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.

$\begin{array}{ccccccc}Rating& 6& 8& 8.5& 9& 7& 10\\ Numberofmonthswiththerating& 2& 8& 10& 7& 8& 5\end{array}$

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

• A. 0.825
• B. 0.85
• C. 0.9
• D. 1

Answer 1

The correct option is A

0.825

$Mean=\frac{\sum FX}{\sum F}$

$Mean,\overline{X}=\frac{6\left(2\right)+8\left(8\right)+\left(8.5\right)\left(10\right)+9\left(7\right)+7\left(8\right)+10\left(5\right)}{2+8+10+7+8+5}=\frac{330}{40}=8.25$

The deviations from the mean are tabulated below.

$\begin{array}{cccc}X& F& D=|X-\overline{X}|& FD\\ 6& 2& 2.25& 4.5\\ 8& 8& 0.25& 2\\ 8.5& 10& 0.25& 2.5\\ 9& 7& 0.75& 5.25\\ 7& 8& 1.25& 10\\ 10& 5& 1.75& 8.75\\ & \sum F=40& & \sum FD=33\end{array}$

$M.D\left(\overline{X}\right)=\frac{\sum FD}{\sum F}=\frac{33}{40}=0.825$

$\therefore$ 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.