The top two players in the 2001-2002 Professional Darts Corporation World Champi

Question

The top two players in the 2001-2002 Professional Darts Corporation World Championship were Phil Taylor and Peter Manley. Taylor and Manley dominated the competition with a record number of doubles. A double is a throw that lands in either the outer ring of the dartboard or the outer ring of the bull's-eye. The following table provides the number of doubles thrown by each of the two players during the five rounds of competition, as found in Chance.

Taylor 21 18 18 19 13
Manley 5 24 20 26 14

a. Obtain the individual population means of the number of doubles.
b. Without doing any calculations, decide for which player the standard deviation of the number of doubles is smaller. Explain your answer.
c. Obtain the individual population standard deviations of the number of doubles.
d. Are your answers to parts (b) and (c) consistent? Why or why not?

Explanation / Answer

The standard deviation for the number of doubles is probably smaller for Taylor. This answer is based on the fact that the range of doubles that Taylor threw is smaller than for Manley. Taylor's range: 21-13 = 8 Manley's range: 26-5 = 21 The number of doubles that Taylor threw is more consistent than Manley. The number of doubles that Taylor threw is grouped together closer than for Manley.

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