5 Number Summary Calculator
Enter a list of numbers to obtain the minimum, first quartile, median, third quartile, and maximum, along with range and interquartile range.
Five-number summary
Minimum: 3.000
Q1: 7.000
Median: 12.000
Q3: 14.000
Maximum: 21.000
Dispersion
Range: 18.000
Interquartile Range (IQR): 7.000
IQR highlights the spread of the middle 50% of observations.
Observation count: 9
Quartiles are computed using linear interpolation of the sorted data (inclusive method).
How to Use This Calculator
- Paste or type your dataset into the input box.
- Confirm that values are separated by spaces or commas.
- Review the generated five-number summary, range, and interquartile range.
- Use the results to build box plots or compare distribution spreads.
Formula
Five-number summary = {min, Q1, median, Q3, max}
Qp = interpolation of sorted data at position (n − 1) · p
Range = max − min
IQR = Q3 − Q1
Quartiles represent the 25th, 50th, and 75th percentiles and divide the sorted data into four equal parts.
Full Description
The five-number summary concisely describes distribution spread and central tendency without assuming a specific shape. It underpins box-and-whisker plots and is particularly useful when data may contain outliers or skewness.
By comparing Q1 and Q3, analysts evaluate the dispersion of the middle half of observations. The range contextualizes extreme values, while the median highlights the central observation. Together they provide a quick snapshot of distribution characteristics.
Frequently Asked Questions
How are quartiles calculated?
We use linear interpolation between sorted data points, consistent with the method in many statistical software packages.
What if I have very few data points?
With small samples, quartiles may coincide or match existing data points; results remain valid but interpret with caution.
Can I use decimals and negative values?
Yes. The calculator accepts any real numbers, including negatives and decimals.
Why focus on the interquartile range?
IQR measures the spread of the middle half of the data and is robust to outliers, making it ideal for comparison across datasets.