Box Plots (Box-and-Whisker Diagrams)
Grade 6The five-figure summary
A box plot (also called a box-and-whisker diagram) displays five key values for a data set on a number line: the minimum, lower quartile (LQ), median, upper quartile (UQ), and maximum.
The box covers the middle 50% of data (LQ to UQ). The whiskers extend from the box to the minimum and maximum.
Drawing a box plot
EXAMPLE
Five-figure summary for a data set: min = 10, LQ = 25, median = 35, UQ = 50, max = 70. Draw the box plot.
Draw a number line covering at least 10 to 70.
Draw a vertical line at 25 (LQ) and at 50 (UQ). Join them to form a box.
Draw a vertical line at 35 (median) inside the box.
Draw a whisker from 25 to 10 (min), and another from 50 to 70 (max).
Box from 25 to 50, median line at 35, whiskers to 10 and 70.
Interpreting a box plot
A box plot lets you see spread and skew at a glance. If the median line is closer to the LQ, the data is positively skewed (more data in the lower half). If it's closer to the UQ, it's negatively skewed.
Read the IQR directly as the width of the box: UQ − LQ. You don't need to look anything up — it's drawn right there for you.
Comparing two box plots
If you have two box plots on the same scale, compare medians (who scores higher on average) and IQRs (who is more consistent). Mention both in your answer — a comparison answer that only talks about one measure will usually drop a mark.
