Section 2.3: Misleading Graphical Representations of Data

Just as with any statistic, graphs can sometimes be misleading. The following section will provide a few examples of the common misleading graphs and give you the means to judge them. Hopefully you will gain insight into how graphs can deceive, intentionally or unintentionally, and you will avoid being misled by graphical misrepresentations of data.

Most often, graphs are made to be misleading by mismanaging the scales of the axes or leaving large amounts of the scale unseen.

Figure 2.28: Associate Degrees Awarded 2019 and 2020

Solution:It is true that more degrees were awarded during the 2018 – 2019 school year. It appears from the bar graph that there were more than twice as many degrees awarded that year as during the 2019 – 2020 school year. But is that correct? The numbers of degrees dropped from 1037 (which really means 1,037,000 degrees) down to 981 (or 981,000 degrees). That is a drop of 56,000 degrees. As a percent, that is a drop of only 5.4%. So why does the small drop look so large in the graph? The problem is that the bars are not in proportion because the vertical axis does not start at zero. The vertical axis begins at 950, so everything lower has been ignored. The result is we see only the top of the bars, and small differences are magnified. A bar graph of the data made using STATBELT Utility is shown in figure 2.29. On that graph you can see that the bars are not as dramatically different as suggested by figure 2.28.

Because the vertical axis now has a scale staring with zero, the two bars are proportionally accurate. There are still more degrees awarded in the year prior to the pandemic, but the difference is far less than the original graph suggested.

Figure 2.30: Crime rate per 100 thousand people.

Solution: This time-series plot suffers from the same problem as the previous bar graph. The vertical axis on this graph does not include zero. This causes the changes in height to appear more drastic. It appears that there was nearly no crime in 2014, at least compared to 1991. But although the rate was lower, it was not as dramatically low as it appears in this graph. Figure 2.31 is a corrected version of the same time-series plot. Comparing, you can see that figure 2.31 is flatter and does not exaggerate the crime rate differences. The crime rate in 2014 correctly appears to be around half the rate of 1991, instead of 10% of it, as it appeared in the first plot.

Figure 2.31: Crime rate per 100 thousand people with corrected vertical axis scale.

Figure 2.32: A problematic bar graph.

Solution:Can you guess what this bar graph represents? The bars are not labeled, so we can tell that the tallest bar is taller than the others, but what does each bar stand for? The vertical axis is labeled, but we don’t even know what the vertical axis represents. Is it percentages? Frequency? There is no way to know. This graph is useless!

Figure 2.33: Issues Americans identify as most important in evaluating the President.

Solution:Look at the vertical scale. Is it marked properly? It appears that the increment between 7 and 10 is the same as the increment between 10 and 28. And the largest increment is between 6 and 7. In short, the scale has been incorrectly marked. Why would someone do that? Most statistical software will automatically create graphs that have correct scales and are proportional. Making misleading graphs takes effort, so you should assume that the creator is attempting to deceive you. In this case, the creator wanted to minimize the impact of the economy and deemphasize the category for “Inequality”. A properly scaled version is shown in figure 2.34. The corrected bar graph (it’s a Pareto chart) contains two additional categories not present in the original graph.

Figure 2.34: Issues Americans identify as most important in evaluating the President, with proper vertical scale.

Figure 2.35: Percent of ethnic groups that suffer from marginal or high levels of food insecurity.

Solution: Here, there is no vertical axis. We can see that the tallest bars are for Black or African American and American Indian or Alaskan Native, but how much taller are they than the others? Did the vertical axis start at zero? What was the scale factor? Was it 1% between the horizontal lines, or 20%? There is no way to correctly interpret this graph. Using the data from the Hope Center, a corrected graph is shown in figure 2.36. Notice that the original vertical scale did not include zero, so differences between categories were magnified in the first graph.

Figure 2.36: Percent of ethnic groups that suffer from food insecurity.

Figure 2.37: Median price of a single-family home in the US.

Solution:Look at the horizontal scale. It appears to be a time-series plot using bars, but the times are not equally spaced. The horizontal categories increase from October 2002 to January 2003 (three months) but then jump to June 2011, a jump of 8.5 years. Then there are several measurements from 2012 through 2014, and then a 7-year gap to 2021. The data were “cherry-picked” to make it appear that housing prices had been stable for many years, until they suddenly spiked in 2021 and 2022. Had data been included between 2014 and 2021, the jump would not have looked so sudden. Figure 2.38 is a correctly scaled time series plot for the median home price since 2012. You can see that the prices have increased, but the spike was not as severe or sudden as it was dramatically shown in the first misleading graph.

