=\sqrt{\frac{164}{4}}=\sqrt{41}\approx6.40\)

Answer:

Standard deviation (Male artists) = \(31.77\)
Standard deviation (Female artists) = \(6.40\)