Statistics Examples

$2$ , $4$ , $6$ , $8$ , $10$ , $12$

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.

$\sqrt{\frac{{(2)}^{2} + {(4)}^{2} + {(6)}^{2} + {(8)}^{2} + {(10)}^{2} + {(12)}^{2}}{6}}$

Simplify the result.

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Remove parentheses around $2$ .

$\sqrt{\frac{2^{2} + {(4)}^{2} + {(6)}^{2} + {(8)}^{2} + {(10)}^{2} + {(12)}^{2}}{6}}$

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

$\sqrt{\frac{4 + {(4)}^{2} + {(6)}^{2} + {(8)}^{2} + {(10)}^{2} + {(12)}^{2}}{6}}$

Remove parentheses around $4$ .

$\sqrt{\frac{4 + 4^{2} + {(6)}^{2} + {(8)}^{2} + {(10)}^{2} + {(12)}^{2}}{6}}$

Raise $4$ to the power of $2$ .

$\sqrt{\frac{4 + 16 + {(6)}^{2} + {(8)}^{2} + {(10)}^{2} + {(12)}^{2}}{6}}$

Remove parentheses around $6$ .

$\sqrt{\frac{4 + 16 + 6^{2} + {(8)}^{2} + {(10)}^{2} + {(12)}^{2}}{6}}$

Raise $6$ to the power of $2$ .

$\sqrt{\frac{4 + 16 + 36 + {(8)}^{2} + {(10)}^{2} + {(12)}^{2}}{6}}$

Remove parentheses around $8$ .

$\sqrt{\frac{4 + 16 + 36 + 8^{2} + {(10)}^{2} + {(12)}^{2}}{6}}$

Raise $8$ to the power of $2$ .

$\sqrt{\frac{4 + 16 + 36 + 64 + {(10)}^{2} + {(12)}^{2}}{6}}$

Remove parentheses around $10$ .

$\sqrt{\frac{4 + 16 + 36 + 64 + 10^{2} + {(12)}^{2}}{6}}$

Raise $10$ to the power of $2$ .

$\sqrt{\frac{4 + 16 + 36 + 64 + 100 + {(12)}^{2}}{6}}$

Remove parentheses around $12$ .

$\sqrt{\frac{4 + 16 + 36 + 64 + 100 + 12^{2}}{6}}$

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

$\sqrt{\frac{4 + 16 + 36 + 64 + 100 + 144}{6}}$

Add $4$ and $16$ .

$\sqrt{\frac{20 + 36 + 64 + 100 + 144}{6}}$

Add $20$ and $36$ .

$\sqrt{\frac{56 + 64 + 100 + 144}{6}}$

Add $56$ and $64$ .

$\sqrt{\frac{120 + 100 + 144}{6}}$

Add $120$ and $100$ .

$\sqrt{\frac{220 + 144}{6}}$

Add $220$ and $144$ .

$\sqrt{\frac{364}{6}}$

Divide $364$ by $6$ .

$\sqrt{60.\overline{6}}$

The result can be shown in both exact and decimal forms.

Exact Form:

$\sqrt{60.\overline{6}}$

Decimal Form:

$7.78888096 \dots$

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