Question

The goals scored by the players of two teams in 10 football matches are shown below.
Using variability, find players of which team are more consistent in scoring the goals?

• A. Cannot be determined
• B. Team A
• C. Both are same
• D. Team B

Answer 1

The correct option is D Team B

To find which team is more consistent, we have to find the Mean Absolute Deviation (MAD) for the both teams.

For calculating MAD, the formulae we require are:
$\text{1) Mean =}\frac{\text{Sum of all observations}}{\text{Total number of observations}}$

2) Absolute deviation = |Mean $-$ No. of goals in the respective row|

3) Total absolute deviation = Absolute deviation x Number of players

$\text{4) MAD =}\frac{\text{Total absolute deviation}}{\text{Number of observations}}$


For Team A:
Hence,

$\text{Mean =}\frac{14}{5}=2.8$

Total absolute deviation = 5.2


$\text{Mean absolute deviation (MAD) =}\frac{5.2}{5}=1.04$

For Team B:
Hence,

$\text{Mean =}\frac{13}{5}=2.6$

Total absolute deviation = 4.4

$\text{Mean absolute deviation (MAD) =}\frac{4.4}{5}=0.88$

$\because$ 0.88 < 1.04, players of Team B are more consistent in scoring the goals than that of Team A.