Concept 3

Interpret data displays (histograms, box plots, scatterplots, two-way tables).

Read only what each display is built to show: shape, quartiles, association, or category counts.

Core Idea

Each display highlights different information. Histograms show shape, box plots show quartiles and spread, scatterplots show association, and two-way tables compare categories. Read only what the display is built to show.

Understanding

Rule: Students often lose points by forcing a graph to say more than it actually says. A box plot does not show the mean or every data value. A histogram shows frequency by interval, not exact individual scores. A scatterplot can show trend and strength, but not automatic cause. A two-way table helps organize counts across categories and is useful for joint and conditional probabilities.

The right habit is to ask, "What information does this display make visible, and what information does it hide?" That keeps your interpretation precise.

Step by Step

  1. Identify what the display makes visible.
  2. Use only the quantities the display can support.
  3. Avoid claiming information that the display does not provide.

Misconceptions

  • Reading the mean from a box plot.
  • Using a histogram to name exact individual values.
  • Treating a scatterplot as proof of causation.
Question

Worked Example

A box plot for 40 quiz scores has minimum 54, first quartile 68, median 74, third quartile 82, and maximum 96. Which statement must be true?

Select an answer to see the explanation