We have all been there, sitting in a college class where a professor is writing down a collection of formulas on the board, asking us to memorize it “because that is what is going to be on the test”—caring mostly about grades, even if I enjoy the subject, because that is how students are evaluated! One such class for me was statistics.
When I think about stat classes, I remember a board full of numbers and statements like: calculate the mean, find the median, work out the standard deviation, draw a graph, or report the p-value.
And then, somehow, we are expected to look at a dataset and understand what it is telling us. I must admit that last part is where the fun is, but it is not how structured classes present statistics.
So, when I started learning on my own and found joy in figuring out the story behind the data, I found statistics very fun. Because knowing how to calculate a statistic is not the same as understanding what the statistic means. And in a world where we are constantly surrounded by numbers, graphs, percentages, polls, studies, and “data-driven” claims, knowing how to interpret data can help you avoid misinformation.
That is why I am writing this article: to better explain 10 things about statistics that often get lost somewhere between the equations and the exam questions.
1. The average isn’t always the “average”
Let’s start with one of the most familiar words in statistics: average. We often use “average” and “mean” interchangeably. Technically, however, average is a broader, informal term, whereas mean is one particular way of describing the center of a dataset.
Let’s take an example: imagine five people earn: 25k, 27k, 29k, 31k and 33k.
If we consider those particular five numbers, the mean is £29k. Everything looks fairly sensible. But what if we change the highest-earning person’s salary to 500k? The mean suddenly becomes £122.4k.
The question now is, did the “typical” person suddenly become a six-figure earner? You will probably answer, of course not. I would argue that, though the calculation is correct, the interpretation is not.
This is why we need to understand what the mean is actually doing. It takes the total of all the observations and divides it equally among them. The mean is therefore particularly sensitive to extreme values.
That is where the median comes in! It gives us a different perspective. Put the observations in order and take the middle one. The median is 29k in both examples!
If we consider the numbers as absolutes, both numbers are statistically “correct,” but they are answering slightly different questions, which is the point of this article.
The mean asks:
If the total were distributed equally, what would each observation get?
The median asks:
What value sits in the middle of the ordered data?
And sometimes that difference is the entire story! This is why you will often see house prices, salaries, and wealth reported using the median rather than the mean. A small number of extremely large values can pull the mean dramatically upward.
2. A number without its distribution can be misleading
Statistics also teaches us to compress information. If we are given datasets with millions of entries, we will need to compress them into a couple of representative numbers to communicate them easily. Though this is useful, it is also dangerous.
Suppose two classes both have an average exam score of 70%. From that alone, we assume they performed similarly. Which is a fair assumption, but not always a correct one. What if the scores look like this:
Class A: 65, 68, 69, 70, 71, 72, 75
Class B: 30, 50, 65, 70, 75, 90, 110
Both could have a mean around 70. But these are clearly not the same dataset.
The first class is tightly clustered, while the second is much more spread out, and considering only the average hides the shape of the data.
This is one of the most important habits you can develop when reading statistics: don’t stop at the summary statistic; that is not enough! We also need to consider the distribution, outliers, spread, and number of observations. A single number summarizes the data. It is not the data itself.
3. Variables don’t exist in isolation
This is where statistics becomes much more interesting, and much easier to misuse.
Suppose a study finds that people who drink more coffee report higher levels of stress. Most people would immediately think: Coffee causes stress! But, but, that is not really what the study says.
Perhaps people who work longer hours drink more coffee and experience more stress. In that case, working hours could be a confounding variable. Or maybe people who are already stressed drink more coffee.
Now the story of the relationship is different! Say, the type of job someone has influences both coffee consumption and stress.
The point is that observing two variables moving together doesn’t automatically tell us why they move together. This is one of the easiest mistakes to make when looking at data.
The missing question is: What else could explain this relationship?
That question is often more valuable than the calculation itself.
4. Control variables aren’t just a technical detail
When researchers try to understand relationships between variables, they often try to account for other variables. This is where ideas such as control variables, confounders, and stratification become important.
Imagine we discover that people who exercise more tend to report better mental wellbeing. Sounds straightforward! But age might affect both exercise habits and wellbeing! Or income might affect access to gyms, free time, and healthcare! Or existing health conditions might affect both exercise and wellbeing.
The more variables we consider, the more complicated the analysis becomes. But that complexity is not necessarily a problem. In fact, sometimes simplifying the story is the problem. Real-world data rarely comes with a neat label saying:
“Here is the one variable responsible for everything.”
Good statistical thinking means being suspicious of overly simple explanations.
5. Correlation is not causation, but the problem is deeper than that!
We all hear “Correlation does not imply causation”; it is probably the most repeated sentence in introductory statistics (and news articles!) But simply memorizing it isn’t enough. We need to ask why correlation does not establish causation.
Consider the famous ice cream sales and drowning deaths statistic. We know that logically, buying ice cream doesn’t cause drowning. We also know that temperature and season are influencing both. This is a simple example of a confounding variable.
But causality can be much harder to point out. Sometimes A affects B, sometimes B affects A, sometimes A and B affect each other, and sometimes a third variable affects both. Sometimes the relationship disappears entirely when the population is divided into meaningful groups.
Or, often the case, we don’t have enough information to know, which can be slightly uncomfortable. But “we don’t know” is a legitimate statistical conclusion.
