Reading Histograms
Grade 6The key move: area = frequency
Every histogram question that asks you to find a frequency comes down to one thing: area of the bar = frequency. Read off the height (frequency density) and the width (class width), then multiply them together.
Worked example — reading off frequencies
Finding what proportion lies in a range
Try this one
The table shows the reaction times, \( t \) seconds, of 56 people in an experiment.
| Reaction time (\( t \) seconds) | Frequency density |
|---|---|
| \( 0 < t \le 0.2 \) | 50 |
| \( 0.2 < t \le 0.4 \) | 120 |
| \( 0.4 < t \le 0.8 \) | 40 |
| \( 0.8 < t \le 1.4 \) | 10 |
Estimate the percentage of these people whose reaction time was greater than 0.5 seconds. Give your answer to 1 decimal place. [4]
This needs frequency = frequency density \( \times \) width, then estimating a count across part of a class, then converting to a percentage.
Ask yourself: 'which classes lie beyond my cut-off, and does the cut-off fall inside one of them?' For a value inside a class, take the fraction of that class's width that lies above the cut-off.
