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, 75Class B: 30, 50, 65, 70, 75, 90, 110Both could have a mean around 70. But these are clearly not the same dataset. The first class is tightly clustered, while the seco...