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There is a very hard mathematics competition in which college students in the US and Canada can participate called the William Lowell Putnam Mathematical Competition. It consists of a six-hour long test with twelve problems, graded 0 to 10 on each problem, so the total score could be anything from 0 to 120 . The median score last year on the Putnam exam was 0 (as it often is, actually). What does this tell you about the scores of the students who took it? Be as precise as you can. Can you tell what fraction (percentage) of students had a certain score or scores? Can you figure out what the quartiles must be?

What must be true about a dataset if its range is \(0 ?\) Give the most interesting example of a dataset with range of 0 and the property you just described that you can think of. What must be true about a dataset if its \(I Q R\) is 0 ? Give the most interesting example of a dataset with \(I Q R\) of 0 and the property you just described that you can think of. What must be true about a dataset if its standard deviation is \(0 ?\) Give the most interesting example of a dataset with standard deviation of 0 and the property you just described that you can think of.