The shape of data: the histogram
Points on a line work while the numbers are few. But the "Mama John's" chain has grown to fifty employees — individual points no longer tell you anything. You need to see the whole shape: where salaries are dense, where sparse, whether a tail stretches out anywhere. So the data is dropped into "bins" — ranges — counting how many people fall into each. That is a histogram.
The height of a bar is how many people earn a salary from that range. The main thing is visible at once: there is a "hump" where most people are (around 33–37k) and thin edges. That is the shape of the data — in a single glance.
Shape is the first diagnosis of data. The salary histogram of "Mama John's" shows at once both the typical level (a hump around 33–37k) and the skew, when a lonely bar for the director appears on the right.
So before computing means and building models, an analyst always looks at the shape: it hints whether the data is symmetric, whether there is a long tail, and whether lone values might distort the conclusions.
Histograms are everywhere: the distribution of grades in a class, app load times, audience ages, store receipts. The shape instantly tells you whether the data is "even" or long-tailed.
The shape also suggests the method: for a symmetric "bell" the mean and σ work well, while for skewed, tailed data the median and percentiles are more honest.
We keep mentioning the "hump" and the "long tail". But data is convenient to describe not only by shape but also by its edges — what share of values lies below a given threshold. That is what we'll take up in the next lesson.