Statistics in practice · 16 January 2026
The normal distribution — indispensable, and routinely assumed where it does not belong
The bell curve shows up everywhere for a real reason — and gets wrongly assumed everywhere else. How to enjoy the first and avoid the second.
Measure something across lots of people — height, shoe size, reaction time — and most values land near the middle, with fewer and fewer as you move out. Draw it and you get a bell shape. That's the normal distribution. Its exact recipe is:
You don't need to memorise that. You only need its two ingredients: (the average — where the peak sits) and (the standard deviation — how wide the bell is). Those two numbers describe the whole curve.
From them comes a rule of thumb worth knowing: about 68% of values fall within one bell-width of the average, 95% within two, and 99.7% within three.
Chapter 1 · Statistics in practice
Why the bell curve is everywhere
There's a real mathematical reason, called the Central Limit Theorem. In plain words: when a result is the sum of many small independent influences, the total tends toward a bell shape — no matter what shape the individual influences have. Heights, measurement errors, monthly averages: all sums of many small things, all roughly bell-shaped. It isn't a coincidence; it's a law.
Chapter 2 · Statistics in practice
Where the assumption quietly lies
- Waiting times. They can't go below zero and they stretch out long on the high side. That's a lopsided shape, not a bell. Plan staffing with a bell-curve assumption and the long waits will surprise you — on paper only, because your customers already knew.
- Extreme events. Real operational data produces "impossible" extreme days far more often than the bell curve predicts. If the curve says once a century and it's happened twice this year, believe your data, not the curve.
- Small samples. The bell-shape law is a promise about many observations. With five data points it's a hope, not a law.
Chapter 3 · Statistics in practice
The practical habit
Before trusting any calculation that assumes a bell curve, look at the picture. Draw the histogram. If it's lopsided or long-tailed, say so in the report. The normal distribution is the right starting guess exactly as far as the data agrees — and not one step further.
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