Exploratory Data Analysis

It is tempting to reduce a dataset to a few tidy numbers: an average, a percentage, a single headline figure. Those summaries are useful, but they compress. And compression throws things away. Two datasets can share the same average, the same spread, even the same trend line, and still describe completely different realities.

Exploratory data analysis, or EDA, is the discipline of actually looking at your data before you draw a conclusion from it. You examine its shape, its range, the places where points cluster and the places where they thin out. You do this not to prove a point but to understand what you are holding. The habit is cheap, and it routinely saves you from confident, wrong answers.

Look at the distribution, not just the middle

An average tells you where the middle sits. It says nothing about whether the data is bunched tightly, spread wide, split into two clumps, or dragged sideways by a handful of extreme values. Plotting the full distribution reveals shape: is it roughly symmetric, lopsided, or bimodal? Shape changes what the average even means.

Outliers are signals, not just nuisances

An outlier is a point far from the rest. Sometimes it is a data-entry error. Sometimes it is the most important thing in the file: the fraudulent transaction, the failing sensor, the customer worth ten of the others. EDA asks you to notice outliers and then investigate them rather than reflexively deleting or ignoring them.

Summaries hide; pictures reveal

The core lesson of EDA is that a picture carries information a table of statistics cannot. A scatter plot shows a curve where a correlation coefficient shows only a number. Looking is not less rigorous than computing. It is the step that tells you which computation is even appropriate.

Suppose a shop reports that average time on its website is four minutes, and takes that as healthy engagement. EDA means plotting the actual times. Doing so reveals two clumps: most visitors leave within twenty seconds, while a small group stays for fifteen minutes. Almost nobody spends anything near four minutes. The average is real but describes no actual visitor. The two-clump shape suggests two audiences, and that insight only appears once you look.

A team computes the correlation between advertising spend and sales and gets a strong positive number, so they conclude more spending reliably lifts sales. But they never plotted the points. Had they done so, they would have seen the relationship flatten completely above a certain budget, with one enormous holiday campaign single-handedly propping up the correlation. The summary number was strong; the story it implied was false.

In 1973 the statistician Francis Anscombe published a short paper, "Graphs in Statistical Analysis," in the journal The American Statistician. He constructed four small datasets, each with eleven points. All four share nearly identical summary statistics: the same mean of x, the same mean of y, almost the same variance, the same correlation of about 0.82, and the same fitted regression line, y = 3 + 0.5x.

Yet when plotted, they look nothing alike. The first is a normal-looking linear scatter. The second is a smooth curve that a straight line badly misfits. The third is a tight line dragged askew by a single outlier. The fourth is a vertical stack of points with one far-off point creating the entire apparent trend. Anscombe's point, echoing the statistician John Tukey, whose 1977 book "Exploratory Data Analysis" championed this whole approach, was blunt: compute if you must, but you must also look.

• "The average summarizes the data." It summarizes the middle; it can hide the shape entirely.
• "Outliers are errors to remove." Some are errors; some are the most valuable observation you have.
• "A strong correlation means a clean straight-line relationship." It can be produced by curves or single leverage points.
• "Looking at data is less serious than calculating." Looking is what tells you which calculation is valid.

Take any two columns of numbers with the same average and imagine three distributions that could produce it: one bunched, one spread, one with an outlier. Sketch each. Notice how much the same average conceals.

Think Like a Maester: Never trust a number you have not first tried to see.

1. What does exploratory data analysis ask you to do before drawing a conclusion?
2. Name one feature of a dataset that an average cannot reveal.
3. Why might deleting every outlier be a mistake?
4. What did Anscombe's four datasets have in common, and how did they differ?
5. Whose 1977 book gave the practice of "exploratory data analysis" its name?

Summary statistics compress data, and compression hides. Exploratory data analysis is the habit of looking at the full shape of a dataset, distribution, spread, gaps, and outliers, before you trust any single number. Anscombe's quartet proves the stakes: four datasets, nearly identical statistics, four utterly different pictures. Look first.

• Visualising Data
• Comparing Groups and A/B Testing