A bar chart displays discrete or categorical data (shoe sizes, favourite colours, goals scored) using bars whose height is proportional to frequency. Four rules are non-negotiable: all bars have equal width; there are equal gaps between bars (showing the categories are separate, not continuous); the frequency axis starts at zero (a non-zero baseline exaggerates differences and misleads the reader); and every axis plus the chart itself has a clear label and title.

The mode is the category with the tallest bar — not the height itself. The total frequency is the sum of every bar's height, needed as the first step in most multi-part questions.

Example: sales were Paperback 12,000, Hardback 5,000, Audiobook 3,000. Total $=20{,}000$. Percentage that were audiobooks: $\tfrac{3000}{20000}\times100 = 15\%$.

The most frequent confusion is treating a histogram's bars like a bar chart's — reading height instead of area, which is only equivalent when class widths are equal. A bar chart should never be drawn with touching bars, and a frequency polygon should never be drawn with a freehand curve or closed shape.

A survey of favourite ice cream flavours gave: Vanilla 8, Chocolate 12, Strawberry 5, Mint Choc Chip 3.

(a) State the mode. (b) Find the total number of students surveyed. (c) What percentage chose Strawberry?

(a) The tallest bar is Chocolate (12), so the mode is Chocolate.

(b) Total $= 8+12+5+3 = 28$ students.

(c) $\dfrac{5}{28}\times100 \approx 17.9\%$ (1 d.p.).

If the frequency axis doesn't start at zero, the bar heights no longer scale honestly with the data — a small real difference can be stretched to look enormous. Examiners sometimes show a "broken axis" chart and ask you to explain why it's misleading; the correct answer is always that the vertical scale doesn't begin at zero, so the visual comparison between bars is distorted even though the numbers themselves may be labelled correctly.