What can a single data point teach you

Short of time? Here are the key takeaways:

❓ Most single data points are misleading when you generalize from them. One experience or anecdote rarely supports broad conclusions about how things usually work, which is why people often draw confident but unjustified beliefs from minimal evidence.

💡 However, a single data point can still be informative by revealing possibilities. One well verified observation can show that something exists or can happen, immediately disproving claims of impossibility and motivating further investigation, even before any statistical confidence is warranted.

🧠 One example can generate hypotheses and causal insight. Seeing something work once can suggest a plausible explanation or mechanism, allowing you to build a mental model that helps you reason about similar situations later, even across different contexts.

🔓 Sometimes one data point unlocks many others. A new observation can shift which hypotheses feel plausible, making previously ignored or rationalized evidence suddenly make sense and allowing large amounts of information to be integrated more coherently.

📊 In special cases, one data point can provide strong evidence. When an observation would be extremely unlikely under one hypothesis but expected under another, or when variability is very low, a single data point can meaningfully update beliefs.

From a scientific or statistical standpoint, it seems ridiculous to think one data point can teach you much. Even a study with ten data points (such as ten observations or ten separate measurements) is laughably small.

It’s also really common to see people overreact to a single experience they’ve had or a single anecdote. For example, when saying things like:

• “I know I don’t like Taiwanese food because I tried it once”

• “I’m convinced this supplement will work because my friend took it and says it worked”

And it's absolutely true that the vast majority of the time, one data point tells you nearly nothing. And yet, in some (special) contexts, one data point can teach you an awful lot. Here are seven ways that you can sometimes learn useful information from just one data point.

Showing Possibilities

1. By Alerting You to a New Possibility

Sometimes, a single data point shows us that a possibility or phenomenon exists that we had never before seen or considered.

Example: Roentgen had a cathode tube covered in heavy black paper and was surprised when an incandescent green light escaped and projected onto a nearby fluorescent screen. Just seeing it once was enough to suggest that something very unusual had happened. In fact, he had discovered a new phenomenon. It eventually led to the discovery of x-rays! Of course, it took gathering a lot more data to be confident in what he had found, but one data point was enough to kick off the investigation process.

Similarly, if you believe that something never happens or is impossible, a single (well-verified) data point can be enough to prove you wrong.

Example: For centuries, Europeans believed that all swans were white. The Roman poet Juvenal even used the phrase “very like a black swan” to describe a possibility he believed was absurd. Black swans never happened - or so it was thought. For any person holding such a belief, a single observation of a black swan is enough to prove them wrong. Hence, when Europeans arrived in Australia, they very quickly learned that they had been mistaken. The philosopher of science Karl Popper famously used this example when advocating for his theory of science, known as ‘falsificationism’. 

2. By Causing You to Think of a Hypothesis

Seeing something just once can give you a hypothesis or make you aware of a concept that may apply to other cases – especially if your hypothesis coheres with other justified beliefs you have.

Example: Suppose that, while bartering over a price at a food stand, you see a friend use a negotiation tactic you have never seen before. Upon seeing this tactic used, it immediately makes sense to you that the tactic works, yet the idea had simply never occurred to you before.

3. By Illustrating a Causal Mechanism

Studying a single data point or example can allow you to see how something works, enabling you to build up a causal understanding or model. You can then apply this understanding to other examples.

Example: You take apart one mechanical clock and pay close attention to how it works. From this experience, you build up a causal model of how such clocks function. Later, when a different mechanical clock stops working, this causal model helps you quickly diagnose the problem. Even if that second clock is made by a different company, many of the causal mechanisms that you figured out from the first example would still apply.

4. By Unlocking Other Data Points

An interesting aspect of learning from one data point is that, every once in a while, one data point unlocks the information from a whole bunch of other data points.

Example: For instance, if your friend is in an unhealthy or abusive relationship but is still convinced that their partner is a good person who means well, a bunch of data points about their partner’s behavior may simply not make sense to them or have been rationalized away. Since your friend is evaluating their partner’s behavior through the lens of “they’re a good person and a loving partner”, those data points either just sit around causing confusion and end up being dismissed or they get integrated in a contrived way (e.g., “It’s weird that they yell at their business partner on the phone so much, but I guess they’re just really passionate about their business. And it’s weird that they sometimes tell me I look terrible – but that’s just because they’re concerned that others will think badly of me, and they’re looking out for my best interests.”)

