Introduction
Quantiles
Instruction
Using standard deviation, we can estimate where the elements of a dataset are located. Suppose we have n elements, \overline{x} is the arithmetic mean, and SD is the standard deviation. By the Laguerre-Samuelson inequality we know that elements from this dataset are located in the interval:
[ \overline{x}-SD\sqrt{n-1}; \overline{x}+SD\sqrt{n-1} ]
Let's see what this means for the particular set sizes where the arithmetic mean is zero (\overline{x}=0) and standard deviation equals one (SD = 1) or two (SD = 2).
| n | Interval for SD = 1 | Interval for SD = 2 |
|---|---|---|
| 10 | [-3.00;3.00] | [-6.00;6.00] |
| 50 | [-7.00;7.00] | [-14.00;14.00] |
| 100 | [-9.95;9.95] | [-19.90;19.90] |
| 500 | [-22.34;22.34] | [-44.68;44.68] |
| 1000 | [-31.61;31.61] | [-63.21;63.21] |
