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, 2014

Algebra Difficulty 2.5 Junior Find the answer Canada

In which set of scores is the median greater than the mean?

$10,20,40,40,40$
$40,50,60,70,80$
$20,20,20,50,80$
$10,20,30,100,200$
$50,50,50,50,100$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The sum of the three numbers in the first column is $13+14+9=36$ .

The sum of the numbers in each column and in each row in the square is the same and so the sum of the three numbers in the second row is also 36.
That is, $14+x+10=36$ or $x+24=36$ , and so $x=36-24=12$ .

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