What Is Statistics?
Thinking Statistically: A Refresher
Statistical thinking begins with something very simple: noticing. We notice events, we notice people, we notice differences. We see rents climbing in our city, or hear friends complain about how much they’re paying, and we wonder: is this just a few unlucky cases, or does it say something bigger about the housing market? This is the heart of thinking statistically. It is not about complicated formulas, but about moving from what we observe to what we might reasonably believe about the world. The post Thinking Statistically: A Primer goes into more detail on this point.
From Observations To Patterns
Sometimes, we observe a single thing — a person, a place, an event — and note several of its features. More interestingly, we often observe many things that are similar in some respects but quite different in others. We notice patterns across people, places, or time. We end up with a collection of observations, or, in the language of statistics, data.
Faced with such a collection, it is natural to start comparing. What is the same? What is different? What might explain those differences? This is where statistical thinking deepens. The overarching question becomes: what can we learn from this data?
One of the great temptations in everyday life is to leap from a vivid example to a sweeping claim. A frustrating encounter with a GP becomes “the NHS is broken.” A handful of pricey flat listings becomes “this city is unaffordable.” But while anecdotes grab attention, they rarely tell the whole story. If we want to understand whether a city is truly unaffordable, for example, we need more than isolated cases: we need patterns.
That means gathering many observations and looking for regularities across them. Instead of just noting that a friend’s rent has doubled, we might ask: what are average rents across the city? How do they compare to incomes? How do they vary between neighbourhoods or over time? These “how much” questions — how much bigger, how much more frequent, how much more difficult — are everywhere in daily life, and they are precisely where statistical thinking deepens. We move from anecdotes to collections of observations, and from collections to evidence that can support or challenge our claims.
This is why statistics is best understood not as a tool for eliminating uncertainty, but as a way of working productively with it. The numbers never speak for themselves. They help us move from stories to systems, from isolated cases to general patterns.
Likelihood and Certainty
Even with careful observation, we rarely get perfect answers. Instead, we learn to talk in terms of likelihood. At its core, statistical thinking is about likelihood, not certainty. We weigh the chances (i.e., probability). We expect patterns to hold “in general” or “on average” or “in the long run,” but it never promises that every case will follow the rule.
This is what makes statistics so powerful for the social sciences. People, places, and societies are complex and unpredictable. But with good data and careful reasoning we can still learn a lot. We can be clear about what we know, open about what we don’t, and realistic about how confident we should be.
Statistics helps us summarize what we have found so we can be clear about the facts. But it also helps us go further: to compare, to explain, and to predict. It reminds us to be cautious. What appears true in one context may not hold in another, as I am sure you are all acutely aware. Before we can test a hypothesis or quantify uncertainty, we need to know what matters, what varies, and what might be related. This requires a theoretical understanding of the problem you are studying just as much as it requires an understanding of what is happening in your data.
If we want to generalize more confidently, the logical starting point is to gather more experience - that is, collect more data. This speaks to the fact that the more contexts, situations, and experiences we observe, the more confident we can be in drawing conclusions and making suggestions. In other words, if we want to generalize more confidently, we need more data, which happens to be the logic underpinning one of the most powerful ideas in statistics: the Central Limit Theorem.
Thinking statistically then, is not about memorising formulas or crunching numbers. It is about developing a habit of mind: noticing variation, looking for patterns, and reasoning in terms of likelihood. Done well, it sharpens our instincts and grounds our judgments. It helps us move beyond stories to understanding, and beyond uncertainty to insight.
In that sense, statistics does not replace your instincts. It organizes and strengthens them. You already ask whether something seems off. You already notice patterns. What statistics offers is a way to build on those instincts: to sharpen them, test them, and sometimes correct them. It helps you become more precise in your questions and more careful in your answers. And that is a powerful skill, no matter what field you are in.
What Is Statistics?
Statistics is a word that causes confusion, not because it is complicated, but because it has so many meanings. It can refer to a subject of study, to methods of analysing data, to the data themselves, or to the specific numbers we calculate. For example, a researcher might study statistics, use statistics to analyse data, interpret official statistics, and report a statistic like average income. This is partly why, in our statistics courses, we tend to adopt the following definition of statistics:
Statistics is the methodology for collecting, presenting, analysing, and interpreting data.
Many students are introduced to statistics so that they can interpret and understand research carried out in their field of interest. But statistics is everywhere — in the news, in sports, in science, in policy, in medicine. Yet it is often misunderstood. Many people see it as dry, overly technical, or even manipulative. Some fear it as a tangle of formulas; others distrust it because numbers can be twisted to tell a story. This suspicion around statistics is understandable. We’ve all seen numbers used to persuade, distract, or deceive. Sometimes statistics are gamed — when a measure becomes a target, it can lose its meaning (Goodhart’s Law). But the problem is rarely the statistics themselves; it’s how they are used, what is being measured, and how we interpret the results.
In fact, modern statistics is less about arithmetic and more about reasoning, exploration, and interpretation. Computers handle most calculations today, freeing us to focus on the questions we ask, the assumptions we make, and the conclusions we draw. In that sense, statistics is a technology — a set of tools for extracting meaning from data, for navigating uncertainty, and for learning from evidence.
At its core, statistics embraces the imperfection of our observations. We know that any single measurement is flawed; our data are simplified representations of a complex world. Statistics gives us ways to measure and reason through these uncertainties, to understand variation, and to weigh how far wrong we might be. Hence why good statistical thinking matters.
This is why data and statistics are inseparable. Data, often numerical but not always, allow us to represent what we are studying. They are never perfect, but they are workable — and with good judgement, they let us move from noticing patterns to understanding systems. Poor data, of course, lead to poor conclusions irrespective of the tools used.
Bibliography
- Statistics: A Very Short Introduction, by David J. Hand
- Statistics Without Tears: An Introduction For Non-Mathematicians, by Derek Rowntree
- Elementary Statistics For Geographers, by James E. Burt, Gerald M. Barber, and David L. Rigby