Given: The table of mean points and Inter Quartile Range in every game by 4 players, Ethan, Adam, Ben and Joaquin.
To Find: The most consistent player.
Solution: Joaquin is the most consistent player since he has the lowest Inter Quartile Range.
Explanation:
Firstly, to measure consistency, note that the performance in every game over the entire season must be roughly stable. In other words, a consistent player would not score many points in one game and very few points in another. Instead, he would score approximately similar points in most of the games.
The Mean is simply a measure of the average points that each player scores. So if one player scores very well in one game and very poorly in the next, the mean would simply be the average of the two games. It does not tell us anything about the consistency.
On the other hand, the Inter Quartile Range or IQR is a measure of variability which signifies how far apart the data points are or how close together they are. To find this, the data set is arranged from lowest to highest and then divided in parts called "quartiles". The middle value is taken of each of these parts/quartiles and the difference in these middle values is known as the IQR.
This gives us a much better idea of the how far apart the data points are "spread out" from one another. Thus, the Inter Quartile Range will be high if the points scored in every game is very spread out (i.e. inconsistent) and it will be low if the points scored in every game is roughly the same (i.e., consistent).
Thus, the player with the lowest IQR will be the most consistent player. Looking at the table, we see Joaquin is the correct answer as his IQR is the lowest.