Box Plot Calculator

The calculator sorts your data in ascending order, then finds the median as the middle value (or average of the two middle values for even-sized datasets). Q1 is the median of the lower half of the data and Q3 is the median of the upper half. This is the inclusive method consistent with most statistics textbooks.

Outliers are identified using the 1.5×IQR rule: any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is flagged as an outlier. The five-number summary (Min, Q1, Median, Q3, Max) always reflects all data points. When you choose to exclude outliers from whiskers, the whiskers extend only to the most extreme non-outlier values.

A box plot requires a minimum, Q1, median, Q3, and maximum — five distinct statistical markers. With fewer than four data points there is not enough data to meaningfully separate these quartiles, making the visualization statistically unreliable.

Yes. The calculator handles any real numbers, including negatives and decimals. Simply enter them comma-separated (e.g. -5, -1.2, 0, 3.8, 10) and all statistics will be computed correctly.

The Interquartile Range (IQR = Q3 − Q1) measures the spread of the middle 50% of your data. It is a robust measure of variability that is not affected by extreme outliers, making it especially useful when your dataset contains skewed values or anomalies.

When your data represents a sample (a subset of a larger group), the standard deviation is calculated using n−1 in the denominator (Bessel's correction) to correct for bias. When it represents the full population, n is used. This affects only the standard deviation output — the five-number summary remains the same.

A box plot summarises your data distribution into five key statistics and clearly highlights the median, spread (IQR), and outliers. A histogram shows the frequency of values across intervals, giving more detail about the shape of the distribution. Box plots are better for comparing multiple datasets side by side; histograms reveal finer distributional patterns.

Box plots are ideal when you want to compare distributions across groups, identify outliers, or understand data spread without being misled by extreme values. They work well for any numeric dataset with at least four values and are widely used in science, finance, and quality control.