Numbers Don’t Lie, But People Can

This essay was inspired by a few people’s responses that include how important knowledge of math is.

Why is learning math so important? We can say the easy things like people need to be able to balance a checkbook- something I don’t think I’ve done in at least ten years. Or, they need to learn math because knowing long division is an essential skill. When was the last time you worked out 875,268 divided by 152 by hand? So really, why do we learn it?

There are practical reasons for us to think mathematically. It is a common language among scientists, economists, engineers, architects, store-owners, politicians, doctors, entertainers, mechanics, … Have I missed anyone? 

Calculus is the math that runs everything from behind a curtain. We are exposed to so many things that are best described by the dynamic systems of calculus. Most people don’t know it’s calculus, but it is there in weather forecasting, building design, and navigation like GPS. While the majority of people don’t use it day to day, they are affected by it in every aspect of modern living.

The same can be said for statistics. And it’s this one that scares me the most. We like to say that we are an informed public. But it seems that many times statistics are used to manipulate the public. There is a famous quote attributed to Mark Twain from his autobiography (1907), but he cited Benjamin Disraeli, though it probably came even earlier in 1891 from Sir Charles Dilke. (Researching this took me down a deep rabbit hole!) The quote is:

“There are three types of lies: lies, damned lies, and statistics.”

Statistics are used a great deal in trying to sway a voter or a consumer in a group’s direction. Examples are:

Cherry-picking data- This is selecting only numbers that support an argument while ignoring the rest. This could be as simple as asking 20 dentists about their favorite toothpaste. Four say it’s Don’s Natural Mint and the other sixteen say baking soda. If I select just five of those responses, I can “honestly” say, “Four out of five dentists prefer Don’s Natural Mint Toothpaste!” And four out of five sounds more credible than five out of five.

Another place we see the cherry-picking of data is with the argument over Global Climate Change. From 2018-2021 some areas of the US had severe winter cold snaps. People disputing human-caused climate change presented this as evidence that there should be no concern about mitigating global climate change and specifically diminishing our fossil fuel use.

Critics of climate change policies don’t take things like continental and global average temperatures into account. They refer only to local phenomena. They won’t mention heat waves in other areas. There is no mention of long-term trends. The problem is that climate change cannot be measured in a few years or seasons. It is a long term observation taking decades of data. They chose the data that would support their argument without paying any attention to all the other measures that point away from their desired conclusions. Statistics cannot be anecdotal.

Dr. Charles Keeling (1928–2005) was an American climate scientist and chemist who pioneered long-term measurements of carbon dioxide (CO₂) in Earth’s atmosphere. He was one of the first scientists to develop continuous, high-precision atmospheric CO₂ measurements that were both systematic and sustained over decades. His work fundamentally changed how scientists understood the global carbon cycle and the human influence on Earth’s climate. 

Keeling first proposed world-wide monitoring of atmospheric CO₂ when it was suspected that these levels were rising due to the burning of fossil fuels. One monitoring site he chose was the top of Mauna Loa Observatory in Hawaii. It is above local vegetation and remote, so this ensured the air sampled would not be as affected by local sources. 

This site has been collecting data of the concentration of atmospheric CO₂ since 1958. Here it is as of January 5, 2026. (https://keelingcurve.ucsd.edu/)

Looks pretty straightforward in that the amount of CO₂ has increased fairly steadily the whole time. It started at 318 ppm (parts per million) and on Jan 5, 2026 it was 428 ppm. One can assume that a change to one thing will probably affect other things and therefore should be alarming. Climate scientists refer to the increase of atmospheric CO₂ as a leading cause of global climate change. This includes:

1. Rising global temperatures and heat extremes
2. Melting ice and rising sea levels
3. More intense and shifting weather patterns
4. Ecosystem disruption and biodiversity loss

But really what is the difference of about 100 parts per million in a mixture? If I had a million dollars and found a $100 bill in a drawer I wouldn’t really consider myself that much richer. But notice what I just did. I compared the increase in CO₂ with the entire atmosphere instead of comparing it with the amount of CO₂ that was already there. 

How could this little change cause all that the scientists are observing? Again, let’s not cherry-pick the data. Don’t compare the CO₂ to all the different types of particles in the air. Compare it to the usual amount found. Now a change of 100 ppm is very important! It’s about a 35% increase from the 1958 levels.

