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Ethan and three friends kept track of their average points scored in each basketball game over the season. The statistics are shown below. Which player is the most consistent?

\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|}{Basketball Scoring Statistics} \\
\hline Player & Mean Score & Interquartile Range \\
\hline Adam & 10.9 & 1.4 \\
\hline Ben & 16.7 & 1.8 \\
\hline Ethan & 14.2 & 2.2 \\
\hline Joaquin & 12.9 & 0.9 \\
\hline
\end{tabular}

A. Adam, because his mean score is the lowest.
B. Ben, because his mean score is the highest.
C. Ethan, because his interquartile range is the highest.
D. Joaquin, because his interquartile range is the lowest.



Answer :

GinnyAnswer
To determine which player is the most consistent, we need to focus on the interquartile range (IQR) rather than the mean score. The IQR is a measure of statistical dispersion and represents the range within which the middle 50% of scores lie. A lower IQR indicates less variability in the player's scores and thus higher consistency.

Given the interquartile ranges for each player, let's compare them:

- Adam has an interquartile range of 1.4.
- Ben has an interquartile range of 1.8.
- Ethan has an interquartile range of 2.2.
- Joaquin has an interquartile range of 0.9.

Among the four players:
- Adam's IQR is 1.4
- Ben's IQR is 1.8
- Ethan's IQR is 2.2
- Joaquin's IQR is 0.9

The player with the lowest interquartile range is the most consistent:
- Joaquin has the lowest interquartile range of 0.9.

Therefore, Joaquin is the most consistent player because his interquartile range is the lowest.

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