Box Plot Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Box Plot.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

A visual display of the five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

A box plot is like an X-ray of your data's skeleton. The box shows where the middle 50% of data lives. The line inside is the median. The whiskers stretch to the extremes. You instantly see the center, spread, and any unusual values.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A box plot shows five key summary statistics at once: minimum, Q1, median, Q3, and maximum. The box covers the middle 50% of the data (the IQR).

Common stuck point: Students misread the whisker length as the sample count. A long whisker just means the data is spread out in that region, not that there are more data points.

Sense of Study hint: First, find the five-number summary: minimum, Q1, median, Q3, and maximum. Then draw a box from Q1 to Q3 with a line at the median. Finally, extend whiskers from the box to the minimum and maximum (or to the last non-outlier values, marking outliers as individual dots).

Worked Examples

Example 1

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Data: 2, 4, 5, 7, 8, 9, 11, 13, 15. Find the five-number summary and describe how to draw a box plot.

Solution

  1. 1
    Step 1: Minimum = 2, Maximum = 15, Median (Q2) = 8 (5th of 9 values).
  2. 2
    Step 2: Lower half: {2, 4, 5, 7}. Q1 = \frac{4+5}{2} = 4.5.
  3. 3
    Step 3: Upper half: {9, 11, 13, 15}. Q3 = \frac{11+13}{2} = 12. Draw a box from Q1 (4.5) to Q3 (12), line at median (8), whiskers to min (2) and max (15).

Answer

Five-number summary: Min = 2, Q1 = 4.5, Median = 8, Q3 = 12, Max = 15.
A box plot (box-and-whisker plot) visualises the five-number summary, showing the spread and centre of the data. The interquartile range (IQR = Q3 − Q1) shows where the middle 50% of data lies.

Example 2

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A box plot shows: Min = 10, Q1 = 20, Median = 35, Q3 = 50, Max = 90. Calculate the IQR and determine if a value of 100 would be an outlier using the 1.5×IQR rule.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

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Data: 3, 5, 6, 8, 10, 12, 14. Find the five-number summary.

Example 2

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A box plot has Min = 4, Q1 = 9, Median = 12, Q3 = 18, Max = 21. Find the interquartile range and state the interval containing the middle 50% of the data.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

median introstat quartiles