Five Number Summary Calculator
Enter a list of numbers to calculate the five number summary: Minimum, Q1 (first quartile), Median, Q3 (third quartile), and Maximum. Includes a visual box plot of your data.
How to Read a Box Plot
| Component | Represents | Tells You |
|---|---|---|
| Left whisker | Minimum to Q1 | Lowest 25% of data |
| Left side of box | Q1 | 25th percentile boundary |
| Line in box | Median | Middle value (50th percentile) |
| Right side of box | Q3 | 75th percentile boundary |
| Right whisker | Q3 to Maximum | Highest 25% of data |
| Box width (IQR) | Q3 − Q1 | Spread of middle 50% |
Related Statistics Calculators
- Median Calculator — find the median and quartiles
- Range Calculator — quick measure of spread
- Standard Deviation Calculator
- Mean / Average Calculator
- All Statistics Calculators
Frequently Asked Questions
What is five number summary?
The five number summary consists of five key values: Minimum, Q1, Median, Q3, Maximum. Together they describe the spread and center of a data set. Q1 is the 25th percentile, the median is the 50th, and Q3 is the 75th percentile.
How to find Q1 and Q3?
Sort the data. Split at the median. Q1 = median of the lower half. Q3 = median of the upper half. Example: for {1, 2, 3, 4, 5, 6, 7}, median = 4, lower half = {1, 2, 3} so Q1 = 2, upper half = {5, 6, 7} so Q3 = 6.
What is a box plot?
A box plot (box-and-whisker plot) is a visual representation of the five number summary. The box spans Q1 to Q3 (the IQR), with a line at the median. Whiskers extend to the minimum and maximum, showing the full data range.
Five number summary vs standard deviation?
The five number summary describes data using quartiles and extremes — works for any distribution shape and is robust to outliers. Standard deviation measures average distance from the mean — best for symmetric/normal distributions.
The five number summary and box plot are foundational tools in exploratory data analysis (EDA).
