Lesson 27: Identifying Misleading Representations of Data

New Concept

When displaying data, components such as the scale or labels can make a graph misleading.

What's next

Next, you'll examine worked examples showing broken axes, large increments, and incomplete data categories. Soon, we'll practice creating non-misleading versions of deceptive graphs.

Property

When there is a large gap between data values, a graph may use a broken axis. On a graph with a broken axis, the scale on an axis is interrupted, often to avoid showing a large empty space from zero to the first data point.

Examples

• A stock price increases from 102 dollars to 108 dollars. A broken axis starting at 100 makes this 6 dollars jump look like a gigantic leap.
• Website visits go from 10,500 to 11,000 in a month. If the y-axis starts at 10,000, the graph will show a steep, impressive climb.
• A graph shows a company's profit grew from 1.2 million dollars to 1.3 million dollars. Using a broken axis from 1 million makes the growth seem enormous.

Explanation

Think of a broken axis as a visual trick to make a molehill look like a mountain! By chopping out the bottom of the graph, tiny changes suddenly appear huge and dramatic. It’s a great way to make a small increase in sales look like a massive success story, even if the real change was quite small.

Property

Using very large increments for the scale on a bar graph can make the data values appear much closer together than they actually are, minimizing their differences.

Examples

• In a school election, Candidate A got 850 votes and Candidate B got 790. A graph with a scale in increments of 500 would make their bars look nearly identical.
• Comparing phone prices, a 700 dollars phone and a 950 dollars phone seem very different. But on a graph with a scale from 0 to 2000 in 1000 dollars increments, they look close in price.
• One car gets 25 miles per gallon and another gets 40. On a bar graph with a scale from 0 to 100 in steps of 50, the 15-mile difference looks tiny.

Explanation

This trick is the opposite of a broken axis—it makes mountains look like molehills! By using huge steps in the scale (like counting by 500s), you can make big differences between bars seem insignificant. It's perfect for when you want to downplay variation and make everything look calm, steady, and practically the same.

Property

A circle graph can be misleading if its title is not specific or if it does not represent all the available categories, making a partial picture look like the whole story.

Examples

• A pet store sold 10 Poodles, 8 Terriers, and 5 Beagles. A circle graph of just these three types is misleading if the store also sold 40 cats.
• A survey shows student lunch choices: 50 bought pizza and 45 bought burgers. This is misleading if it omits the 100 students who packed a lunch from home.
• A graph shows a library's collection is 40% fiction and 60% non-fiction, but fails to mention this is only for the adult section, ignoring the entire children's department.

Explanation

A circle graph should represent 100% of something, like a whole pizza. This trick is like showing you a pizza box with only the pepperoni and sausage slices left and calling it a 'Pizza'. You're not seeing the whole picture because the veggie, cheese, and mushroom slices are missing! It misleads you by leaving out important data.