Five Number Summary Calculator
Min, quartiles, median, max, IQR, and outliers for any list.
What it does
Five number summaries compress a list into minimum, lower quartile, median, maximum spread, and maximum: the exact skeleton of a box plot. The interquartile range between hinges measures typical spread while fences flag outliers.
The tool above takes a plain list with commas or spaces. It returns the median with IQR and outlier list, spelling all five numbers in the note.
The default 4, 8, 15, 16, 23, 42 reads min 4, Q1 8, median 15.5, Q3 23, max 42 with IQR 15 and no outliers. Hinges split at the middle: lower half median 8, upper half median 23.
Hinge definitions follow NIST statistics handbook practice with the same Tukey fence rules in Khan Academy units. Both split halves excluding the median on odd counts.
How to use
- Type the numbers with commas or spaces.
- Include 4 to 200 plain numbers.
- Read the median first for the center.
- Read IQR for the typical spread.
- Check outliers before averaging.
Formula
- hinges
- Q1 and Q3 medians of each half.
- IQR
- Middle fifty percent spread.
- 1.5x
- Tukey fence multiplier for outliers.
Even counts split cleanly; odd counts drop the median from both halves (Tukey hinges). Other software averages different pairs, so cross tool decimals can differ slightly.
Worked example
Example: 4, 8, 15, 16, 23, 42
Six values entered with commas.
- Sort: already ordered 4 to 42.
- Median: (15 + 16) / 2 = 15.5.
- Q1 of (4, 8, 15) = 8. Q3 of (16, 23, 42) = 23.
- IQR: 23 - 8 = 15. Fences -14.5 to 45.5, nothing outside.
- Tool shows 15.5, 15, none.
Reference table
| Part | Value | Role |
|---|---|---|
| Min | 4 | Left whisker end |
| Q1 | 8 | Box left edge |
| Median | 15.5 | Box line |
| Q3 | 23 | Box right edge |
| Max | 42 | Right whisker end |
Limits
- Tukey hinges here; software methods vary.
- Four values minimum for hinges.
- Outlier flags explore, never delete blindly.
- Skewed lists still need plots beside numbers.
Common mistakes
- Averaging quartiles across methods.
- Forgetting to sort before splitting.
- Deleting flagged outliers automatically.
- Reading IQR as total range.
- Using means on skewed lists instead.
Try it yourself
Quick checks. Answers sit tucked under each question.
1, 2, 3, 4, 100?
Median 3, Q1 1.5, Q3 52, IQR 50.5, no outliers.
Outlier in 1 to 9 plus 50?
Q1 3, Q3 8, IQR 5, fence 15.5: 50 out.
IQR of 10, 20, 30, 40?
Q1 15, Q3 35: IQR 20.
Questions
What are the five numbers?
Min, Q1, median, Q3, max: here 4, 8, 15.5, 23, 42.
What is IQR?
Q3 minus Q1: the middle fifty percent spread, 15 here.
How are outliers found?
Past Q1 minus or Q3 plus 1.5x IQR.
Why hinges differ by tool?
Odd count median handling varies; this page excludes it (Tukey).
Box plot from this?
Box Q1 to Q3 with median line, whiskers to fenced extremes.
When is median better?
Skewed lists where means chase tails.