Calculate Q1, Q2 (median), Q3, IQR, midhinge, trimean, and five-number summary using 3 quartile methods. Box plot, method comparison, and decile table included.
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 tool 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.
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.
Exclusive: Q1 = median of lower half (median excluded). Inclusive: Q1 = median of lower half (median included). Interpolated: Q1 = value at rank 0.25 × (n−1). IQR = Q3 − Q1. Midhinge = (Q1 + Q3) / 2. Trimean = (Q1 + 2 × Median + Q3) / 4.
Result: Q1 = 73, Median = 82.5, Q3 = 89, IQR = 16
Sorted: 68,70,72,74,76,81,84,85,88,90,92,95. Lower half: 68,70,72,74,76,81, median = 73. Upper half: 84,85,88,90,92,95, median = 89. IQR = 89 − 73 = 16.
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.
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.
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.
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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.
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.
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.
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%.
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.
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.