Histograms, step by step

A histogram groups the data before drawing it, so a bar stands for a range rather than for one value.

The question
Standing long jump (cm)
0123456100–109110–119120–129130–139140–149

How many are under 120?

Standing long jump (cm)

bands:100–109110–119120–129130–139140–149
100–109:6 jumps
110–119:3 jumps
120–129:3 jumps
130–139:1 jumps
140–149:1 jumps
100–109:6 jumps
110–119:3 jumps
120–129:3 jumps
130–139:1 jumps
140–149:1 jumps
9
  1. The bars touch, and that is the clue: this is not a bar graph of separate things, it is a number line cut into stretches of 10 cm. Each bar is a BAND, not a value.
  2. So a bar's height counts how many fell ANYWHERE inside its band — the 100–109 bar says 6 jumps, but not what any single one of them was.
  3. How many are under 120? Only the 100–109 and 110–119 bands count — 6 + 3 = 9 jumps. The 120–129 band falls on the other side of the line, so it is left out even though it is right next to it.

How it works.

  1. 01

    The bars touch, and that is the clue: this is not a bar graph of separate things, it is a number line cut into stretches of 10 cm. Each bar is a BAND, not a value.

  2. 02

    So a bar's height counts how many fell ANYWHERE inside its band — the 100–109 bar says 6 jumps, but not what any single one of them was.

  3. 03

    How many are under 120? Only the 100–109 and 110–119 bands count — 6 + 3 = 9 jumps. The 120–129 band falls on the other side of the line, so it is left out even though it is right next to it.