Box Plot Calculator

The calculator sorts your data in ascending order, then uses the inclusive quartile method. Q2 (the median) is the middle value — or the average of the two middle values when the dataset has an even count. Q1 is the median of the lower half and Q3 is the median of the upper half, with the median itself excluded from both halves when the count is odd.

The Interquartile Range (IQR) measures the spread of the middle 50% of your data and is calculated as IQR = Q3 − Q1. A larger IQR indicates greater variability in your dataset, while a smaller IQR means values are more tightly clustered around the median.

Outliers are identified using Tukey's fences: any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged as an outlier. By default, all data points — including outliers — are used in the five-number summary. If you check 'Exclude Outliers,' those points are removed before recalculating the statistics.

A box plot requires at least 4 values to meaningfully define the five-number summary (Min, Q1, Median, Q3, Max). With fewer than 4 points, the quartile calculations become trivial or undefined, making the resulting plot statistically uninformative.

Yes, the calculator fully supports negative numbers and decimal values. Simply enter them in the data field separated by commas or spaces. The five-number summary, IQR, mean, and outlier detection all work correctly regardless of whether values are negative, fractional, or both.

For population data, standard deviation divides by N (the total count). For sample data, it divides by N − 1 (Bessel's correction) to produce an unbiased estimate of the true population standard deviation. Choose 'Sample' if your data represents a subset of a larger group.

Box plots are ideal for quickly comparing the spread, skewness, and central tendency of multiple datasets side by side, and for spotting outliers. Histograms are better when you want to see the full shape and distribution pattern of a single dataset in detail. For comparing groups, box plots are typically more concise.

If the median line is closer to Q1, the data is right-skewed (positively skewed), meaning most values are lower with a long tail of higher values. If the median is closer to Q3, the data is left-skewed (negatively skewed). A symmetric box plot suggests the data is roughly normally distributed.