Five-Number Summary & Boxplots (College Board AP® Statistics): Revision Note

Five-number summary

What is a five-number summary?

• A five-number summary is the collection of the following five values from a data set:

  1. the minimum data value

  2. the first quartile (Q1)

  3. the median (Q2)

  4. the third quartile (Q3)

  5. the maximum data value

• It is a concise way to summarize a set of data without showing all the data values

What can I calculate from a five-number summary?

• From a five-number summary, you can:

  • find a measure of the center of the data

    • The median

  • find a measure of the spread (variability) of the data

    • Either the range (maximum - minimum)

    • or the interquartile range (Q3 - Q1)

  • find the shape of the distribution of the data

    • by comparing the difference Q2 - Q1 with the difference Q3 - Q2

Boxplots

What is a boxplot?

• A boxplot is a graph that shows the five-number summary

  • The minimum data value, first quartile, median, third quartile and maximum data value of a set of data

• A box is used to represent the middle 50% of the data

  • The width of the box is the interquartile range

    • The difference between the first and third quartile (also known as the lower and upper quartiles)

  • Two whiskers (horizontal lines) are extended from either side of the box to the minimum data value and the maximum data value

  • The median is shown by a vertical line inside the box

    • This is not necessarily in the center of the box

• Outliers (extreme values) are represented with a cross and are outside of the whiskers

  • The maximum and minimum data values do not include outliers

    • The whisker ends at the most extreme non-outlier