Then a single new data point can suddenly cause a reconsideration of the hypotheses that their partner is a good person, and allow your friend to consider that maybe their partner is actually a highly manipulative and selfish person (e.g., walking in on them cheating with another person). Once this new hypothesis becomes available, suddenly, all of those previously ignored data points make sense and can be integrated quickly. Hence, processing one data point can sometimes unlock the possibility of processing a whole bunch of others by making them psychologically available to us or by allowing us to see them from a different angle.

Providing Evidence

5. By Giving You a Bayes Factor

Sometimes, a single well-verified data point tells you a lot because of how surprising it would be under different scenarios.

Example: Suppose you've had a rash for ten years, non-stop. Your single data point is that it suddenly went away, two hours after you applied a rash cream that you bought from a shady website. You are confident that your senses aren’t deceiving you, and you did nothing else unusual around the time that your rash got better. In that case, you might reflect on these two hypotheses:

A: That the rash cream worked to eliminate your rash

B: That the rash cream did not work and your rash got better by some other means (perhaps on its own)

If the cream didn’t work (i.e., if hypothesis B was true), your data point would be extremely surprising. After all, nothing else had worked for many years, you did nothing else unusual, and the effect happened very quickly after you applied the cream. The probability of it getting better on its own or due to other means during that 2-hour window is incredibly small.

However, your data point would not be at all surprising if the cream did work (i.e., if hypothesis A was true). Given that your data point is much more likely under hypothesis A than under hypothesis B, it is strong evidence in favor of A. The ratio of [how likely your data point is if A is true] to [how likely your data point is if B is true] is called the Bayes Factor. The higher the Bayes Factor, the more the evidence favors one hypothesis over the other. We have discussed this elsewhere, and if you’re interested in learning even more, you could try our free mini-course about Bayesian reasoning - it’s called The Question of Evidence:

Launch The Question of Evidence Mini-Course

6. By Providing the Mean When There is Very Low Variance

Normally, a single data point doesn’t allow an accurate estimate of any statistics. But in situations of very low variability, a single data point can be an accurate approximation of the mean!

Example: Suppose there is very little variability in how long it takes to walk to the store from your home. Hence, walking that route just once allows you to estimate quite accurately how long it will take in the future (e.g., it takes about 40 minutes to walk to the store). Perhaps sometimes it will take 42 minutes or 38 minutes, but unless a very unlikely event happens (e.g., an earthquake), it's not going to take 30 minutes or 50 minutes. 

7. By Showing What’s Not Extremely Unlikely

If you witness just one example of a thing, chances are that its traits are not extremely unrepresentative of the class from which it comes. Of course, it’s possible they are, but the substantial majority of the time, a single data point will not have extremely rare traits.

Example: You see an adult Spider Monkey for the first time (in the wild, let’s say). Chances are that this Spider Monkey is somewhere between the 1st percentile and 99th percentile for size. It’s unlikely that the only Spider Monkey you’ve ever seen is one of the very largest or smallest that exists (unless there is a special reason for that to be the case - for instance, you went to a zoo advertising that they have one of the largest spider monkeys). You can expect that most of the traits this particular Spider Monkey has are not incredibly rare.

What Counts as One Data Point, Anyway?

An important consideration is that it’s not always clear what “one data point” means. In health, social science, or economics studies, a single data point can mean one person, one task completed, or one school, or the statistics for one country. In ordinary life, you’re experiencing lots of information all the time, though you can still sometimes think of “one data point” as being one example or one experience or one attempt, etc.

So, can you learn a lot from one data point?

Mostly, one data point tells us nearly nothing. There are times when one data point is exactly what you’re interested in. For instance, when you want to know whether you like that dish or what’s true of that exact thing (not that type of dish, nor that sort of thing). In such cases, it’s more obvious that one data point can be enough to learn from. But, as we have seen above, there are many more ways to get genuine insights from a single observation - these are not common, but each of them sometimes occurs.

Unfortunately, we humans often err on the side of overreacting to a single data point. We take one example, anecdote, or life experience, and generalize it inappropriately. But, if we are very careful, there are (perhaps surprisingly) sometimes valid ways to learn a lot from just one data point!