Standard error of an espresso-shot average

Question

A cafe weighs its espresso shots for quality control. A sample of n = 64 shots has a sample standard deviation of s = 1.6 grams. What is the standard error of the average shot weight?

Accepted Answer

The standard error of the mean measures how much the average of your sample would bounce around if you repeated the whole sampling exercise. It is not the spread of individual shots, it is the spread of the average. The rule is simple: take the spread of one observation and divide by the square root of how many you averaged. 	ext{SE} = \frac{s}{\sqrt{n}} = \frac{1.6}{\sqrt{64}} = \frac{1.6}{8} = 0.2 	ext{ grams}. So while any single shot can be off by roughly 1.6 grams, the average of 64 shots is pinned down to about 0.2 grams. Averaging many noisy readings gives a much steadier number, bec…

Standard error of an espresso-shot average

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