Statistics Examples

9

$9$ ,

11

$11$ ,

13

$13$ ,

15

$15$

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{{(9)}^{2} + {(11)}^{2} + {(13)}^{2} + {(15)}^{2}}{4}}

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

Step 2

Simplify the result.

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Step 2.1

Raise

9

$9$ to the power of

2

$2$ .

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

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

Step 2.2

Raise

11

$11$ to the power of

2

$2$ .

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

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

Step 2.3

Raise

13

$13$ to the power of

2

$2$ .

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

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

Step 2.4

Raise

15

$15$ to the power of

2

$2$ .

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

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

Step 2.5

Add

81

$81$ and

121

$121$ .

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

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

Step 2.6

Add

202

$202$ and

169

$169$ .

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

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

Step 2.7

Add

371

$371$ and

225

$225$ .

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

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

Step 2.8

Divide

596

$596$ by

4

$4$ .

\sqrt{149}

$\sqrt{149}$

\sqrt{149}

$\sqrt{149}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\sqrt{149}

$\sqrt{149}$

Decimal Form:

12.20655561 \dots

$12.20655561 \dots$

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