Boxplots (SQA National 5 Applications of Mathematics): Revision Note

Boxplots

What are boxplots?

• A boxplot is a diagram that clearly shows key statistics from a data set

  • It shows the median, the quartiles, and the minimum and maximum values

  • It does not show any other individual data items

• The middle 50% of the data is represented by a box

• The lower and upper 25% of the data are each represented by "whiskers"

How do I draw a boxplot?

• You need to draw vertical lines at the following five values

  • Lowest data value

  • Lower quartile

  • Median

  • Upper quartile

  • Highest data value

• Draw a rectangle using the lines for the upper and lower quartiles as two of the sides

  • This is the middle 50%

• Draw a horizontal line from the box to the lowest value

  • This is the lowest 25%

• Draw a horizontal line from the box to the highest value

  • This is the highest 25%

How do I interpret a boxplot?

• You can read off the five values

• You can calculate the range and interquartile range (IQR)

  • range = highest value - lowest value

  • interquartile range = upper quartile - lower quartile