Interpret box plots informally

Detailed Explanation: Interpret box plots informally

A box plot is a picture that summarizes a data set using five values:

• Minimum: the smallest value
• Lower quartile, $Q_1$: about one-fourth of the data is at or below this value
• Median: the middle value
• Upper quartile, $Q_3$: about three-fourths of the data is at or below this value
• Maximum: the largest value

The box goes from $Q_1$ to $Q_3$, so it shows the middle $50\%$ of the data. The lines called whiskers extend from the box to the minimum and maximum.

Worked example

Suppose a box plot has these values:

10        14        18        22                  30
|---------|---------|---------|-------------------|
          [---------|---------]

The five-number summary is:

• Minimum: $10$
• Lower quartile: $14$
• Median: $18$
• Upper quartile: $22$
• Maximum: $30$

Step 1: Find the center.

The median is the line inside the box:

So, the middle of the data is about $18$.

Step 2: Find the overall range.

The range goes from the minimum to the maximum:

So, the data values spread across $20$ units.

Step 3: Find the interquartile range.

The interquartile range, or IQR, describes the width of the box:

So, the middle $50\%$ of the data is spread across $8$ units, from $14$ to $22$.

Step 4: State what the box plot tells you.

A good interpretation is:

The data has a median of about $18$. The values range from about $10$ to $30$. The middle $50\%$ of the data lies between about $14$ and $22$.

Remember that a box plot shows a summary, not every individual data value. You cannot tell the exact values of all the data points from the box plot.