Statistics Examples

$12$ , $15$ , $45$

Step 1

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.

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

Step 2

Simplify the result.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Add $144$ and $225$ .

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

Step 2.5

Add $369$ and $2025$ .

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

Step 2.6

Divide $2394$ by $3$ .

$\sqrt{798}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{798}$

Decimal Form:

$28.24889378 \dots$

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