Standard error of an average bolt length

Question

A factory measures the length of bolts coming off a line. A sample of n = 100 bolts has a sample standard deviation of s = 3 mm. What is the standard error of the average bolt length?

Accepted Answer

The standard error of the mean tells you how tightly the average of your sample is pinned down, as opposed to how much individual bolts vary. Individual bolts scatter by about 3 mm, but their average is far steadier. Divide the spread of one measurement by the square root of the sample size: 	ext{SE} = \frac{s}{\sqrt{n}} = \frac{3}{\sqrt{100}} = \frac{3}{10} = 0.3 	ext{ mm}. Averaging 100 readings shrinks the wobble in the average by a factor of \sqrt{100} = 10, from 3 mm down to 0.3 mm. Takeaway. Standard error of the mean = s/\sqrt{n}: the average of many measurements is roughly ten times…

Standard error of an average bolt length

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