Frequency Density
Grade 6Why histograms are different to bar charts
In a bar chart, the height of a bar shows the frequency. That works fine when every category is the same width. In a histogram, bars can have different widths (class intervals), so it's the area of the bar — not the height — that represents frequency.
If you used height directly, a wider bar would look more important than a narrower one with the same frequency. That would mislead you. So we use frequency density on the y-axis instead.
Worked example — drawing a histogram
Finding frequency from a histogram
Reverse the formula: Frequency = frequency density × class width
This is the area of the bar. So when you're reading a histogram, identify the height and width of each bar, multiply, and you get the frequency for that class.
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.
