A basketball player recorded her points for 11 consecutive games. Her points are listed below.13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?

First sort the 11 scores: 13, 15, 17, 18, 20, 20, 21, 22, 24, 25, 27. The original lower and upper quartiles are 17 and 24, so the interquartile range is 7; decreasing it by 1 means the new IQR must be 6. If she scores 23, the sorted list has 12 values, with Q1 = (17 + 18) ÷ 2 = 17.5 and Q3 = (23 + 24) ÷ 2 = 23.5, giving an IQR of 6. So she would need to score 23 points.

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