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 computes the five key values that describe a dataset's distribution: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Together, these five numbers reveal the center, spread, and shape of your data at a glance.
Beyond the basic five numbers, this calculator computes the interquartile range (IQR), detects outliers using Tukey's fences, shows a box plot visualization, provides a full decile table, and calculates the Bowley skewness coefficient. Enter data as comma-separated values and use presets to explore different data shapes.
The five-number summary is resistant to outliers (unlike mean and standard deviation), making it ideal for skewed distributions, salary data, housing prices, and other real-world datasets. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case. Use the example pattern when troubleshooting unexpected results. Validate that outputs match your chosen standards.
The five-number summary is the most concise description of a dataset's distribution. It reveals center, spread, skewness, and outliers in just five values — making it the foundation of exploratory data analysis and the basis for box plots.
Essential for students, data analysts, researchers, and anyone who needs a quick yet thorough summary of numeric data.
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.
For symmetric, normal-like data, mean ± standard deviation is perfectly adequate. But real-world data is often skewed: income has a long right tail, medical costs are heavily right-skewed, and response times have occasional extreme values. The five-number summary handles all these cases because quartiles are resistant to outliers — they depend on data ranks, not values.
The box plot is the visual representation of the five-number summary. The box spans Q1 to Q3 (the IQR), the line inside marks the median, and whiskers extend to the most extreme non-outlier values. Points beyond the whiskers are plotted individually as outliers. The box plot makes it easy to compare distributions across groups.
There are at least nine different methods for computing percentiles, and they can give different results for small datasets. This calculator uses linear interpolation (Method 7 in R, "PERCENTILE.INC" in Excel). For large datasets, all methods converge to the same values. The differences matter most when n < 20.
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.