Frequency is area, not height
On a histogram the bar's area equals the frequency. The height is the frequency density .
Two formulas, rearranged as needed
and .
Drawn from real examiner reports.
Reading the bar height as the frequency
Treating the vertical axis as frequency rather than frequency density.
Mistakes were common on Nov 2024 Paper 1H (Q18), especially reading the vertical scale.
Totalling bar heights instead of areas
Some students simply add the heights; you must use area = frequency.
Seen on Nov 2024 Paper 1H (Q18).
Forgetting to divide by class width
Frequency density is , so plotting the raw frequency as the bar height is wrong whenever class widths differ. A class of values over a width of has density , not .
(general exam technique)
Miscalculating unequal class widths
Class width is the upper boundary minus the lower boundary, and the intervals often differ: has width but has width . Using one width for every bar, or misreading the boundaries, throws off every frequency you recover.
(general exam technique)
Misreading the frequency-density axis
The vertical scale is frequency density, and its gridlines rarely go up in ones. Read the actual value on the axis before multiplying by the width — assuming each square is unit is a frequent, avoidable slip.
(general exam technique)
Read the vertical scale carefully
Misreading the frequency-density axis is a frequent, avoidable error — check the gridline values.
Use area = frequency for totals
To find how many values lie across several classes, add the bar AREAS (density × width), never the heights. Bars with densities over width and over width give , not .
Label each bar with its frequency
Before answering, work out and jot the frequency (density × width) on each relevant bar. Having the counts written down turns "how many over 25" questions into simple arithmetic and avoids re-reading the scale repeatedly.
Histograms are used when class intervals are unequal. The vertical axis is frequency density, not frequency: Rearranged: — this is the area of the bar.
What does the height of a histogram bar represent?
On a histogram, the bar for the class has a frequency density of . Find the frequency for this class.