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Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?

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Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
To work out the variance you have to sum the squares of the differences of all the numbers from the mean.

To do this question you could think of the set of numbers as a point in space and use geometrical reasoning to help you to decide which position(s) of the point gives the greatest variance. A 'special' point occurs where all the numbers in the set are equal to the mean. Can you see how the variance for any set of numbers relates to the distance of the corresponding point from the 'special' point?

The constraints that the mean of the numbers is given, and that the numbers are all positive, restrict the points to lie in a certain region.