Building a bar chart
A bar chart displays a categorical frequency distribution. The horizontal axis lists categories, and the vertical axis shows either frequency or percentage
- Match the vertical scale Label the vertical axis to match the table. For percentage p, use the category count f and total n. \(\displaystyle p=\frac{100f}{n}\)
- Keep categories separate Use one bar for each category and leave gaps between the bars
- Use each category's height The height of a bar is the frequency or percentage for its own category \(\displaystyle \text{bar heights: }4,7,2\)
- Choose a useful maximum Start at zero and use equal tick steps. For a tallest bar of 8, ticks from 0 to 10 in steps of 2 give one step of headroom \(\displaystyle 0,2,4,6,8,10\)
Worked example
A canteen records four snack choices with frequencies 5, 8, 3 and 4. Construct the bar heights on a frequency scale using vertical steps of 2.
- \(\displaystyle 5+8+3+4=20\)The frequencies describe 20 recorded choices in total
- \(\displaystyle \text{bar heights}=5,8,3,4\)Each bar keeps the frequency of its own category
- \(\displaystyle \max(5,8,3,4)=8\)The tallest bar has height 8.
- \(\displaystyle 2\times5=10>8\)An axis maximum of 10 uses equal steps of 2 and leaves one step above the tallest bar
Common mistakes
Difficulty levels
Questions about this topic
When should I use a percentage axis?+
Use percentages to compare shares, particularly for groups of different sizes. State each group’s total and label the axis clearly
Can I put counts and percentages on one shared bar-height axis?+
Not as if they were the same unit. Use a consistent scale or clearly separated displays. The experiment uses percentage bars and a separate count readout
Is changing category order always wrong?+
No. Nominal categories can be reordered while preserving each label’s frequency. Ordinal categories have a meaningful order that usually should be retained
What makes a bar chart different from a histogram?+
A categorical bar chart has separate bars for labels. A histogram uses adjoining numerical intervals; adjacent columns touch, except an empty interval has zero height
Must the tallest bar reach the top of the axis?+
No. Leave a sensible amount of space and use readable equal tick steps. When a question asks for one exact maximum, it must state a rule that makes that answer unique
Can a percentage chart end below 100%?+
Yes, if every bar fits and the axis is clearly labelled. The percentages still refer to the whole group even if no one category approaches 100%
Does the larger count always mean the larger percentage?+
No. Twenty out of 100 is 20%, while twelve out of 40 is 30%. Always use the relevant group total
Why check the zero baseline?+
Bar lengths encode magnitude. Starting above zero can make a modest count difference look much larger, so inspect the scale before accepting a comparison
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 5: Statistics