9. ERA Champions In 2014, Clayton Kershaw of the Los Angeles Dodgers had the low
ID: 3195979 • Letter: 9
Question
9. ERA Champions In 2014, Clayton Kershaw of the Los Angeles Dodgers had the lowest earned-run average (ERA is the mean number of runs yielded per nine innings pitched) of any starting pitcher in the National League, with an ERA of 1.77. Also in 2014, Felix Hernandez of the Seattle Mariners had the lowest ERA of any starting pitcher in the American League with an ERA of 2.14. In the National League, the mean ERA in 2014 was 3.430 and the standard deviation was 0.721. In the American League, the mean ERA in 2014 was 3.598 and the standard deviation was 0.762. Which player had the better year relative to his peers? Why?Explanation / Answer
Variance is the expectation of the squared deviation of a random variable from its mean. Basically the point being, it measures how far are the values of a given dataset are spread out from their average value.
Var(X)= Square of Standard deviation.
Var(national league)=0.5198
Var(American league)=0.5806
Clayton Kershaw had a better year as the variance is lesser than the american league showing that he performed very differently from the rest and that others are having a very similar ERA scores.
On the other hand, Felix Hernandez also played well but variance of data of his year is wide scattered and hence, his performance is very close to the others of his league.
Hence, proved.
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