Statistics Examples

$9$ , $11$ , $13$ , $15$

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.

$\sqrt{\frac{{(9)}^{2} + {(11)}^{2} + {(13)}^{2} + {(15)}^{2}}{4}}$

Simplify the result.

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Raise $9$ to the power of $2$ .

$\sqrt{\frac{81 + {(11)}^{2} + {(13)}^{2} + {(15)}^{2}}{4}}$

Raise $11$ to the power of $2$ .

$\sqrt{\frac{81 + 121 + {(13)}^{2} + {(15)}^{2}}{4}}$

Raise $13$ to the power of $2$ .

$\sqrt{\frac{81 + 121 + 169 + {(15)}^{2}}{4}}$

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

$\sqrt{\frac{81 + 121 + 169 + 225}{4}}$

Add $81$ and $121$ .

$\sqrt{\frac{202 + 169 + 225}{4}}$

Add $202$ and $169$ .

$\sqrt{\frac{371 + 225}{4}}$

Add $371$ and $225$ .

$\sqrt{\frac{596}{4}}$

Divide $596$ by $4$ .

$\sqrt{149}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{149}$

Decimal Form:

$12.20655561 \dots$

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