Difference between revisions of "TDSM 2.9"
From The Data Science Design Manual Wikia
(Created page with "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}\times nx_0</math>") |
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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}\times nx_0</math> | + | The arthmetic mean is <math>\frac{1}{n} \sum_{i = 0}^{n-1} = \frac{1}{n}\times nx_0 = 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. | ||
Revision as of 17:25, 11 September 2017
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}\times nx_0 = 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.
