The five-number summary is the minimum, lower quartile, median, upper quartile and maximum.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Each section holds a quarter
The four sections each contain about a quarter of the data points, not a quarter of the width.
Width means density
A wide section means the values there are spread thin. A narrow one means they are packed tightly. The counts are equal either way.
The interquartile range
The IQR is the upper quartile minus the lower. It measures the spread of the middle half and ignores the extremes entirely.
The outlier rule
A value is an outlier if it sits more than 1.5 IQRs below the lower quartile or above the upper quartile.
What a box plot hides
Two very different distributions can share a five-number summary. A box plot cannot show two peaks.
Five numbers, one picture
Minimum, first quartile, median, third quartile, maximum. Those five determine the box plot entirely and describe centre and spread without assuming any distribution shape.
Each section holds a quarter
The box spans the middle half and each whisker a quarter of the data. A long whisker means those values are spread out, not that there are more of them — a very common misreading.
The interquartile range
IQR is Q3 − Q1, the width of the box. It ignores the extremes, so a single unusual value cannot inflate it. That resistance is why it is the spread measure of choice for skewed data.
Box plots compare well
Side by side on a common scale, box plots make differences in centre and spread immediately visible. They hide shape, though — a bimodal distribution and a uniform one can produce identical boxes.
Step 2: Try It Yourself
Tap and try it out.
- 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 Sana Test for an Outlier
A data set has lower quartile 5, upper quartile 13, and one value at 30.
- Step 1
The IQR is 13 − 5 = 8.
Step 4: Your Turn
Practice makes it stick.
The Spread
Problem 1 of 2
Lower quartile 5, upper quartile 13. What is the IQR?
The Fence
Problem 2 of 2
IQR 8 and upper quartile 13. What is the upper outlier fence?
Five Numbers
1 of 8
Q1 = 10, Q3 = 22. What is the IQR?
2 of 8
Data 3, 5, 7, 8, 9, 13, 19. What is the median?
3 of 8
Same data. What is Q1?
4 of 8
Same data. What is Q3?
5 of 8
Q1 = 4, IQR = 6. What is the lower outlier fence?
6 of 8
What fraction of the data lies in the box, as a decimal?
7 of 8
Match each part of the summary with what it reports.
Tap a card on the left to start.
8 of 8
A box section is very wide. Does it hold more points or the same? 1 more, 2 the same.
Step 5: Quick Check
Show what you know.
Question 1 of 2
Q1 = 12, Q3 = 20. What is the IQR?
Question 2 of 2
What does a wide section of a box plot mean?
What You Learned
- The five-number summary is minimum, Q1, median, Q3 and maximum.
- The IQR measures the middle half and ignores extremes.
- A value beyond 1.5 IQRs past a quartile counts as an outlier.