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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.  


  1. 0.825

  2. 0.85

  3. 0.9

  4. 1


Solution

The correct option is A

0.825


Mean=FXF

 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)=FDF=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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