Bar Charts and Pictograms

The method, step by step

1. 1

   Read the scale before reading any bar

   gridlines every 2 → a bar at the 7th line is 14

   Scales rarely go up in ones. Counting gridlines and assuming each is one unit is the commonest error in reading charts, and it produces answers that are wrong by a consistent factor across the whole question.

2. 2

   Check the key on a pictogram

   one symbol = 5 people → 3 symbols = 15 people

   The key controls every answer on the chart. Counting symbols instead of applying the key gives 3 rather than 15, and the error repeats for every row, so the whole question is lost from one misreading.

3. 3

   Interpret part symbols proportionally

   half a symbol with key 5 → 2.5

   Pictograms use fractions of a symbol for values between multiples. Reading a half symbol requires the same key, so a half where one symbol is 10 means 5 — a detail worth checking rather than assuming.

4. 4

   When drawing, label both axes and leave gaps

   axis labels, a title, equal bar widths, gaps between bars

   Marks for drawing a bar chart are given for the labelling as much as the bars. Bars must be of equal width and separated by gaps, because the categories are discrete and the gaps say so.

5. 5

   Choose a scale that fits the data

   largest value 46 → scale to 50 in steps of 5

   The scale should reach just past the largest value and use sensible intervals. A scale in steps of 3 or 7 is technically valid and makes every value hard to plot and read, which costs accuracy marks later in the question.

The scale is where the marks are lost

Most errors in chart questions are not about the chart at all — they are about the scale. A student who assumes each gridline is one unit will read every bar wrongly by the same factor, producing a set of internally consistent answers that are all incorrect.

The habit worth building is to work out the value of one gridline before looking at any bar, and to write it down. It takes five seconds and it protects every subsequent answer in the question.

• Find the value of one gridline first
• Pictograms: the key decides everything
• Part symbols scale with the key
• Bar charts have gaps; histograms do not
• Label both axes and give the chart a title

Gaps mean discrete categories

Bar charts have gaps between bars because the categories are separate things — favourite colours, modes of transport, days of the week. Histograms have no gaps because they show continuous data, where each bar covers a range that meets the next.

This is not a stylistic choice. The gap carries meaning, and drawing a bar chart without gaps or a histogram with them misrepresents what kind of data is being shown.

How charts mislead

A vertical axis that does not start at zero exaggerates differences dramatically: two bars of 98 and 100 look like a doubling if the axis starts at 96. This is common in advertising and news graphics and is examined directly.

Students should check the axis origin whenever asked to comment on a chart. 'The scale does not start at zero, so the difference looks larger than it is' is exactly the answer these questions want.

How we teach charts

We ask for the value of one gridline before any question is attempted, written at the top of the working. Nearly all chart errors trace back to that single number, so fixing it first fixes most of them.

We also show a deliberately misleading chart in every course. Students remember the truncated axis far better once they have been taken in by one, and the interpretation marks it prepares them for are among the easiest on a statistics paper.