Finite Math Examples Average Descriptive Statistics

Find the Quadratic Mean (RMS)

$1$ , $2$ , $3$ , $4$ , $5$

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.

$\sqrt{\frac{{(1)}^{2} + {(2)}^{2} + {(3)}^{2} + {(4)}^{2} + {(5)}^{2}}{5}}$

Step 2

Simplify the result.

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Step 2.1

One to any power is one.

$\sqrt{\frac{1 + {(2)}^{2} + {(3)}^{2} + {(4)}^{2} + {(5)}^{2}}{5}}$

Step 2.2

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

$\sqrt{\frac{1 + 4 + {(3)}^{2} + {(4)}^{2} + {(5)}^{2}}{5}}$

Step 2.3

Raise $3$ to the power of $2$ .

$\sqrt{\frac{1 + 4 + 9 + {(4)}^{2} + {(5)}^{2}}{5}}$

Step 2.4

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

$\sqrt{\frac{1 + 4 + 9 + 16 + {(5)}^{2}}{5}}$

Step 2.5

Raise $5$ to the power of $2$ .

$\sqrt{\frac{1 + 4 + 9 + 16 + 25}{5}}$

Step 2.6

Add $1$ and $4$ .

$\sqrt{\frac{5 + 9 + 16 + 25}{5}}$

Step 2.7

Add $5$ and $9$ .

$\sqrt{\frac{14 + 16 + 25}{5}}$

Step 2.8

Add $14$ and $16$ .

$\sqrt{\frac{30 + 25}{5}}$

Step 2.9

Add $30$ and $25$ .

$\sqrt{\frac{55}{5}}$

Step 2.10

Divide $55$ by $5$ .

$\sqrt{11}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{11}$

Decimal Form:

$3.31662479 \dots$

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Find the Quadratic Mean (RMS)

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