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#### Mean, Median and Mode mini-challenge (MathPickle, 2015)

This puzzle gets students involved in calculating mean, median and mode. As well as teaching these statistical terms, it is also appropriate for an algebra challenge.

Compared to other MathPickle challenges this one has a relatively high entry level. Top students will get into it, but some average students will not know where to begin.  Instead of starting with the challenge above; try experimenting with just two of mean, median and mode.  For example, just use Median < Mode.  The set with the smallest largest number might be {0,1,3,3}, but you might want to ask the class to improve upon something that looks like this: {0,0,1,2,3,4,5,6,7,7,7}. An ugly looking solution like this can be obtained by asking students to contribute elements to the set or say “stop.” Most sets acquired in this way will be horribly poor and that’s where you want to begin.

If you want a super hard challenge, investigate the same challenge with mean, median, mode and standard deviation.

#### Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

##### MP1 Toughen up!

This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

##### MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

##### MP6 Be precise!

This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

##### MP7 Be observant!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.