Calculate the five-number summary (min, Q1, median, Q3, max) with IQR, outlier detection, box plot visualization, decile table, and Bowley skewness for any dataset.
The five-number summary calculator reports the minimum, first quartile, median, third quartile, and maximum for a dataset. Those five values give a compact picture of center, spread, and asymmetry without relying on the mean.
This calculator also computes the interquartile range, applies Tukey fence outlier detection, shows a box plot, and lists deciles for a more detailed look at the distribution. It is designed for datasets where quartiles tell the story better than averages.
Use it for skewed or outlier-prone data such as salaries, housing prices, wait times, and other real-world measurements where the middle of the data matters more than the extremes.
Use the five-number summary when you want a quick description of a dataset that is still resistant to outliers. It is the simplest way to compare the middle 50% of values across groups and to see whether the data is symmetric or skewed.
Because it underpins box plots, this summary is also useful when you need a clean visual representation for reports or presentations.
Q1 = 25th percentile, Q2 = 50th (median), Q3 = 75th percentile. IQR = Q3 − Q1. Lower fence = Q1 − 1.5×IQR. Upper fence = Q3 + 1.5×IQR. Bowley skewness = (Q3 + Q1 − 2×Median) / IQR.
Result: Min=12, Q1=20, Med=28, Q3=38, Max=50, IQR=18
The 13-value dataset has median 28 (7th value). Q1 is the median of the lower half (20), Q3 is the median of the upper half (38). IQR = 38 − 20 = 18. No outliers detected with standard 1.5×IQR fences.
The minimum and maximum give the full span of the data. Q1 and Q3 mark the edges of the middle half. The median marks the center. When Q1 and Q3 are far from the median on one side, the distribution is skewed.
Quartiles are rank-based, so one extreme value does not distort them the way it can distort the mean. That is why the five-number summary is a better fit for salaries, prices, medical costs, and other data with long tails.
The five-number summary is the numeric backbone of a box plot. The box is drawn from Q1 to Q3, the line inside is the median, and whiskers typically extend to the last non-outlier values.
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It's a set of five descriptive statistics: minimum, Q1 (25th percentile), median (50th percentile), Q3 (75th percentile), and maximum. Together they divide the data into four groups of roughly equal size, showing center, spread, and range.
The median is the middle value when data is sorted — half the values are below and half above. The mean is the arithmetic average. The median is resistant to outliers: adding a millionaire to a salary dataset changes the mean dramatically but barely affects the median.
Q1 is the median of the lower half of data, Q3 is the median of the upper half. This calculator uses the linear interpolation method (same as Excel PERCENTILE.INC). Different methods exist — results may vary slightly for small datasets.
Using Tukey's method, any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is an outlier. Values beyond Q1 − 3×IQR or Q3 + 3×IQR are "extreme" outliers. These thresholds capture values that are unusually far from the middle 50%.
Use the five-number summary when data is skewed, has outliers, or is non-normal. Salary data, housing prices, medical costs, and wait times are typically right-skewed — the five-number summary describes them more accurately.
Bowley (quartile) skewness = (Q3 + Q1 − 2×Median) / IQR. It measures asymmetry using only quartiles, so it's robust to outliers. Values near 0 indicate symmetry; positive values indicate right skew; negative values indicate left skew.