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Problem 527

Geometry Difficulty 2.5 Multiple choice CEMC Gauss (Grade 8) · Canada · 2014

In the diagram, $ABCD$ is a rectangle.

If the area of triangle $ABP$ is 40, then the area of the shaded region is

Pick one

Official solution

Reading from the graph, Riley-Ann scored 8 points in Game 1, 7 points in Game 2, 20 points in Game 3, 7 points in Game 4, and 18 points in Game 5.

Therefore the mean number of points that she scored per game is $\frac{8+7+20+7+18}{5}=\frac{60}{5}=12$ .

Since the ordered list (smallest to largest) of the number of points scored per game is $7,7,8,18,20$ , then the median is 8, the number in the middle of this ordered list.
The difference between the mean and the median of the number of points that Riley-Ann scored is $12-8=4$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.