Question 2: (13 marks) The result of a golf game is the number of times the ball

Question

Question 2: (13 marks) The result of a golf game is the number of times the ball was hit to complete an 18-hole course. The following tables summarize the results of 40 games of a golfing couple, Luc and Carole. Number of games Results of Luc 80 81 82 83 84 85 86 13 Total 40 Results of Carole 95 96 97 98 100 101 102 103 104 105 Total Number of games 6 40 Find the (population) standard deviation for each data set. Keep 4 decimals. c) (Advice: Use the computational formula.) d) Using the coefficient of variation, determine which player has the most consistent game.

Explanation / Answer

c)
LUC
mean = sum(Xi*Fi)/sum(Fi)
mean = 3351/40
mean = 83.775

popn sd = sqrt{sum(Xi^2*Fi)/sum(Fi) - mean^2}
=SQRT(280823/40-83.775^2)
1.5246

Carole
mean = sum(Xi*Fi)/sum(Fi)
mean = 4031/40
mean = 100.775

popn sd = sqrt{sum(Xi^2*Fi)/sum(Fi) - mean^2}
=SQRT(406495/40- 100.775^2)
2.6028

d)

CV = SD/Mean * 100%

CV_LUC =1.5246/83.775 1.8199%

CV_Carole =2.6028/100.775 2.5828%

with lower Coefficient of variation, I can say that LUC is consistent

results of Luc # games Xi*Fi Xi^2*Fi 80 1 80 6400 81 2 162 13122 82 5 410 33620 83 8 664 55112 84 9 756 63504 85 13 1105 93925 86 1 86 7396 88 1 88 7744 total 40 3351 280823

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