These two problems from Open Middle turn traditional mean/median/range problems inside out and feel more like puzzles than problems. They encourage multiple approaches and different answers.

• Problem 1: Create a set of five positive integers from 1 to 20 that have the same mean, median, and range.

• Problem 2: Create a statistical data set of at least 10 numbers such that:
  • All of the numbers in the data set are whole numbers.
  • The median is not a whole number.
  • The median is not part of the data set.

The pdf link above links to a student handout with the two puzzles above. The url link above links to more statistics & probability problems from Open Middle.