What Is Box Plot Range?
A box plot has more than one range. The overall range runs from the minimum to the maximum. The box range is the interquartile range, Q3 − Q1. The whiskers span the values that are not outliers.
Paste your data and the calculator sorts it, finds the five-number summary, and works out all three. Outliers are the points beyond the 1.5 × IQR fences, and they are listed separately.
Compare the full range with the IQR. A big gap usually means outliers or a skewed distribution.
How to Use the Box Plot Range Calculator
- Paste your data.
- Read the three ranges.
- Look at the box plot to see the box, whiskers and any outliers.
Box Plot Range Formula
Range
Box range
Box Plot Range Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| Range | Maximum minus minimum | |
| IQR | Q3 − Q1, the range of the box | |
| Fences | Q1 − 1.5 IQR and Q3 + 1.5 IQR | Set where whiskers end |
| Whiskers | Lines to the most extreme non-outliers |
Box Plot Range Worked Example
With the example values loaded in the calculator above, the steps are:
- Sorted data: 4, 7, 9, 10, 11, 12, 13, 15, 40.
- Five numbers: min 4, Q1 8, median 11, Q3 14, max 40.
- Overall range = 40 − 4 = 36. Box range (IQR) = 14 − 8 = 6.
- Whiskers reach the most extreme values inside the fences -1 and 23: 4 to 15.
Result: Range of the whole data (max − min) = 36; Range of the box (IQR) = 6; Range of the whiskers = 4 to 15 (width 11).
Worked example
Take 4, 7, 9, 10, 11, 12, 13, 15, 40. Q1 = 8, median = 11, Q3 = 14.
The full range is 40 − 4 = 36. The box range is 14 − 8 = 6. The upper fence is 14 + 9 = 23, so 40 is an outlier and the upper whisker stops at 15.
Which range to report
Report the IQR when the data has outliers or is skewed. Report the full range when you want the total spread, and say so if outliers drive it.
Where Box Plot Range Is Used
Reading box plots
Get the range, IQR and whisker ends behind a box plot.
Comparing spread
See how much outliers inflate the range.
Statistics coursework
Check box plot answers with the five-number summary shown.
Common Box Plot Range Mistakes to Avoid
- Compare the full range and the IQR. A big gap points to outliers or skew.
- Different quartile methods can shift the box slightly.
Box Plot Range Terms and Definitions
- Whisker
- The line from the box to the most extreme non-outlier value.
- IQR
- The width of the box, Q3 − Q1.
Box Plot Range FAQs
What is the range of a box plot?
It can mean the full range from minimum to maximum, or the interquartile range that is the width of the box.
How do you find the range from a box plot?
Subtract the left end from the right end for the full range, or Q1 from Q3 for the box range.
Do whiskers always reach the minimum and maximum?
No. They stop at the most extreme values inside the fences. Points beyond are outliers.
Which range ignores outliers?
The IQR.