Difference between revisions of "TDSM 2.9"
From The Data Science Design Manual Wikia
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When all terms <math> x_0 = x_1 = \dots = x_{n-1} </math> | When all terms <math> x_0 = x_1 = \dots = x_{n-1} </math> | ||
| − | The arthmetic mean is <math>\frac{1}{n} \sum_{i = 0}^{n-1} = \frac{1}{n}\ | + | The arthmetic mean is <math>\frac{1}{n} \sum_{i = 0}^{n-1} = \frac{1}{n}\cdot x_0 = x_0</math> |
The geometric mean is <math> \sqrt[n]{\prod_{i = 0}^{n-1}} = \sqrt[n]{x_0 ^n} = x_0</math> | The geometric mean is <math> \sqrt[n]{\prod_{i = 0}^{n-1}} = \sqrt[n]{x_0 ^n} = x_0</math> | ||
So the arithmetic mean equals the geometric mean when all terms are the same. | So the arithmetic mean equals the geometric mean when all terms are the same. | ||
Latest revision as of 18:48, 11 September 2017
When all terms x0=x1=⋯=xn−1
The arthmetic mean is 1nn−1∑i=0=1n⋅x0=x0
The geometric mean is n√n−1∏i=0=n√xn0=x0
So the arithmetic mean equals the geometric mean when all terms are the same.
