A box plot shows minimum, lower quartile, median, upper quartile, and maximum.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Each region holds a quarter
Whatever their widths, the four regions each contain a quarter of the values.
What a narrow box means
A narrow box means the middle half is packed close together, not that it holds fewer values.
The interquartile range
Q3 − Q1 measures the spread of the middle half, and ignores extremes entirely.
The five-number summary
Minimum, first quartile, median, third quartile, maximum. Those five values fix the box plot completely, and they describe centre and spread without assuming any particular distribution shape.
Each region holds a quarter of the data
The box spans the middle 50% and each whisker covers 25%. A long whisker means the data are spread out on that side, not that there are more points there — a common misreading.
The interquartile range
IQR is Q3 − Q1, the width of the box. Unlike the range it ignores the extremes, so a single unusual value cannot inflate it. That resistance is why it is preferred for skewed data.
The outlier rule
A point more than 1.5 × IQR beyond a quartile is conventionally flagged as an outlier. It is a convention, not a law — a flagged point may be a genuine extreme value rather than an error, and it deserves investigation not deletion.
Step 2: Try It Yourself
Change a value and watch which summary numbers move.
- Minimum3
- Lower quartile5
- Median8
- Upper quartile13
- Maximum19
- Interquartile range8
Each of the four sections holds a quarter of the values, however wide it looks. A narrow box means the middle half of the data is packed close together.
Step 3: Watch an Example
One step at a time.
Watch Naomi Test What Moves
Naomi raises the largest value from 19 to 20.
- Step 1
The maximum moves, because it was that value.
Step 4: Your Turn
Practice makes it stick.
The Spread
Problem 1 of 2
Q1 = 5 and Q3 = 13. What is the IQR?
The Share
Problem 2 of 2
What percent of values lie between Q1 and Q3?
Read the Box
1 of 8
Q1 = 10, Q3 = 22. IQR?
2 of 8
What percent of values lie below the median?
3 of 8
What percent lie above Q3?
4 of 8
Does a wider region hold more values? 1 for yes, 0 for no.
5 of 8
How many numbers make up the five-number summary?
6 of 8
Sort each statistic by whether raising the largest value changes it.
Tap something to move it.
- Empty
- Empty
7 of 8
Min 2, max 30. What is the range?
8 of 8
Does the IQR use the extremes? 1 for yes, 0 for no.
Step 5: Quick Check
Show what you know.
Question 1 of 1
Q1 = 4, Q3 = 15. IQR?
What You Learned
- A box plot shows five numbers: minimum, Q1, median, Q3, and maximum.
- Each of the four regions holds a quarter of the values, however wide it looks.
- The IQR measures the middle half and ignores the extremes.