What Is the Difference Between Probability and Statistics?

Many people, especially during high school, assume that probability & statistics are intertwined words. However, that is the furthest from the truth. More often than not, you’ll see both subjects taught under the same course or class. Despite that, the core difference between the two is the knowledge behind it. 

Don’t get things confused; they both share some similar terminology. However, one cannot replace the other in the real world of mathematics. In this article, you’ll find the differences between the two through three main methods.

1. Topics and Definitions

Let’s start with the first question: what are statistics? Statistics is a study that compromises the collection and organization of information. It is used as an analysis tool to display a specific trend or outcome of past events. While studying either subject, you’ll require some probability and statistics help to enable you to excel. On the other hand, prob is a method of predicting the outcome of something. In other words, it calculates how likely an event would occur. A simple way to distinguish between them is to remember statistics focuses on the past, while statistics predict the future.

2. Applications

Let’s consider some examples to notice the difference. “What’s the probability of picking up a red ball from a box with 2 red balls, 1 white, and 3 blue ones?” As clearly stated in the question, this is an example of probability. The main aim of answering this question is to predict the possible outcome of the experiment.

On the contrary, let’s say we have the same box as mentioned above, but the phrasing of the word changes. The question is, “you have a box with 2 red balls, 1 white one, and 3 blue ones. What’s the ratio of blue balls to red ones?” This question circulates an event, or a situation, that has already taken place. In other words, the balls are already in the box, and no action is required except to make calculations.

Hence, remember that stats estimate a quantity when considering the battle of probability vs statistics. Prob, on the other hand, works with certainty, not estimations.

3. Real World Relatability

When wondering what prob and stats are, the simplest way to remember the distinction is by associating them with the real world. Probability measures the outcome of a random event and figures how likely it could happen. For instance, you have a population of 1,000 people. You’re asked to “find the percentage of people who are likely to die within 10 years”. Many elements factor in here; weather, age, activity, and genetics.

As for statistics, the question would be completely different when having the same sample size of 1,000. You would, for instance, be asked to “calculate how many people have died within the last 10 years”. In other words, statistics deal with actual events that have happened. On the contrary, probability works in an ideal world where the outcome depends solely on calculated risks.

Bottom Line

While it’s vital to distinguish between the two terms, keep in mind that they’re often tied together. They share similar expressions and might revolve around the same question. However, remember that stats deal with problems that have already occurred, while probability aims to establish what will.