Measures of spread

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May the best person win

How can people be divided into groups fairly for events in the Paralympics, for school sports days, or for subject sets?
problem
Maximum scattering

Age

16 to 18

Challenge level

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?
problem
How would you score it?

Age

11 to 14

Challenge level

Invent a scoring system for a 'guess the weight' competition.
problem
About average

Age

11 to 14

Challenge level

Can you find sets of numbers which satisfy each of our mean, median, mode and range conditions?
problem
Half a minute

Age

11 to 14

Challenge level

Anna, Ben and Charlie have been estimating 30 seconds. Who is the best?
problem
David and Goliath

Age

14 to 18

Challenge level

Does weight confer an advantage to shot putters?
problem
Spread

Age

16 to 18

Challenge level

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