Creating a Box Plot

Algebra 1 · Axiom Academy

Build a box plot step-by-step: order the data, find the five-number summary, check for outliers, then draw it. Eleven students took a test. Their scores are listed below. Construct a box plot by finding the five-number summary and identifying any outliers. Nice work! You built a box plot from a raw data set by finding its five-number summary and checking for outliers. Order first: Every box-plot value depends on position, so sort the data from least to greatest before anything else. Five-number summary: Minimum, Q₁, Median (Q₂), Q₃, and Maximum describe the whole distribution. Quartiles: Q₁ is the median of the lower half and Q₃ is the median of the upper half (each excluding the overall median). Outliers: Using the 1.5 × IQR rule, any value beyond Q₁ − 1.5(IQR) or Q₃ + 1.5(IQR) is an outlier — here 72. Box-plot shape: The box runs Q₁ to Q₃, the inside line is the median, whiskers reach the smallest and largest non-outlier values, and outliers are plotted as separate points. Box plots show center, spread, and unusual values at a glance — which makes them ideal for comparing several data sets side by side.

This is the written version of the interactive lesson above. See the full Algebra 1 course.