Box plot range and IQR, step by step

Two spreads live in a box plot: the range across the whole diagram and the interquartile range across the box.

The question
Scores on the spelling test (points)
0102030405060

What is the interquartile range?

Scores on the spelling test (points)

left whisker end:15 points
left whisker end:15 points
left edge of the box:25 points
left whisker end:15 points
left edge of the box:25 points
line inside the box:30 points
left whisker end:15 points
left edge of the box:25 points
line inside the box:30 points
right edge of the box:40 points
left whisker end:15 points
left edge of the box:25 points
line inside the box:30 points
right edge of the box:40 points
right whisker end:55 points
left whisker end:15 points
left edge of the box:25 points
line inside the box:30 points
right edge of the box:40 points
right whisker end:55 points
left whisker end:15 points
left edge of the box:25 points
line inside the box:30 points
right edge of the box:40 points
right whisker end:55 points
15 points
  1. A box plot is five numbers drawn to scale — not a bar, and nothing here is a total. Read the five marks off one at a time, and the question answers itself.
  2. Left whisker end: 15 points — the smallest value.
  3. Left edge of the box: 25 points — the quarter mark — a quarter of the data is below it.
  4. Line inside the box: 30 points — the MEDIAN, not the mean and not the middle of the box's width.
  5. Right edge of the box: 40 points — the three-quarter mark.
  6. Right whisker end: 55 points — the largest value.
  7. Now the question. It is asking for the left whisker end, and that has already been read off — no arithmetic is owed.
  8. So the answer is 15 points. Nothing is added or averaged — a box plot is read, not calculated.

How it works.

  1. 01

    A box plot is five numbers drawn to scale — not a bar, and nothing here is a total. Read the five marks off one at a time, and the question answers itself.

  2. 02

    Left whisker end: 15 points — the smallest value.

  3. 03

    Left edge of the box: 25 points — the quarter mark — a quarter of the data is below it.

  4. 04

    Line inside the box: 30 points — the MEDIAN, not the mean and not the middle of the box's width.

  5. 05

    Right edge of the box: 40 points — the three-quarter mark.

  6. 06

    Right whisker end: 55 points — the largest value.

  7. 07

    Now the question. It is asking for the left whisker end, and that has already been read off — no arithmetic is owed.

  8. 08

    So the answer is 15 points. Nothing is added or averaged — a box plot is read, not calculated.