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Featured Article: “Air Travel Surges by 123%! (Beware of Misleading Data Like That)” by Neil Irwin

On Feb. 28, the stock market had its largest loss since the 2008 financial crisis. By April 11, more than 22 million Americans had lost their jobs. By May 27, 100,000 Americans had died from Covid-19. Note that these are all counts, not percentages.

And the airline industry? In a typical year, April and May have, on average, about 2.4 million air travel passengers per day. But, for the week ended April 17, 2020, the count was only 95,161 per day. The week ended May 17, the count was 212,580 per day. The May count was only a slight recovery, but the percentage change makes it seem like a surge. The headline “Air Travel Surges 123%!” is accurate, but is it misleading?

In this lesson, you will learn that even when percentage change is calculated accurately, it may give misleading impressions. This happens especially when the data values vary significantly. With these insights, you will better know when it is appropriate to use percentage change to describe growth and when it may be better to use counts to describe change.

The May 20 article begins:

Did you hear about the booming air travel industry? It’s up 123 percent in just the last month!

Technically, that’s an accurate number. Over the seven days ended Sunday [May 17], an average of 212,580 people went through U.S. airport security checkpoints, up from 95,161 in the week ended April 17.

How did the article’s authors come up with the 123 percent statistic? What is the math they used? (If you’re not sure, then see below.) Is the statistic accurate?

For background, remember a typical year when there isn’t a pandemic keeping people from traveling, the months of April-May have, on average, about 2.4 million air travel passengers per day.

With that in mind, is the 123 percent statistic misleading? Why?

Who might want to use a statistic like that? Who might not?

Read the article, then answer the following questions:

1. The article states that growth rates (percentages) or levels (counts) can both be accurate. However, when there are big swings in data, the growth rates can be misleading. According to the article, how could politicians use the difference in growth rates and levels to their advantage?

2. The authors state: “When something falls by 10 percent and then rises by 10 percent, it might seem as if it ends up back where it started. But that’s not how the math works.” Calculate where it ends up. Why doesn’t it end up back where it started?

3. The headline of the print version of this article is “Air Travel Surges 123% (Beware a Data Yo-Yo).” Describe the yo-yo that is referred to in that headline. This excerpt from the article may help you:

A 10 percent drop from 100 to 90, followed by a 10 percent gain, would return it only to 99. With bigger swings, those effects become more striking. A 40 percent drop followed by a 40 percent gain would result in a quantity 16 percent below the starting point.

At even greater extremes, you end up with bonkers numbers like those in the air traffic example, in which a 96 percent drop followed by a 123 percent gain leaves you with a number that is still 91 percent below normal.

Use 100 as your starting point. Apply the air travel percentage changes to confirm the 91 percent below normal “yo-yo” effect. What in the arithmetic makes the “yo-yo” effect happen? What should be reported in an article to clarify what is really happening to air travel?

4. The article concludes with some advice: “more than anything, it means thinking carefully about what a given number really means, and not just taking a seemingly breathtaking percentage change at face value.” What do you think it means to not take a “breathtaking percentage change at face value”?

1. Create your own example of misleading percentage changes.

We can see the misleading effect of using percentage changes with this very simple example. Suppose there are two students. Chris has a grade of 10 and Alex has an 80. Let’s say that the teacher decides to give students 10 more points to celebrate the end of the school year. Alex thinks that’s fair until Chris brags about a grade that has increased by 100 percent. What happened here? Why can percentages that are calculated correctly sometimes be misleading?

The above example illustrates how it’s easier to show a big percentage change in grades when grades are low than when they are higher. Create your own example when this happens that relates to something in your life, like sports, your job pay, shopping or anything else.

2. Identify the best measure of percentage change to demonstrate what is taking place in the airline travel.

When comparing the daily average air travel for the weeks ending in April 17 (95,161) and May 17 (212,580), the article correctly stated the increase as 123 percent (((212,580 – 95,161)/95,161) x 100 = 123%). Rather than calculating the percentage change in the amount of daily air travel between two weeks during the pandemic, let’s calculate the change from before the pandemic. The months of April-May have a daily average of about 2.4 million passengers.

What was the percentage change from the typical average of 2.4 million passengers per day to the April 17 count and to the May 17 count? Compare these two percentages to the headline’s 123 percent. Explain which better reflects what is happening in the airline industry.

3. Identify the best measure of percentage change to demonstrate what is taking place in the economy.

Read in the article, starting with the paragraph “When it comes to gross domestic product…,” about how reporting changes in the gross domestic product (G.D.P.) can be misleading. (G.D.P. is a measure of the size of the economy and is the sum of the prices of the goods and services produced in a country during a period of time.)

Why would some prefer to express changes in G.D.P. by growth rate from quarter-to-quarter? Why would others prefer to express changes in G.D.P. by comparing this quarter’s G.D.P. to the G.D.P. from the same period last year? Which measure better reflects what is happening to the economy?

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