Constructing clear, accurate graphs

Turn a dataset into a representation that another person can read and check.

Lesson 04 · Statistics
Your learning goal

Construct a graph with accurate values, a suitable scale, meaningful labels and a defensible graph type.

Plan before you plot

Write the question and choose a graph type. Identify categories or the independent numerical variable for the horizontal axis, and the quantity being compared for the vertical axis. Choose a title that names the subject and context. ‘Lunch orders, Friday’ is more informative than ‘My graph’ and more neutral than ‘Everyone loves pizza’.

Use equal numerical intervals

Choose a scale that includes every value and is easy to read. Equal distances must represent equal changes: 0, 5, 10, 15 is valid, but equally spaced marks labelled 0, 5, 20, 25 are not a uniform scale. On a bar graph, a zero baseline allows the full lengths to represent the values. If a display truncates the axis, make that visible and avoid interpreting bar-length ratios as value ratios.

Make bars and points mean what you intend

Use equal bar widths and consistent gaps for categories. Place points at the correct numerical coordinates. Keep time spacing proportional when intervals differ. Use labels or a legend in addition to colour so the graph remains understandable in greyscale. Distinguish zero from missing data: no observation is not the same as an observed value of zero.

Check the graph against the source

Read each plotted value back from the graph and compare it with the source table. Check totals, percentages, units and category names. For a circle graph, divide each part by the whole and multiply by 360° for its angle. Rounded displayed percentages can sum to 99.9% or 100.1%; explain rounding rather than secretly changing the original values.

Explore · predict, test, explain

Make your thinking visible.

Graph Lab

Enter one label and value per line, separated by a comma. This tool supports 2–12 non-negative values. The table and graph always use the same data.

Line graphs use equally spaced positions here: use observations at equal time intervals. Do not use a line to connect unrelated categories. Circle graphs require a positive total.

Worked examples

Follow the reasoning.

Choose a useful vertical scale

  1. Recorded counts are 12, 18, 25 and 22.
  2. A vertical axis from 0 to 30 with an interval of 5 includes all values.
  3. Plot the bar for 12 between the 10 and 15 gridlines, not on the 10 gridline.
  4. Label the vertical axis ‘Number of orders’ and the horizontal categories by name.

Build a circle sector

  1. There are 8 salad orders out of 50 orders.
  2. The share is 8 ÷ 50 = 0.16, or 16%.
  3. The sector angle is 0.16 × 360° = 57.6°.
  4. Check all sector angles total 360° before judging the finished circle.
Guided Practice

Build an explanation.

Your values are 14, 21 and 28. Suggest an axis maximum and interval.

Give me a hint

Choose an easy scale with enough space for 28.

Compare a worked response

A maximum of 30 and interval of 5 work. A maximum of 40 and interval of 10 also work, though smaller differences are less prominent. Explain the choice using readability.

The table has no observation for Wednesday. Should you plot a zero?

Give me a hint

A zero states that something was measured and found to be none.

Compare a worked response

No. Mark the value as missing and explain why if known. Do not invent an observation or connect a gap in a way that implies measurement.

Independent Practice

Test the idea, then check your reasoning.

Feedback explains your chosen response. These activities are practice, not a school mark.

1. Which equally spaced axis labels form a uniform scale?

2. A category has 15 of 60 observations. Its circle sector should be…

Connections

Use it beyond this page.

Use Graph Lab to build a graph, download the SVG and compare it with your data table. Add the exported graph to your assigned work in Google Classroom.

Take it further

Create two defensible scales for the same dataset. Explain how each choice affects detail and visual emphasis without changing the values.

What are you curious about?

Search lessons, class notes and interesting questions.