<pclass='rosetta__paragraph'>Compute all three of the <aclass='rosetta__link--wiki'href='https://en.wikipedia.org/wiki/Pythagorean means'title='wp: Pythagorean means'>Pythagorean means</a> of the set of integers <big>1</big> through <big>10</big> (inclusive).</p><pclass='rosetta__paragraph'>Show that <big>$A(x_1,\ldots,x_n) \geq G(x_1,\ldots,x_n) \geq H(x_1,\ldots,x_n)$</big> for this set of positive integers.</p> The most common of the three means, the <aclass='rosetta__link--rosetta'href='http://rosettacode.org/wiki/Averages/Arithmetic mean'title='Averages/Arithmetic mean'>arithmetic mean</a>, is the sum of the list divided by its length: <big>$ A(x_1, \ldots, x_n) = \frac{x_1 + \cdots + x_n}{n}$</big>The <aclass='rosetta__link--wiki'href='https://en.wikipedia.org/wiki/Geometric mean'title='wp: Geometric mean'>geometric mean</a> is the $n$th root of the product of the list: <big>$ G(x_1, \ldots, x_n) = \sqrt[n]{x_1 \cdots x_n} $</big>The <aclass='rosetta__link--wiki'href='https://en.wikipedia.org/wiki/Harmonic mean'title='wp: Harmonic mean'>harmonic mean</a> is $n$ divided by the sum of the reciprocal of each item in the list: <big>$ H(x_1, \ldots, x_n) = \frac{n}{\frac{1}{x_1} + \cdots + \frac{1}{x_n}} $</big>
<pclass='rosetta__paragraph'>Assume the input is an ordered array of all inclusive numbers.</p>
<pclass='rosetta__paragraph'>For the answer, please output an object in the following format:</p>