Concept 2

Read and interpret histograms and box plots (including median, quartiles, IQR).

Reading histogram shapes and box plots, including quartiles, median, and IQR.

Core Idea

Histograms group data into intervals (bins), so you lose individual values but see the overall shape. Box plots compress the data into five numbers: minimum, Q1, median, Q3, and maximum. Both are standard SAT graph types.

Understanding

A histogram bar shows how many data points fall in a range. A bar from 10 to 20 with height 5 means five values land somewhere between 10 and 20 — you don't know exactly where. That's why histogram questions usually ask about shape, approximate center, or which interval has the most data, not exact values.

A box plot shows the five-number summary directly:

  • The left whisker end = minimum
  • The left edge of the box = Q1 (25th percentile)
  • The line inside the box = median (50th percentile)
  • The right edge of the box = Q3 (75th percentile)
  • The right whisker end = maximum

The box contains the middle 50% of the data. Its width is the IQR: 𝑄3 −𝑄1.

The most tested skill: reading Q1, median, and Q3 directly off a box plot and computing the IQR. Second most common: comparing two box plots side by side.

Step by Step

  1. For histograms: read the height of each bar to find the frequency for that interval. Add all bar heights for total 𝑛.
  2. For box plots: identify the five-number summary — min, Q1, median, Q3, max — by reading the endpoints of the whiskers, the edges of the box, and the interior line.
  3. Compute IQR as 𝑄3 −𝑄1.
  4. Compute range as max − min.

Misconceptions

  • Thinking a taller histogram bar means larger values — it means more data points in that interval, not bigger values.
  • Reading Q1 as the minimum or Q3 as the maximum on a box plot.
  • Assuming the median is in the center of the box — it can be anywhere inside it, depending on the data's skew.
Question

Worked Example

A box plot displays test scores for a class. The left whisker ends at 55, the left edge of the box is at 65, the line inside the box is at 74, the right edge of the box is at 82, and the right whisker ends at 98. What is the interquartile range of the test scores?

Select an answer to see the explanation