#### Introduction

Imagine that you regularly go camping and want to build a log cabin for maximum comfort. To make your new home, you’ll have to cut down a bunch of trees. However, an unfamiliar species of owl also makes its home in the trees.

Feeling unsure, you call up the Cabin Construction Company for a consultation. Upon hearing your concerns, they reassure you that it’s fine, citing a graph of the owls’ change in population over the years. Based on the graph, the owls’ population has barely dwindled.

Great! Then, you’re perfectly fine to build your log cabin because they aren’t an endangered species. You happily hire the Cabin Construction Company, as there’s nothing to worry about.

After all, “the numbers don’t lie.” Right?

#### The Revelation

However, the next day, you wake up to a ruckus. Exiting your new cabin, you face a crowd of protestors. They claim that you shouldn’t have cut down the trees and that you’ve hurt the owls.

Confused, you show them the graph from yesterday. In response, they show you another graph of the owls’ population and condemn the other graph for misrepresenting the data.

Despite having the same data points, the two graphs look so different. Your graph made it seem like the owls’ population stayed strong while their graph demonstrated that it was sharply declining. Upon closer inspection, you find that your graph was sponsored by the Cabin Construction Company.

And now, you’ve learned a new lesson - the *presentation* of numbers can be misleading, and sometimes *intentionally *at that.

#### Ways Graphs Can Be Misleading

Presenting data in a way that misleads an audience can be done intentionally or unintentionally. Thus, a graph can only be as accurate as its maker allows it to be. Well-made graphs are the result of meticulous research, presenting the data as it is, and fitting graphing decisions. However, poorly made graphs result from sloppy research, omitting important data points, tampering with axes, and poor graphing decisions.

#### How It Works

Understanding how these factors cause graphs to be misleading is essential for being able to think critically about data that is presented by the media, politicians, and researchers. Here are some key ways graphs can be misleading:

**1. First, there are issues with the study itself.**

Data presentation may be misleading because the study was poorly designed and conducted. When collecting data, carefully considering how it will be measured, and later visually depicted, is the first step. Otherwise, the resulting graph will depict unuseful information and inaccurately portray the research subject, as flawed data results in flawed graphs.

For example, a flawed study on Confirmed (COVID-19) Cases By Region generated a problematic graph that confused readers and gave unhelpful information. The first mistake was using numbers of cases instead of cases per population because raw numbers by themselves don’t tell us that much useful information. Two cities having the same raw number of cases doesn’t necessarily mean that they also have the same severity. The less populated city would be in a worse situation because it would have a higher proportion of COVID-19 cases to population.

The second mistake was setting the upper limit of cases to 101. Thus, they failed to record the very possible instances of COVID-19 cases being higher than 101. Consequently, higher numbers of cases, like 10,000, were wrongly presented as the same severity as 101.

**2. Second, data has been cherry-picked.**

Because a graph consists of many data points, to understand what the data is really saying, you must look at the overall trend. However, people may choose to only present data points that support their agenda rather than show the whole picture. This biased selecting of data is called **cherry-picking**. By zooming in on a particular section of the graph, you can come to a different conclusion from the overall trend, one that is false.

**3. Third, the y-axis has been manipulated.**

People can also misrepresent data by manipulating the graph’s y-axis in at least two ways. The first way is **compressing or expanding the scale of a graph** to make changes in data look more or less significant than they really are.

The second way is **portraying unequal increments as equal**. On a line graph, this will distort the trend line. For example, you can make exponential growth look more linear by skipping values on the y-axis without correctly spacing out the jump.

**4. Fourth, the y-axis is not set to zero. **

Typically, the y-axis of a graph will start at zero. However, **truncated graphs** do not begin at zero, which can make an insignificant change appear much larger than it is. This can lead people to the wrong conclusions about the data. After all, most people will simply accept the information without question and not calculate the actual numerical difference.

**5. Fifth, the wrong type of graph is used.**

While using the wrong type of graph could be an honest mistake, it still causes data to be misrepresented or difficult to understand.

Often misused is the pie chart, which illustrates parts of a whole, allowing for easy comparison of sizes. The issue arises when people try to use pie charts to depict portions that don’t add up to a meaningful whole. For example, putting together answers to *different* questions can result in a pie chart exceeding 100%, which distorts the portion sizes. Another issue is having too many slices to the pie, causing the smaller slices of data to be unreadable. In these cases, a bar graph would be more appropriate.

**6. Lastly, the graph does not follow expected graphing conventions.**

There are standards for how graphs should look and how they should be labeled. While these are not outright rules, people tend to assume that graphs are following them.

One graphing standard is using lighter colors to indicate lower severity and darker colors for higher severity. If you flip the standard, people will get confused. Worse, they may read the graph incorrectly and move on, not suspecting a thing.

Another graphing standard is that numbers should increase as you go up the y-axis and right on the x-axis. Flipping one or more of the graph’s axes will also flip the way the graph should be read. Consequently, people will have difficulty interpreting the graph because it’s formatted in a way they’re not accustomed to.

## Why Care?

Typical math classes don’t teach how real world entities like the media can manipulate graphs to mislead people. We’re also usually busy or distracted, so we don’t often question the information fed to us. Thus, it’s easy to fall for a bad graph. And, falling for bad graphs can lead to poor decision making. Therefore, it’s important to learn how graphs can be manipulated to avoid being misled by them.

Next time you see a graph, make sure to look closer at its axes, taking note of the labels, numbers, and increments. Also, consider if the study’s data is useful and provides a good representation of the research objective. Finally, remember that behind each graph is a person or organization. Think about the motivations and biases they may have, and whether or not these factors have influenced the depiction of the graph.