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Question

Steven Gerard, arguably one of the most consistent and skilled player in English premier league was given ratings by a Football website. The ratings are given on monthly basis. The following are the ratings for the past 40 months.

Rating688.59710Numberofmonthswiththerating2810785

Calculate how his rating is deviating from his average performance in terms of mean deviation about mean.


A

0.825

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B

0.75

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C

0.9

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D

1

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Solution

The correct option is A

0.825


Mean = ni=1fixini=1fi
Here, n = 6
=6(2)+8(8)+(8.5)(10)+9(7)+7(8)+10(5)2+8+10+7+8+5=33040=8.25=¯x
Now , mean deviation about mean would be ,

ni=1fi|xi¯x|ni=1fi = 2(2.25)+8(0.25)+10(0.25)+7(0.75)+8(1.25)+5(1.75)40=3340=0.825

Mean deviation about mean for his performance across 40 months about his average performance rating of 8.25 is 0.825 which shows he is quite consistent.


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