standard deviation
/ STAN-derd dee-vee-AY-shun /
Imagine two archers who both, on average, hit the centre of the target. One groups every arrow in a tight cluster; the other scatters them all over the board. Their averages are the same, but they are clearly not equally reliable. The standard deviation is the single number that captures that difference: how widely the shots are spread around the bullseye.
For a set of measurements, the standard deviation tells you the typical distance of an individual reading from the mean. You take each reading's gap from the mean, square those gaps, average them, and take the square root, which brings the answer back into the original units. A small standard deviation means the measurements huddle close together; a large one means they are spread out.
It matters because it is the everyday yardstick of precision: it says how repeatable a method is, regardless of whether it hits the right answer. The caveat is subtle but important — a tight standard deviation only proves the results agree with each other, not that they are correct. A biased method can be beautifully precise and still wrong.
Lab A reports a copper content of 64.0 percent with a standard deviation of 0.1 percent; lab B reports the same 64.0 percent but with 2.0 percent. Both averages match, yet lab A's measurements are twenty times tighter.
Same average, very different spread — the standard deviation tells them apart.
When you only have a sample of a few measurements, the sum of squared gaps is divided by n minus one (the degrees of freedom), not by n, which makes the estimate of the true spread less biased.