Quartile Calculator
Sort up to 30 values and calculate Q1, the median, Q3, the interquartile range, and the five-number summary in one live view.
Values
Separate values with commas, spaces, tabs, or line breaks. Use a dot for decimals (for example, 21.5). Scientific notation and decimal-comma notation are not accepted.
Results
Five-number summary
| Statistic | Value | Interpretation |
|---|
Ordered data
| Rank | Value | Position |
|---|
How to use this Quartile Calculator
What this calculator does
This calculator summarizes a numeric dataset with quartiles. It sorts the observations, finds the first quartile (Q1), the median (Q2), and the third quartile (Q3), then reports the interquartile range (IQR), range, and five-number summary. These statistics describe location and spread without requiring a distributional assumption. They do not, by themselves, establish whether a dataset is normally distributed, whether a value is an error, or whether one group differs significantly from another.
When to use it
Use quartiles when you want to compare a score with the middle of a class, summarize skewed prices or waiting times, describe the central half of a small dataset, or prepare the five-number summary used in exploratory data analysis. The IQR is especially useful when extreme values make the full range look much wider than the bulk of the observations. NIST describes the IQR as the difference between the 75th and 25th percentiles and as a measure focused on variability near the center of the data.
How to calculate
- The calculator opens with a ready-to-use 24-score demonstration dataset, so Q1, Q2, Q3, the IQR, both tables, and a validated Excel export are available immediately.
- Replace the demonstration numbers in Values (2 – 30 numbers) with your own data. Separate entries with commas, spaces, tabs, or line breaks. Results update live as soon as the complete entry is valid.
- Read First quartile (Q1), Median (Q2), Third quartile (Q3), Interquartile range (IQR), and Range, then inspect the Five-number summary and Ordered data tables. Use Download Excel to save the current analysis. Reset clears the demonstration data; because an empty dataset cannot be analyzed, Excel export remains disabled until you enter a complete valid dataset again.
Input guide
Values (2 – 30 numbers) is the only data input and is required. Enter between 2 and 30 finite numbers. Plain integers and dot-decimal values such as 21.5 are accepted; separators may be commas, spaces, tabs, or line breaks. To avoid locale ambiguity, decimal-comma notation such as 21,5 is interpreted as two comma-separated values rather than one decimal value, so use a dot for decimals. Scientific notation such as 1e3, currency symbols, percent signs, and mixed text are rejected. Negative observations and zero are valid because quartiles can summarize datasets on any ordinary numeric scale. Changing any observation can alter the sorted order and therefore one or more quartiles.
Output guide
First quartile (Q1) is the median of the lower half of the sorted data and marks the lower boundary of the middle half. Median (Q2) is the central value, or the average of the two central values when the dataset size is even. Third quartile (Q3) is the median of the upper half. Interquartile range (IQR) equals Q3 minus Q1 and measures the width of the middle 50% of observations; a larger IQR means that central observations are more dispersed on the dataset's own unit scale. Range equals maximum minus minimum and is more sensitive to extreme endpoints. The live Values pill gives the observation count, while the IQR pill repeats the current IQR for quick scanning.
The Five-number summary table lists Minimum, Q1, Median, Q3, and Maximum. The Ordered data table lists each Rank, the sorted Value, and a Position label showing where that observation sits relative to the quartile boundaries. These are exact deterministic summaries under the quartile convention used here, not forecasts or recommendations. Different software packages can use different quartile conventions, so compare methods before expecting identical Q1 and Q3 values across tools. NIST's overview of measures of scale provides additional context for how the range and interquartile range emphasize different parts of a dataset.
Worked example
The opening data are 24 test scores. After sorting, the middle two observations are 30 and 30, so the median is 30. The lower half contains 12 observations; its two middle values are 21 and 22, giving Q1 = (21 + 22) / 2 = 21.5. The upper half also contains 12 observations; its two middle values are 38 and 40, giving Q3 = (38 + 40) / 2 = 39. Therefore IQR = 39 – 21.5 = 17.5. The minimum is 9, the maximum is 48, and the range is 39. Those values match the first-open cards, tables, and Excel workbook checkpoints.
Learn more
For a standards-oriented explanation of quartiles, IQR, and their relationship to exploratory plots, see NIST's discussion of quartiles and the interquartile range in box plots. It explains why Q1 and Q3 delimit the middle portion of a dataset and how IQR is used when examining tails and possible outliers.
How the quartile method works
The data are first sorted from smallest to largest. For an even number of observations, the dataset is split cleanly in half: Q1 is the median of the lower half and Q3 is the median of the upper half. For an odd number of observations, this calculator follows the convention in which the dataset's central observation participates in both halves. The calculator then takes the median of each half. This convention is important because quartiles are not defined identically by every statistics package.
Range = Maximum – Minimum
The IQR deliberately ignores the outer quarters when measuring spread. NIST's interquartile range reference describes it as a robust measure of scale that is less affected by extremes than measures that rely strongly on tail behavior.
Interpreting quartiles carefully
A quartile is a positional summary, so its meaning depends on the scale and context of the original data. A Q1 of 21.5 points and a Q1 of 21.5 minutes are numerically identical but substantively different. A large gap from Q1 to the median suggests more spread in the lower-middle part of the data; a large gap from the median to Q3 suggests more spread in the upper-middle part. The range adds information about endpoints, but a single extreme observation can change it dramatically while leaving the IQR much less affected.
Quartiles are also the core of a box plot. NIST's box plot guidance explains how Q1, the median, and Q3 define the central box and how the IQR can be extended into fence-based outlier checks. This calculator intentionally reports the underlying numbers and sorted data rather than drawing a chart, so every displayed result can be checked directly against the observations.