Averages/Pythagorean means: Difference between revisions
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{{task heading}}
Compute all three of the
Show that
* The most common of the three means, the
* The [[wp:Geometric mean|geometric mean]] is the
* The
▲* The most common of the three means, the [[Averages/Arithmetic mean|arithmetic mean]], is the sum of the list divided by its length:
▲::::: <big><big><math> A(x_1, \ldots, x_n) = \frac{x_1 + \cdots + x_n}{n} </math></big></big>
▲* The [[wp:Geometric mean|geometric mean]] is the <math>n</math><sup>th</sup> root of the product of the list:
▲::::: <big><big><math> G(x_1, \ldots, x_n) = \sqrt[n]{x_1 \cdots x_n} </math></big></big>
▲* The [[wp:Harmonic mean|harmonic mean]] is <big><big><math>n</math></big></big> divided by the sum of the reciprocal of each item in the list:
▲::::: <big><big><math> H(x_1, \ldots, x_n) = \frac{n}{\frac{1}{x_1} + \cdots + \frac{1}{x_n}} </math></big></big>
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