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Question

# Steven Gerrard, arguably one of the most consistent and skilled players in the English premier league was given the following monthly ratings by a football website for the past 40 months. Rating688.59710Number of months with the rating2810785 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

0.85

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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=∑FX∑F Mean, ¯X=6(2)+8(8)+(8.5)(10)+9(7)+7(8)+10(5)2+8+10+7+8+5=33040=8.25 The deviations from the mean are tabulated below. XFD=|X−¯X|FD622.254.5880.2528.5100.252.5970.755.25781.25101051.758.75 ∑F=40 ∑FD=33 M.D(¯X)=∑FD∑F=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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