Data Summaries and Displays

A box plot squeezes a whole data set into five numbers: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. To find them, put the data in order, split it at the median, then find the median of the lower half (Q1) and the median of the upper half (Q3). Because a box plot only shows those five landmarks, two very different-looking data sets can produce nearly identical boxes. A histogram keeps every value and sorts them into bins, so clumps, gaps, and outliers that a box plot hides show up as tall or short bars. That is why the same data can look calm in one display and dramatic in the other: one throws away detail on purpose, the other keeps it.

Choosing a display means asking what kind of variable you have and what you want to show. A line plot works for a small set of numerical data where you want to see every individual value stacked above a number line. A histogram suits numerical data with many values, when you care about overall shape, like how test scores cluster. A box plot is best when you want to compare center and spread between groups quickly, without clutter. A bar chart is for categorical data, categories, not numbers, where each bar is a separate count.

This topic connects directly to mean, median, and quartiles elsewhere in the unit, since every display is built from the same ordered-list skills: sort, split, find the middle. Expect problems that mix a verbal description of a data set with a quick calculation of a quartile or mean, often using a variable standing in for an unknown data value.