Figure 2.38: Median price of a single-family home in the US. Source: DQYDJ

Another common problem with graphs involves pie charts. Occasionally, a pie chart will have percentages that are either not proportional, or do not add up to 100%. Consider the following examples.

Figure 2.39: Favorite Super-Hero Movie Franchise.

Solution: At first glance, the observer would think that Spiderman was the most popular franchise because the dark blue sector of the pie is the largest. But 22% should be less than one-fourth of the pie, so that sector is drawn much too large. In fact, Batman had a popularity of 32%, which should have been the largest sector. Instead, it is not only smaller than Spiderman, but appears to be less then 25% of the pie as drawn. Ironman and Superman had very close percentages at 17% and 18%, but the slice of pie for Iron Man far more than 1% larger. The slices total 100%, but the sectors are out of proportion. Thankfully, STATBELT Utility will create the correct sizes of pie slices without you needing to do anything. Figure 2.40 is a graph with the same data created using STATBELT Utility. The colors are different, but the proportions are correct.

Figure 2.40: Favorite Super-Hero Movie Franchise by STATBELT Utility.

Another common mistake some make is to treat a bar graph as a pie chart. This is a remake of a famous example from FOX News.

Figure 2.41: Remake of a famous FOX News graphic.

Solution:This graph attempted to force data that was appropriate for a bar graph into a pie chart. The problem was that the responders were able to select more than one option. A pie chart can only be used if the sectors of the pie do not overlap. In this case, there were many responders who would have supported all three candidates. So, a bar graph would have been a better choice to display the data. Instead, they created a pie chart that, instead of adding to 100% (as any reasonable pie chart should), instead totals 193%.

Finally, you should always be wary of Pictographs. A pictograph is a picture, intended to be partly entertainment, but that includes numerical information. The intent of a pictograph is not to convey meaningful relationships between categories, but instead to make cute eye-grabbing pictures that will get your attention. Occasionally, they may be created to hide or magnify the importance of a category, idea, or factor.

Figure 2.42: Pictograph of top orthopedic injuries in children requiring hospitalization.

Solution:It’s a cute picture, right? Using crutches for the bars gives the sense that it is like a bar graph. But does the bar include the handle, or just the shaft? It’s difficult to tell. Regardless, the lengths of the crutches are drawn, one would suppose, to make the picture more attractive to the eye. There is no scale provided, so we can’t use the length of the crutches to compare the injury categories. For instance, the crutch for spinal injuries at 5.2% looks like it is too long. Two of them placed end-to-end should result in a crutch that is 10.4% long. But that would appear to be longer than the crutch for thighbone which is 21.7%. How can 10.4% be more than 21.7%? It can look that way if you don’t use a scale!

Two of the spinal crutches should measure 10.4%, but that appears longer than 21.7% for thighbone injuries.

Also, note that the percentages add up to 80.1%, leaving 19.9% of childhood injuries requiring hospitalization unstated. In other words, all other injuries add up to more than all but two of the categories in the graph. This not so much misleading as incomplete.

If a devious person wanted to suppress scales to increase the importance of a small quantity or idea, or to decrease the importance of a large quantity or idea, the use of a pictograph is a perfect solution. Scales are not required or expected, so the creator can make small things as large as they wish or make large things as small as they wish. As a result, you should never trust the graphic nature of a pictograph. The numbers may be accurate, but the graph is usually meaningless, if not misleading.

Additionally, it is important to watch out for pictographs that use enlarged two or three-dimensional pictures to represent a linear relationship.

Figure 2.43: Pictograph of the Gray Wolf population in Greater Yellowstone National Park.

Solution:The graphic provides a vertical scale, showing the population in 2002 at approximately 264. In 2015, the population is approximately 528, or exactly double. The graphic has doubled the height, but the picture is 3-dimensional. The wolf from 2015 is twice as tall as the wolf from 2002 but would be about 8 times the volume because it is also twice as wide and twice as deep. If the smaller wolf weighed 10 pounds, the larger would weigh 80 pounds. Even though we don’t think that when we view the image, we tend to feel it. That is how these types of graphs can mislead. The use of the wolf picture instead of a simple bar graph is attractive but makes the increase in population appear to be more than doubled. A time-series graph or even a bar graph, shown in figures 2.44 and 2.45 would fix the problem. But they aren’t as cute!

Figure 2.44: Time-series plot of the Gray Wolf population in Greater Yellowstone National Park.

Figure 2.45: Bar graph of the Gray Wolf population in Greater Yellowstone National Park.