Reading a Graph Honestly

A brief note on Reading a Graph Honestly, with a checklist for reading any graph. Try each question at the end before you open its answer.

Tables first

• A frequency table lists each value and how many times it appears.
• The relative frequency is the frequency divided by the total. As a percentage, the shares add up to $100\%$.
• Use shares, not counts, to compare surveys of different sizes.
• Numbers with many values go in groups that do not overlap.

Which graph?

• Categories, to compare: bar chart, with gaps
• Shares of one whole: pie chart: angle $= \dfrac{\text{frequency}}{\text{total}} \times 360^\circ$
• Numbers in groups: histogram, bars touching
• Change over time: line graph

The checklist

1. Read the title and the labels. What is measured, and in which unit?
2. Look at the numbers on the axes. A bar chart should start at zero.
3. Look at the spacing. Equal steps on an axis must be equal amounts.
4. Ask if the graph fits the data. A line joining categories, or a pie chart over time, is wrong.
5. Ask how many were counted, and how they were chosen. A small or biased sample makes any graph weak.

A worked example

Two teams score 52 and 50 points. A chart draws them with its axis from 49.

1. What the eye sees. Above 49, the bars are $52 - 49 = 3$ and $50 - 49 = 1$ tall. Team A looks three times as good.
2. The truth. The gap is 2 points out of about 50, a difference of $4\%$.
3. The fix. Start the axis at 0. Then the bars look almost equal, which is the truth.

Practice with new numbers

A program to try

The program draws the worked example twice, once from 0 and once from 49.

Mistakes to avoid

• Judging a bar by its height without reading the axis.
• Comparing counts from surveys of different sizes. Compare the shares.
• Using a pie chart for change over time. A pie chart shows shares of one whole.
• Joining categories with a line. A line suggests a trend that is not there.

Check yourself

1. A bar chart has an axis from 49 to 53, and bars of 50 and 52. How is a reader misled?

2. A newspaper shows the temperature on each day of a week as a pie chart. What would be better?

3. A report says that $80\%$ of students like cricket. Later you find that five students were asked. What would you say?

4. In a survey of 160 people, 56 chose rice. What is the angle of the rice slice in a pie chart?