Lesson 8 of 8 · Grades 3 to 5
Making a good graph
Anyone can draw bars. A good graph is easy to read and honest: it has a title, a numbered scale that starts at zero, equal steps and bars that match the data.
Easy to read and honest
Two graphs can show the same data and still be very different. One can be clear at a glance, while the other hides the numbers or makes a small difference look huge. A good graph follows a short set of rules, and every rule has the same purpose: to tell the truth about the data.
Give the graph a title. Label the scale. Start the scale at zero. Use equal steps and equal gaps. Make the bars the same width, and make every bar match its number.
A good graph
This graph shows books read by three classes. The title says what the graph is about, the scale is numbered and starts at zero, and each bar ends at a value printed above it.
Show the data as a table
| Class | Books |
|---|---|
| 3A | 8 |
| 3B | 6 |
| 3C | 10 |
A reader can tell at once that class 3C read the most books and class 3B read the fewest. If a friend asks how many books 3B read, the top of its bar leads to the scale and to the printed 6.
A graph with a hidden scale
Now compare the same three bars without any numbers on the scale. The shapes are the same, but the reader cannot tell 6 from 60.
Show the data as a table
| Class | Books |
|---|---|
| 3A | 8 |
| 3B | 6 |
| 3C | 10 |
A graph without a scale can still show which bar is tallest, but it cannot answer "how many?". That is why the numbered scale is not decoration. It is the part of the graph that turns a shape into a number.
Why the scale starts at zero
Suppose a graph starts its scale at 6 instead of 0. A bar of 7 would be drawn only a little above 6, while a bar of 10 would be four times as tall as it should look. Starting above zero makes small differences look big, so a careful graph always begins the scale at zero.
The steps must be equal, too. If one step means 5 and the next means 20, the bars no longer match the data. Bar widths stay equal as well, with equal gaps between them.
Checking a graph against its data
Before you trust a graph, compare it with the table it came from. The table is the raw data, and the graph is a picture of it. If the table says 9 books but the bar ends at 5, the graph is wrong and the table wins.
When you build your own graph, work in this order: write the title, choose a scale that starts at 0 and reaches the largest value in even steps, draw equal bars, and label each bar with its category. Then read the graph back as if you were a stranger. If every value is easy to find, the graph is ready.
Worked example
The table shows goals scored by four teams: 4, 9, 6 and 2. A friend offers two scales for a bar graph: 0 to 4 in steps of 1, or 0 to 10 in steps of 2. Which scale should you use, and what is its top number?
Step 1: find the tallest value in the data. It is 9 goals.
Step 2: test the first scale. A top of 4 is below 9, so the tallest bar would run off the graph.
Step 3: test the second scale. A top of 10 is at least 9, and it starts at 0 with equal steps of 2.
Step 4: check that the steps stay equal and the scale does not stretch far above the data. The 0 to 10 scale works, so its top number is 10.
Answer: The 0 to 10 scale, with a top of 10.
Watch out for this
A missing title or a missing scale turns a graph into a puzzle. A scale that starts above zero exaggerates small differences. Both mistakes are easy to avoid and both change what a reader believes about the data.
Remember
- Give the graph a title that names the data.
- Number the scale and start it at zero.
- Keep the steps, the bar widths and the gaps equal.
- Make every bar match its value, and check the graph against the table.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
-
What number should the scale of a good bar graph start at?
Show answer
0. Starting at zero keeps the bar heights honest.
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The tallest bar in a graph is 12. Which is the best top for the scale: 5, 12 or 100?
Show answer
12. The scale must reach the tallest bar, and it should not be much bigger.
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A scale shows 0, 5, 10 and 15. How many units does each step show?
Show answer
5 units. Each number is 5 more than the one before.
-
A table says 8 books, but the bar is drawn at 6. How many books is the bar short?
Show answer
2 books. 8 - 6 = 2.
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Four bars have values 4, 8, 6 and 10. Which is the best top for the scale: 6, 10 or 20?
Show answer
10. The tallest bar is 10, so the scale must reach 10.
Puzzle · Spot the good graph
Puzzle time
Three children made a bar graph of the same data: 8, 6 and 10 books. Graph A has a numbered scale and bars that match the numbers. Graph B has no numbers on the scale. Graph C has numbers, but its bars do not match them. Which graph can you read correctly?
Show a hint
A good graph needs both a numbered scale and bars that match the data.
Show the answer
Answer: Graph A. Graph A has a numbered scale starting at 0 and bars that match the values. Graph B has no numbers, so no value can be read from it. Graph C draws its bars at the wrong heights, so it is not honest.