Statistics · Averages & range
Chapter 1 · 3
The idea
Mean, median, mode & range
The three averages and the range from a raw list — what each one is actually for, why the median needs the data sorted first, why the range is a measure of spread and not an average, and why every reverse-mean question is really a question about the total.
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Statistics · Averages & range
Mean, median, mode & range
The three averages and the range from a raw list — what each one is actually for, why the median needs the data sorted first, why the range is a measure of spread and not an average, and why every reverse-mean question is really a question about the total.
Why it works
One number to stand for fifty
A set of data is unwieldy: fifty numbers say fifty things at once. An average is the bargain you strike with that mess — one number you are willing to send out into the world in place of all of them. "The average rainfall in June is mm" is a promise that if you had to describe June with a single figure, is the figure you would stand behind.Nothing decides which single number that should be, which is why there are three of them. Each answers "what is typical here?" honestly, but in a different way, and each is the right answer to a different question.
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The rest of the explanation, plus 3 worked examples you step through move by move.
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