Question

To achieve a Triple Crown in baseball is to lead the league in Home Runs, Runs Batted In and Batting Average in the same season. Since 1900, the players in the table (data courtesy of Major League Baseball) have performed this feat. year player HR RBI BA 2012 Cabrera 44 139 0.330 1967 Yastrzemski 44 121 0.326 1966 Robinson 49 122 0.316 1956 Mantle 52 130 0.353 1947 Williams 32 114 0.343 1942 Williams 36 137 0.356 1934 Gehrig 49 165 0.363 1933 Foxx 48 163 0.356 1909 Cobb 9 115 0.377 1901 Lajoie 14 125 0.422 Table 1: Triple Crown numbers

a. Find the mean of this triple crown population and a real world 10% trimmed mean.

b. Find the variance for this sample.

c. Find the standard deviation for this sample. d. Find the scatterplot and give the Pearson’s r coefficient for HR and RBI, and comment on the strength and nature of the association. Copy and paste excel trendline if you can

Answer 1

ANSWER

(a)

	HR	RBI	BA
mean	37.70	133.10	0.35420

	HR	RBI	BA
trimmed mean	37.7	133.1	0.3542

(b)

	HR	RBI	BA
sample variance	229.57	333.21	0.00091

(c)

	HR	RBI	BA
sample standard deviation	15.15	18.25	0.03012

(d)

The plot is:

r = 0.512

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