The five-number summary consists of the upper and lower extremes, the median, and the upper and lower quartile.

• The upper and lower extremes are the greatest and least numbers that occur in the set.
• The median is the middle term when the data is arranged from least to greatest.
• The upper and lower quartiles are the median of the upper and lower halves of the data, respectively. Note that there are various methods used for determining the upper and lower quartiles of a set of data; refer to your local curriculum for the method that should be used with your students. If there is no recommended method for your district or state, then you can use the following process for identifying the upper and lower quartiles:
  • Arrange the data in order from least to greatest, and identify the median.
  • Identify the middle term of each half of the data on either side of the median. These values are the upper and lower extremes.

Example: Consider the set {1, 3, 4, 5, 6, 7, 9}.

• The lower extreme is 1.
• The lower half is {1, 3, 4}, and the middle term of that half is 3. Therefore, the lower quartile is 3.
• The median is the middle term, 5.
• The upper half is {6, 7, 9}, and the middle term of that half is 7. Therefore, the upper quartile is 7.
• The upper extreme is 9.