Normal distribution (bell curve)
A normal distribution is the bell shape a lot of data takes: most values near the average, fewer and fewer out to the sides, evenly on both.
Select any words here to ask your Maestro about them.
The bags average 16.0 oz, with a standard deviation of 0.2 oz. The roaster pulls every bag under 15.6 oz. How many of the 400 does it pull?
What it's for: telling how unusual a value is. In a bell curve, what matters is how many standard deviations a value sits from the mean: the farther out, the rarer, and three out is very rare. That's how factories set tolerances and how you check whether an order is an outlier.
Before you assume it: draw a histogram. Weights, heights and measurement errors are usually bell-shaped; amounts, salaries and times almost never are. If your data has a tail, use percentiles.
It's also called the bell curve or the Gaussian distribution.
Practice it in How do I draw and read a histogram of a numeric column?.
How it's used
How to calculate it in Excel
The 400 weights in B2:B401
- =AVERAGE(B2:B401)
- 16.0The week's average.
- =STDEV.S(B2:B401)
- 0.2The standard deviation.
- marked: =NORM.DIST(15.8,16.0,0.2,TRUE)
- 15.9%The share of bags that would weigh under 15.8 oz if they follow the bell curve.
When to look closer
When the data isn't a bell
Receipts: mean $28, standard deviation $26. By the bell-curve rule, between what amounts does 95% fall?
Ask your Maestro about Normal distribution
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You: What does "Normal distribution" mean, in plain words?
Your Maestro: I'll explain it with a case of yours: it sticks better than a definition. Which data at work do you think forms a bell curve?
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Related terms
- Standard deviation
Standard deviation measures how far data lands from the average: with an average of 30 and an SD of 2, most values fall from 28 to 32. In Excel: =STDEV.S.
- Histogram
A histogram shows how the values in a column of numbers are spread out: it cuts them into ranges of equal width and draws one bar per range, as tall as the number of values that fall in it.
- Mean (average)
To find the mean (the average), add up all the values and divide by how many there are: 15, 7, 8, 13 and 7 add up to 50, and 50 ÷ 5 = 10.
- Percentile (and quartiles)
A percentile is the value a given share of the data falls at or below: 90% falls at or below the 90th. Quartiles are the 25th, 50th and 75th.