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
Female Artists with the most platinum albums
Artist
Platinum Albums
Artist
Platinum Albums
Artist 1
142
Artist 1
63
Artist 2
102
Artist 2
61
Artist 3
78
Artist 3
53
Artist 4
75
Artist 4
51
Artist 5
66
Artist 5
45
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Part 1
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 greater than the greatest data item for the women.
Your answer is correct.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 less than the greatest data item for the women.
Part 2
b. Verify your conjecture from part​ (a) by calculating the mean number of platinum albums for each data set.
Mean​ (Male ​artists)equals
  
92.6
Mean​ (Female ​artists)equals
  
54.6
​(Round to two decimal places as​ needed.)
Part 3
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 lower spread in the data for men.
D.
Male artists have the greater standard deviation because there is a greater spread in the data for men.
Explain your answer.Mean (Male artists)Mean (Female artists)Mean (Female artists)(Round to two decimal places as needed.)Explain your answer.
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Answer 1

Here are the answers and explanations for parts (a)–(d).

a) Which data set has the greater mean (without calculating)?
- Answer: A. Male artists have the greater mean because every male data value is larger than every female data value.

b) Verify by calculating the means.
- Mean (Male) = (142 + 102 + 78 + 75 + 66) / 5 = 463 / 5 = 92.60
- Mean (Female) = (63 + 61 + 53 + 51 + 45) / 5 = 273 / 5 = 54.60

c) Which data set has the greater standard deviation (without calculating)? Explain.
- Answer: D. Male artists have the greater standard deviation because their data are spread out much more (range 142 − 66 = 76) than the women’s (range 63 − 45 = 18). Larger spread means larger standard deviation.

d) Compute the standard deviations (rounded to two decimals).
Using the population formula (divide by n):
- SD (Male) ≈ sqrt([ (142−92.6)^2 + (102−92.6)^2 + (78−92.6)^2 + (75−92.6)^2 + (66−92.6)^2 ] / 5) ≈ 27.42
- SD (Female) ≈ sqrt([ (63−54.6)^2 + (61−54.6)^2 + (53−54.6)^2 + (51−54.6)^2 + (45−54.6)^2 ] / 5) ≈ 6.62

(If you instead use the sample formula (divide by n−1), the SDs would be about 30.66 for males and 7.40 for females — the conclusion that males have the larger standard deviation remains the same.)