You’re Being Lied to

Counterintuitive Math

Don’t blindly believe numbers you see. This article is a follow up to a previous article: Lying with Statistics, which demonstrates how in settings such as ads, numbers you see don’t necessarily lie but may be designed to be interpreted in the wrong way. In simple terms, ads lie to you without actually lying for some motive, such as profit. In this article, I will show some examples of counterintuitive math to convince you that what is shown to you may not be the reality.

Fuel Efficiency

Imagine there are 2 people who have a car each. Both travel the same distance using their cars everyday. Person 1’s car has an efficiency of 10 km/L; person 2, 3 km/L. Let’s say their annual income increases and they decide to get an upgrade. Person 1 upgrades to a car with a fuel efficiency of 14 km/L; person 2, 4 km/L.

The question is: Who saves more from this upgrade?

It doesn’t matter who spends more; that’s obviously person 2. We want to know who saves more from the upgrade.

Person 1’s upgrade is better both numerically (4 km/L vs 1 km/L) and percentage-wise (40% vs 33%). Hence, at first, you may think that person 1 obviously saves more from this upgrade than person 2. However, the surprising result is that person 2 saves about 3x more than person 1.

Let’s do the math: say they both travel 100km everyday, and fuel costs 5$ per liter (made-up numbers):

We can see that person 1 saves 15$, while person 2 saves a much bigger 40$. Lowering the fuel prices will lower these numbers, but the proportion of savings 15:40 (or 1:2.66) will stay constant.

This shows us that, even though it seems like person 1 would save more, person 2 ends up saving more than twice as much.

(Note: I got this example from Zach Star’s video, feel free to check it out)

Conclusion

Misrepresenting data is often shown on ads, private firm’s websites, etc. For example, a protein bar company may do an experiment to obtain results to display to customers. If they want to prove that eating the protein bar increases muscle size, they may go to a gym and give 10 muscular people the protein bar, and then record their muscle mass. Even though the bar may not have much of an effect on muscle mass, the mass would be large due to the years of working out, not as a result of the protein bar. Finally, they would show that “people who eat the bar have big muscles”, which is not necessarily false, but is conveyed in a way to make you buy the product.

The purpose of this article was to show you that you shouldn’t blindly believe things. The numbers (as shown by percentages and numerical increase in fuel efficiency) may lie to you and may not represent the whole story. Ads or billboards you see in your daily life do this to convey something false in a way that seems true.