Box Plots and Histograms

Algebra 2 · Axiom Academy

LESSON Box Plots and Histograms Two ways to picture a data set — one built from five key numbers, the other from the shape of the whole distribution. Everything starts by putting the data in order . Once sorted, three cut-points slice the values into four groups of roughly equal size. The median splits the data in half; the median of the lower half is the first quartile Q_1 , and the median of the upper half is the third quartile Q_3 . Together with the smallest and largest values, these give the five-number summary. A box plot draws the five-number summary directly on a number line. A box stretches from Q_1 to Q_3 , spanning the middle 50% of the data. A line inside the box marks the median . Two whiskers reach out from the box to the minimum and the maximum, showing the full range. The width of the box is the interquartile range (IQR) — the spread of the middle half of the data. A wide box means the central values are spread out; a narrow box means they are tightly clustered. A histogram tells a different story. Split the number line into equal-width intervals called bins , then count how many values land in each one. The height of each bar is that frequency (count). Where a value sits exactly on a boundary, we place it in the bin that starts there — so each bin covers [a, b) : it includes its left edge and excludes its right. 4. Reading Them — Spread, Shape, and Outliers

This is the written version of the interactive lesson above. See the full Algebra 2 course.