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Trading Math
What Is Standard Deviation, in Plain Words
Standard deviation is the typical distance of a set of values from their average. This paper shows you ten real days as dots around their average, the five steps that turn the distances into one number, which of the ten days sat outside one deviation, and the one spreadsheet function that does the five steps at once.
A standard deviation answers one question about a set of numbers: how far, typically, do they sit from their average? The ten numbers here are the ten days of the list — one lot of the euro against the dollar bought at each day's open and sold at its close, 24 August to 4 September 2026 — each written as a share of the balance the day began with. Their average is minus 0.88 per cent. Some days sit within a point or two of it; 28 August sits nearly fourteen points below. The standard deviation is the typical distance, and here it is 7.0.
The five steps
The number is made in five steps, and none of them is hard. Take the average of the ten: minus 0.88. Take each day's distance from that average: 28 August is 13.87 below, 3 September 10.08 above. Square every distance, so that below and above both count and the large ones count more than the small. Add the squares and divide by one less than the count — nine, for a sample of ten. Take the square root, which brings the answer back to the units the days were in. On the ten days the result is 7.03.
