Box Plot & IQR Calculator
Calculate all five-number summary statistics for a box plot: minimum, lower quartile (Q1), median, upper quartile (Q3), maximum, and IQR with outlier detection.
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Box Plot Statistics Guide
What's the key thing to understand about 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.
What should I know about 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 is the value at a specific fractional position in the ordered data, giving a more precise result than the simple inclusive method when the dataset doesn't divide evenly.
What should I know about 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 statistics, outliers are typically identified using the 1.5 × IQR rule, marking any point beyond this range from the quartiles as worth investigating separately.
What's the key thing to understand about 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 students are commonly asked to compare the spread, median, and skew of two or more box plots side by side, describing the differences in plain, comparative language.