Estimation · Chapter 8

Bounds and the Middle

When the bounds are far apart, the plain average hugs the top. The middle on the ladder is the square root of low × high.

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Opens on Chapter 8’s example: the leaves on Dez’s oak: surely more than 1,000 and fewer than 1,000,000.

Bounds along a chain
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From the book, Chapter 8. For the oak, the plain average of 1,000 and 1,000,000 is 500,500, but the ladder middle is 31,623, 31.6 times the low bound and the same number of times below the high. The piano tuners with every factor bounded: from about 2 to about 67, middle about 12, a span of 32 times.

Rounding is half up, the way the book rounds. Numbers can be typed as 1,450, $38, 12%, 1/20, 2.5 million or 3 × 10⁷. Everything stays in your browser: no sign-up, nothing stored or sent.