Construct a histogram
Use a labelled numerical axis and match every height to the chosen vertical scale
- Horizontal axis Use a numerical scale with equal widths and put each column over its own interval
- Vertical axis For these equal-width classes, use frequency or percentage frequency as labelled. Do not use cumulative totals as column heights
- Empty classes A zero-frequency class has height zero but keeps its place and width on the axis
- Check the result Label axes and units, start the frequency scale at zero, and compare every column with the table
Worked example
Draw an equal-width frequency histogram for time intervals 0–<10, 10–<20, 20–<30, 30–<40 minutes with counts 4, 6, 0, 8.
- \(\displaystyle \text{boundaries}:0,10,20,30,40\)Use equal spacing on the horizontal axis
- \(\displaystyle \text{heights}:4,6,0,8\)The third class is empty but retains its width
- \(\displaystyle y_{\min}=0\)Label both axes and check each column against the table
Common mistakes
Difficulty levels
Questions about this topic
Is an empty column a gap error?+
No. A zero-height class is legitimate. Arbitrary spaces between positive-height columns are different
What if the tallest column is on a tick?+
Follow the exact request. If it asks for the first tick strictly above, choose the next tick
Must all histograms use frequency height?+
No. Percentage frequency is also common; unequal class widths can require frequency density
Where do integer-score columns go?+
Centre each unit-width column on its score, with half-unit boundaries
Does the app grade my full drawing?+
Selected heights and graph recognition are automatically marked. A complete drawing and justification need self or teacher review
Does a wider column prove that more observations were collected?+
No. Regrouping combines old classes without changing the sample. Check the total count before making a claim
How should I compare histograms for different sample sizes?+
Use common class boundaries and consider percentage frequency to compare relative distributions. Check centre, spread, shape and outliers, not just the tallest column
Is there one required vertical-axis maximum for every histogram?+
No. Several readable scales can work. Practice questions that ask for one numerical answer state an exact rule, such as the first marked value strictly above the largest height
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 11, VCE Units 1 & 2, General Mathematics, chapter 2: Data distributions