Carson bowled 6 games in a bowling tournament. The box-and-whiskers plot below represents his 6 scores.
CARSON'S SCORES
+++
120 160 200
+
280
240
According to the rules of the tournament, his final score is based on the following.
• Drop the least and the greatest of the scores.
• Find the mean of the 4 remaining scores.
Both the mean and the median of Carson's scores are the same before and after the least and the greatest of the scores are dropped.
Which of these can be concluded? Choose all that are correct.
□ If the scores are listed in order, the two middle scores must be within 10 points of one another.
□ If the scores are listed in order, the two middle scores must be within 40 points of one another.
The mean of the 6 scores is approximately the same as the median of the 6 scores.
The mean of the 6 scores must be greater than the median of the 6 scores.
The variance for the set of 4 scores is approximately the same as the variance for the set of 6 scores.
The variance for the set of 4 scores must be greater than the variance for the set of 6 scores.