Compared to other gases, the amount of CO₂ is tiny. Nitrogen is 780,800 ppm, oxygen is 209,500 ppm, argon is 9,300 ppm. While nitrogen and argon carry heat and energy, they aren’t directly involved with the Greenhouse Effect like CO₂ and water are.

The Keeling Curve can be expanded by measuring the atmospheric CO₂ from earlier times. This is done mainly by getting air bubbles trapped in Antarctic ice. An ice core sample from there is a record of the atmosphere through time. Through other means we can reliably estimate the concentration of CO₂ going back 70 million years. The graph for the past 10,000 years looks like this:

The amount of CO₂ now seems a great deal more alarming. Even looking back over 800,000 years, the concentration has never been more. This is the trend we need to look at, not how cold it was last year.

Misleading percentages / relative risk- One can make things seem a lot more dangerous, or a lot safer than they actually are. As an example, there are many people who are afraid of swimming in the ocean because of the possibility of a shark attack or even a jelly fish sting.

In the United States less than 1 person per year dies of a jelly fish sting, so let’s compare deaths by shark encounter (they really don’t attack people) to the old standby, death by vending machine. This is the usual statistic when people try to stress how unlikely a shark attack is.

Vending Machine deaths = ~10–15 people / year

Shark Encounter deaths =  ~0–1 people / year

Even if we take the best case from vending machines (10 people) and worst case from sharks (1 person), this means ten times as many people die from trying to get a bag of chips as would swimming in the sea! 

This assumes the same size and populations are assuming the same risks. But that is not true. Vending machines are found everywhere in the US while sharks are only found in the oceans. So you really don’t have to worry about sharks if you are visiting Nebraska!

So maybe we equalize things by only counting vending machine deaths that occur at the beach? Or, another example might be comparing shark encounters with what else might kill you at the beach. Jelly fish are already out. How about falling coconuts?! It was once thought that about 150 people per year died because of falling coconuts. That turned out to be an urban myth initiated by a small study done in 1984 that got extrapolated out. While I encourage you to not sit under a coconut tree, there is still a small chance of you dying there.

So maybe we equalize things by comparing the risks people actually face when they go to the beach. Driving there certainly seems more dangerous than sharks. But now I’ve created another statistical problem. How many people drive to the beach? How far do they drive? How often? How many traffic deaths actually occur during trips to or from beaches? Without knowing those numbers, I can’t calculate the relative risk. I can make the numbers sound convincing, but I can’t honestly make the comparison.

And wear sunscreen! Each year in the US there are ~8000 deaths attributed to melanoma (skin cancer). 

Manipulating graphs / visual distortion- Graphs and charts are wonderful ways to display data in a form that allows us to see trends quickly. Alas, they can also be manipulated to make you see trends that may not be as straightforward as you think.

Here is a bar graph comparing the highest and lowest batting averages of starting Red Sox players so far this year (2026).

It looks obvious that Rafaela is a demonstrably better hitter than Rutschman. At least this is what you see if you start the y-axis at 0.23. If the axis started at zero, the graph looks like this:

Now the difference isn’t so large. Both graphs have exactly the same data shown, but if you were Rafaela’s agent, you might use the first graph when negotiating his next contract. Rutschman’s agent would most likely use the second graph. 

For every 100 at bats, Rafaela would average 29 hits while Rutschman only averages about 24.

Confusing correlation with causation- Just because the graphs align doesn’t mean one was caused by the other. Looking at these graphs of ice cream sales and drownings for a year shows a strong correlation, but no causation. A third variable explains both—it’s hotter in the summer. More people buy ice cream, and more people go swimming.

So why not use this argument with climate scientists when they compare increased atmospheric CO₂ to average global temperatures? This graph shows a strong correlation, but that is not enough! 

The alignment with causation is supported by understanding the infrared absorption abilities of CO₂, climate modeling, paleoclimate records, and energy-balance measurements. There has to be a lot more done to ensure that the correlation is not coincidental and is actually caused one by the other.

So why bother?! The majority of the public gets its news and information in small, curated reports. While the news is on 24 hours a day, there is little deep reporting/understanding. Much of what reaches us comes in sound bites, headlines, clips, and social-media posts.

The general audience doesn’t have the time or resources to research everything that is presented to them as fact. Our responsibility is to call the politicians, news agencies, and special interest groups on it when we see things being presented in an unobjective and manipulative way. Most people inherently trust math. We need to be more critical and aware of the goals some groups have in swaying our decisions.*

*I tried to make this as apolitical as I could. It was tough!