Statistics Examples

$12$ , $15$ , $45$

The quadratic mean (rms) of a set of numbers is the square root of the sum of the squares of the numbers divided by the number of terms.

$\sqrt{\frac{{(12)}^{2} + {(15)}^{2} + {(45)}^{2}}{3}}$

Simplify the result.

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Remove parentheses around $12$ .

$\sqrt{\frac{12^{2} + {(15)}^{2} + {(45)}^{2}}{3}}$

Raise $12$ to the power of $2$ to get $144$ .

$\sqrt{\frac{144 + {(15)}^{2} + {(45)}^{2}}{3}}$

Remove parentheses around $15$ .

$\sqrt{\frac{144 + 15^{2} + {(45)}^{2}}{3}}$

Raise $15$ to the power of $2$ to get $225$ .

$\sqrt{\frac{144 + 225 + {(45)}^{2}}{3}}$

Remove parentheses around $45$ .

$\sqrt{\frac{144 + 225 + 45^{2}}{3}}$

Raise $45$ to the power of $2$ to get $2025$ .

$\sqrt{\frac{144 + 225 + 2025}{3}}$

Add $144$ and $225$ to get $369$ .

$\sqrt{\frac{369 + 2025}{3}}$

Add $369$ and $2025$ to get $2394$ .

$\sqrt{\frac{2394}{3}}$

Divide $2394$ by $3$ to get $798$ .

$\sqrt{798}$

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