Box Plot & IQR Calculator

Box Plot Statistics Guide

Five Number Summary

A box plot (box-and-whisker plot) displays 5 key statistics: Minimum — smallest non-outlier value (whisker end). Q1 — lower quartile (25th percentile). Median (Q2) — middle value (50th percentile). Q3 — upper quartile (75th percentile). Maximum — largest non-outlier value (whisker end). IQR = Q3 - Q1 (the box width). The box contains the middle 50% of data. The whiskers extend to the furthest values within 1.5×IQR of the box. Points beyond 1.5×IQR are plotted individually as outliers.

Calculating Quartiles

For a dataset of n values sorted in order: Median: if n is odd, median = middle value. If n is even, median = average of two middle values. Q1: lower half of data (below median) — median of lower half. Q3: upper half of data (above median) — median of upper half. Whether to include the overall median in the halves (inclusive/exclusive) varies by convention — GCSE in the UK typically uses the inclusive method. Interpolation method (used by many calculators and statistical software): Q1 = value at

Outliers

Definition: a value is an outlier if it falls more than 1.5×IQR below Q1 or above Q3. Lower fence = Q1 − 1.5×IQR. Upper fence = Q3 + 1.5×IQR. Example: IQR = 10, Q1 = 20, Q3 = 30. Lower fence = 20 − 15 = 5. Upper fence = 30 + 15 = 45. A value of 50 would be an outlier. Extreme outliers (beyond 3×IQR): sometimes plotted differently from mild outliers. Outliers are NOT necessarily errors — they may be genuine extreme values. Always investigate outliers before removing them. In GCSE and A-level stat

Comparing Box Plots

Box plots are particularly useful for comparing distributions of two or more groups. Comparing: median positions (central tendency). Box widths/IQR (spread of middle 50%). Overall range (total spread). Symmetry: symmetric box (median in centre of box) vs skewed (median nearer one end). Skewness: positive skew — longer upper whisker and median nearer Q1. Negative skew — longer lower whisker and median nearer Q3. Multiple box plots on the same scale allow direct comparison of distributions. GCSE s