Class widths
Write the width of every class, including the ones that differ from the rest.
AQA 8300 · S3 · Unequal-width histograms
Histograms with unequal class widths: frequency density
The frequency density mark. In a histogram the frequency is the AREA of the bar, so plotting frequency as height is wrong the moment the classes stop being equal.
Reviewed family · Studara-authored items · No grade-uplift claim
The lost mark
One answer. Several places the method can fail.
Studara does not reduce the response to right or wrong. The reviewed contract checks these states independently.
Frequency density
Divide each frequency by its class width and record the density column.
Plot to the density scale
Draw every bar continuously against frequency density, with the axis labelled as density.
Why it goes wrong
The diagnosis stays uncertainty-safe.
A wrong response can support a specific measured diagnosis. A blind multiple-choice diagnostic records only a possible cause until later working provides stronger evidence.
01
The error
Plotting frequency up the vertical axis when the class widths differ, which makes the bars proportional to height rather than to area.
02
Why it survives revision
When every class has the same width, frequency and frequency density are proportional — the graph is identical either way. So the method is confirmed by every bar chart a student has ever drawn, and fails only on the one question that changes the widths, which is exactly the question the specification asks.
The worked repair
Repair the smallest broken step.
Teaching is not evidence. This one move is the repair; the proof checks begin after it disappears.
Divide each frequency by its class width and write the density column before drawing anything.
What happens after the repair
Correction is the start, not the result.
Immediate
Asked again straight away, on a different question
The repair leaves the screen and a new authored item checks the method unassisted. Being taught something is never evidence that it was learned, so this is the first stage that counts at all.
Delayed
Asked again after at least 1 day
A parallel form of the same method, unassisted, with the repair no longer on screen. A retest in the same session does not count.
Transfer
Asked again when the surface changes
The transfer form runs it backwards: given the histogram, find the frequency in a part-interval — which needs area read back out, not height read off.
Exam
Asked again under exam conditions
Timed, carrying the mark tariff, in an exam-like response format and aligned to the specification. Any one of those missing and the evidence is refused.
REVIEWED BOUNDARY
This page covers one reviewed family: S3 · Unequal-width histograms. Turn class widths into frequency density, then construct every continuous bar exactly. Other families within the same GCSE Maths topic are outside this reviewed journey, and Studara does not apply the proof label to material that has not been reviewed. No grade-uplift claim is made anywhere on this site.
Straight answers
Before you use this guide.
Why is the y-axis frequency density and not frequency?
In a histogram the frequency is the AREA of the bar. When class widths differ, plotting frequency as height makes the areas wrong, so the graph no longer represents the distribution.
How do I find a frequency from a histogram?
Multiply the frequency density by the class width — you are reading the area back out. For part of an interval, take the matching fraction of that bar's area.
Does Studara guarantee a higher grade?
No. Studara has not run a controlled outcome study and publishes no grade-uplift claim. What has been measured, what is withheld, and the metric that failed its bar are all on the public evidence page.
Turn this method into evidence