Quartile Calculator
Calculate quartiles Q1, Q2 (median) and Q3, the interquartile range, minimum and maximum of a data set using the median-of-halves method.
Last reviewed by the Radiatus Cloud team
Find the five-number summary and interquartile range of a data set.
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Find quartiles and the interquartile range
Quartiles divide an ordered data set into four equal parts. The first quartile Q1 is the value below which a quarter of the data falls, the second quartile Q2 is the median, and the third quartile Q3 marks the three-quarter point. The interquartile range, Q3 minus Q1, measures the spread of the middle half of the data and is a robust alternative to the range because it ignores extreme outliers.
This calculator uses the median-of-halves method, also known as Tukey's method and taught in most statistics courses: the data is sorted, split at the median, and Q1 and Q3 are the medians of the lower and upper halves. For an odd count, the central median value is excluded from both halves.
Reading the five-number summary
Together the minimum, Q1, median, Q3 and maximum form the five-number summary that underlies the box plot. Analysts use quartiles to describe distributions, detect skew and flag outliers, which commonly lie more than one and a half interquartile ranges beyond Q1 or Q3.
Numbers can be separated by commas, spaces or new lines, and the tool ignores any surrounding text. Note that other quartile methods exist and may give slightly different Q1 and Q3 values. All calculation happens locally in your browser.
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Frequently Asked Questions
Which quartile method does this use?
It uses the median-of-halves method (Tukey\'s method): sort the data, split at the median, and take the medians of the lower and upper halves as Q1 and Q3.
What is the interquartile range?
The IQR is Q3 minus Q1, the spread of the middle fifty percent of the data. It resists outliers better than the full range.
Why might my answer differ from another tool?
There are several accepted quartile definitions. Spreadsheet functions may use linear interpolation, giving slightly different Q1 and Q3 than the median-of-halves method.
How is the median found for an even count?
With an even number of values, the median is the average of the two central values after sorting.
How do I separate my numbers?
Use commas, spaces or new lines. The tool extracts every number it finds, including decimals and negatives, and ignores other text.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Paste or type numbers separated by commas, spaces or new lines.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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