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Square Mean

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

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AMGM

Choose any two numbers. Call them a and b. Work out the arithmetic mean and the geometric mean. Which is bigger? Repeat for other pairs of numbers. What do you notice?

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Cubic Rotations

There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

The Mean Problem

Stage: 4 Challenge Level: Challenge Level:1
Students are often familiar with the process of creating a mean value, but do not always see that process in reverse : this problem offers an opportunity to use the fact that the mean value implies the sum.