6. Your brain wants to confirm the story you already believe
This might be the most important statistical lesson of all. We don’t approach data as blank slates. We have opinions, experiences, political beliefs, assumptions, expectations, and stories we have heard before.
And once we have a hypothesis, we naturally start looking for evidence that supports it. This is known as confirmation bias.
Imagine someone tells you:
“Young people don’t read books anymore.”
You might see a group of teenagers looking at their phones and think, Exactly. But that’s not evidence of the original claim. You have selected one observation because it fits the story you were already given.
A better approach is to ask: What data would change my mind? That is a surprisingly a very difficult question! If you cannot think of an observation that could convince you that you are wrong, you are no longer testing a hypothesis… you are defending a belief.
7. Read the graph before reading the conclusion
Graphs are particularly good at exploiting our assumptions. A graph can be technically accurate and still give you a misleading impression. Because that is used often in presenting data, whenever I look at a graph, I ask myself:
-
Does the y-axis start at zero?
-
Is the scale linear?
-
Are the intervals equal?
-
Is the graph showing absolute numbers or percentages?
-
How large is the sample?
-
What is being compared?
-
What has been left out?
This is important because you often read article titles that say something like “Cancer risk doubles after drinking X!”, which makes you think “Doubles” sounds enormous.
But suppose the original risk was 1 in 1,000 and increased to 2 in 1,000. Though that is a doubling, is it also an increase of 1 percentage point per 100 people? No, it is actually an increase of 0.1 percentage points.
The wording hasn’t necessarily lied, but the framing can dramatically change how we perceive the result. This is why relative risk and absolute risk should never be treated as interchangeable.
8. Sample size matters — but bigger isn’t automatically better
Another statistic we tend to treat as a magic number is sample size. “It’s based on 100,000 people!” sounds more convincing than “it’s based on a 1000 person” but a large sample can still have a poor conclusion if the sample is systematically biased.
Imagine asking 100,000 people who own electric cars:
“Do you like electric cars?”
You may get a very reliable answer about electric-car owners. What you haven’t learned is… what the entire population thinks.
This is a question of sampling. Who was included? Who wasn’t? How were they recruited? Were people randomly selected? Did some groups have a greater chance of participating? Did people with particularly strong opinions respond more often?
A huge biased sample is still biased, and how those observations were obtained matters just as much.
9. Statistical significance doesn’t necessarily mean practical significance
Here’s another trap. Let’s assume a new teaching method increases average test scores from 72.1% to 72.4%. With a sufficiently large dataset, that difference might be statistically significant.
The question now is, should we care? Maybe. Maybe not.
Statistical significance is broadly about whether an observed difference is unlikely to have arisen under a particular statistical model or null hypothesis. It doesn’t automatically tell us:
-
whether the effect is large,
-
whether it matters in practice,
-
whether it is useful,
-
whether it is worth the cost,
-
or whether you would notice the difference in real life.
A statistically significant result can be practically meaningless; and a result that fails to reach statistical significance is not necessarily evidence that “nothing happened.”
The study did not have enough information for us to see the separation of the effect from noise. So, again, the number alone isn’t the conclusion.
10. Learn to ask what isn’t in the dataset
Perhaps the most underrated statistical skill is knowing what the data cannot tell you. If we have a dataset that contains:
-
age
-
income
-
education
-
location
-
employment status
You can analyze relationships between these variables fairly easily…But what about motivation? Family circumstances? Personality? Access to opportunities? Historical events?
Things that weren’t measured cannot magically appear in the analysis… I know what you are thinking: this sounds obvious, but it is surprisingly easy to forget.
A statistical model can only work with the information you give it. And sometimes the most important variable is the one you didn’t collect.
The next time you encounter a statistic, study, or impressive-looking graph, don’t ask:
“What does this prove?” Instead, ask: What exactly is being measured? How was it defined? What is the population? How was the sample selected? Who might be missing?
Try to see if it answers what the summary statistic actually means. Where are the clusters? How spread out is the data? Are there unusual observations? Could there be confounding variables?
But most importantly, ask what the data does not tell us. What wasn’t measured? What assumptions are being made? And what conclusions would go beyond the available evidence?
Statistics is less about numbers and more about thinking.
The irony behind this article is that statistics is often taught as mathematics, and yes, the mathematics matters. After all, you need to know how to calculate a mean. You need to understand distributions. You need to know what variance, confidence intervals, and statistical tests are doing.
But knowing the calculation isn’t the same as understanding the result. The real skill is learning to look at a number and resist the urge to turn it into a story immediately.
50,000 average salary → Okay. Average how?
A 20% increase → 20% of what?
A strong correlation → Between what variables? Based on how many observations? And what else could explain it?
A statistically significant effect → How large is the effect? Does it matter?
A study of 100,000 people → Who were those people, and how were they selected?
The world produces an enormous amount of data! Every day, we see many numbers, graphs, and news articles. The challenge isn’t simply learning how to calculate statistics. It’s learning how to interrogate them, because data doesn’t arrive with its interpretation attached.
And if we aren’t careful, we can make statistics say almost anything we want. The goal of statistical literacy isn’t to become better at finding numbers that support what we already believe. It is to encourage us to think critically about what the data are truly saying.