Statistics in practice · 16 January 2026
The normal distribution, and 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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