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. R a t i n g 6 8 8.5 9 7 10 N u m b e r o f m o n t h s w i t h t h e r a t i n g 2 8 10 7 8 5 Calculate how his rating is deviating from his average performance in terms of mean deviation about mean. Options: A . &nbsp 0.825 B . &nbsp 0.85 C . &nbsp 0.9 D . &nbsp 1

Answer: Option A : A M e a n = ∑ F X ∑ F M e a n , ¯ X = 6 ( 2 ) + 8 ( 8 ) + ( 8.5 ) ( 10 ) + 9 ( 7 ) + 7 ( 8 ) + 10 ( 5 ) 2 + 8 + 10 + 7 + 8 + 5 = 330 40 = 8.25 The deviations from the mean are tabulated below. X F D = | X − ¯ X | F D 6 2 2.25 4.5 8 8 0.25 2 8.5 10 0.25 2.5 9 7 0.75 5.25 7 8 1.25 10 10 5 1.75 8.75 ∑ F = 40 ∑ F D = 33 M . D ( ¯ X ) = ∑ F D ∑ F = 33 40 = 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.

Steven Gerrard, arguably one of the most consistent and skilled players in the

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.

$\begin{matrix} R a t i n g & 6 & 8 & 8.5 & 9 & 7 & 10 N u m b e r o f m o n t h s w i t h t h e r a t i n g & 2 & 8 & 10 & 7 & 8 & 5 \end{matrix}$

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

Options:

A . 0.825

B . 0.85

C . 0.9

D . 1

Answer: Option A
:
A

$M e a n = \frac{\sum F X}{\sum F}$
$M e a n, ¯ X = \frac{6 (2) + 8 (8) + (8.5) (10) + 9 (7) + 7 (8) + 10 (5)}{2 + 8 + 10 + 7 + 8 + 5} = \frac{330}{40} = 8.25$
The deviations from the mean are tabulated below.
$\begin{matrix} X & F & D = | X - ¯ X | & F D 6 & 2 & 2.25 & 4.5 8 & 8 & 0.25 & 2 8.5 & 10 & 0.25 & 2.5 9 & 7 & 0.75 & 5.25 7 & 8 & 1.25 & 10 10 & 5 & 1.75 & 8.75 \sum F = 40 & \sum F D = 33 \end{matrix}$

$M . D (¯ X) = \frac{\sum F D}{\sum F} = \frac{33}{40} = 0.825$

$∴$ 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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