Quartile Calculator

About the Quartile Calculator

The quartile calculator divides sorted data into four equal parts using Q1, Q2 (median), and Q3. Quartiles are the backbone of the five-number summary, the box plot, and the interquartile range (IQR).

This calculator computes quartiles with three standard methods: exclusive/Tukey, inclusive, and interpolated/Excel. It also shows the five-number summary, IQR, semi-IQR, midhinge, trimean, quartile coefficient of dispersion, and a box plot for visual comparison.

Enter your data, choose a quartile method, and use the comparison table to see how the result changes when the dataset is small or the middle values are tied.

When This Page Helps

Use this calculator when you need a percentile-based summary that is less sensitive to outliers than the mean and standard deviation. It is especially helpful for small datasets, skewed data, and any comparison where the middle 50% matters more than the extremes.

The method comparison makes it clear why different textbooks or software can report slightly different quartiles for the same ordered list.

How to Use the Inputs

1. Enter numbers separated by commas or spaces (minimum 4 values).
2. Select the quartile method: exclusive (Tukey), inclusive, or interpolated (Excel).
3. Read Q1, Median, Q3 from the main output — they divide data into fourths.
4. Check the IQR (Q3 − Q1) for the spread of the middle 50%.
5. View the box plot for a visual summary of the five-number summary.
6. Compare all three quartile methods in the comparison table.
7. Expand the decile table for detailed percentile breakpoints.

Example Calculation

Tips & Best Practices

• Different software uses different quartile methods — Excel uses interpolation, R default uses exclusive (Tukey). The method comparison table shows how they differ for your data.
• The midhinge (Q1 + Q3) / 2 is a robust version of the midrange — the center of the middle 50% instead of the center of the full range.
• The trimean weights the median double: (Q1 + 2×Median + Q3)/4. It combines the resistance of the median with information about spread.
• For small datasets (n < 10), the three methods can give noticeably different results. For large datasets, they converge.
• Quartiles are ordinal statistics — they use ranks, not values, so they're robust to outliers.
• The quartile coefficient of dispersion (QCD) is useful for comparing spread across datasets with different scales, like CV but based on quartiles.

Quartiles in a Box Plot

In a box plot, Q1 and Q3 form the edges of the box and the median sits inside it. That makes quartiles useful for spotting asymmetry, spread, and possible outliers at a glance.

Why Methods Differ

Different quartile methods handle the middle of the dataset in different ways. The differences are usually small for large samples, but they can matter for short lists or data with repeated values.

A Practical Interpretation

Q1 marks the lower quarter of the distribution, Q2 marks the middle, and Q3 marks the upper quarter. Together they describe where the bulk of the data sits without relying on a normal-distribution assumption.

Frequently Asked Questions

• What are quartiles?

  Quartiles divide sorted data into four equal groups. Q1 (first quartile) is the 25th percentile — 25% of values fall below it. Q2 is the median (50th percentile). Q3 (third quartile) is the 75th percentile — 75% of values fall below it. Together with min and max, they form the five-number summary.

• Why do different calculators give different quartile values?

  There are at least 9 different methods for computing quartiles (Hyndman & Fan, 1996). The three most common are exclusive (Tukey), inclusive, and interpolated (Excel). They differ in how they handle the median when splitting data into halves, and whether they interpolate between adjacent values. For large datasets, the differences are usually tiny.

• What is the exclusive (Tukey) method?

  The exclusive method splits the data at the median, excluding the median value if n is odd. Q1 is the median of the lower half, Q3 is the median of the upper half. This is the method used in most introductory statistics textbooks and is the standard for constructing box plots.

• What is the trimean?

  The trimean = (Q1 + 2 × Median + Q3) / 4 was introduced by John Tukey as a resistant measure of central tendency. It gives 50% weight to the median and 25% each to Q1 and Q3. Unlike the mean, it resists outliers. Unlike the median alone, it uses information about the shape of the middle 50%.

• How do quartiles relate to box plots?

  In a box plot, the box spans from Q1 to Q3 (the IQR). A line inside the box marks the median (Q2). Whiskers extend to the farthest non-outlier values (within 1.5×IQR of Q1 and Q3). Points beyond the whiskers are plotted individually as outliers. The entire box plot is built from quartiles.

• What is the five-number summary?

  The five-number summary consists of Min, Q1, Median, Q3, Max. These five values describe the center (median), spread (IQR = Q3−Q1), range (max−min), and symmetry of a distribution. It's the basis for box plots and is preferred over mean/SD for skewed or outlier-prone data.