Find the Variance 3 , 15 , 75 , 375 , 1875

$3$ , $15$ , $75$ , $375$ , $1875$

The mean of a set of numbers is the sum divided by the number of terms.

$\overline{x} = \frac{3 + 15 + 75 + 375 + 1875}{5}$

Simplify the numerator.

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Add $3$ and $15$ .

$\overline{x} = \frac{18 + 75 + 375 + 1875}{5}$

Add $18$ and $75$ .

$\overline{x} = \frac{93 + 375 + 1875}{5}$

Add $93$ and $375$ .

$\overline{x} = \frac{468 + 1875}{5}$

Add $468$ and $1875$ .

$\overline{x} = \frac{2343}{5}$

Divide.

$\overline{x} = 468.6$

Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.

$s^{2} = \sum_{i = 1}^{n} \frac{{(x_{i} - x_{a v g})}^{2}}{n - 1}$

Set up the formula for variance for this set of numbers.

$s = \frac{{(3 - 468.6)}^{2} + {(15 - 468.6)}^{2} + {(75 - 468.6)}^{2} + {(375 - 468.6)}^{2} + {(1875 - 468.6)}^{2}}{5 - 1}$

Simplify the result.

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Simplify the numerator.

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Subtract $468.6$ from $3$ .

$s = \frac{{(- 465.6)}^{2} + {(15 - 468.6)}^{2} + {(75 - 468.6)}^{2} + {(375 - 468.6)}^{2} + {(1875 - 468.6)}^{2}}{5 - 1}$

Raise $- 465.6$ to the power of $2$ .

$s = \frac{216783.36 + {(15 - 468.6)}^{2} + {(75 - 468.6)}^{2} + {(375 - 468.6)}^{2} + {(1875 - 468.6)}^{2}}{5 - 1}$

Subtract $468.6$ from $15$ .

$s = \frac{216783.36 + {(- 453.6)}^{2} + {(75 - 468.6)}^{2} + {(375 - 468.6)}^{2} + {(1875 - 468.6)}^{2}}{5 - 1}$

Raise $- 453.6$ to the power of $2$ .

$s = \frac{216783.36 + 205752.96 + {(75 - 468.6)}^{2} + {(375 - 468.6)}^{2} + {(1875 - 468.6)}^{2}}{5 - 1}$

Subtract $468.6$ from $75$ .

$s = \frac{216783.36 + 205752.96 + {(- 393.6)}^{2} + {(375 - 468.6)}^{2} + {(1875 - 468.6)}^{2}}{5 - 1}$

Raise $- 393.6$ to the power of $2$ .

$s = \frac{216783.36 + 205752.96 + 154920.96 + {(375 - 468.6)}^{2} + {(1875 - 468.6)}^{2}}{5 - 1}$

Subtract $468.6$ from $375$ .

$s = \frac{216783.36 + 205752.96 + 154920.96 + {(- 93.6)}^{2} + {(1875 - 468.6)}^{2}}{5 - 1}$

Raise $- 93.6$ to the power of $2$ .

$s = \frac{216783.36 + 205752.96 + 154920.96 + 8760.96 + {(1875 - 468.6)}^{2}}{5 - 1}$

Subtract $468.6$ from $1875$ .

$s = \frac{216783.36 + 205752.96 + 154920.96 + 8760.96 + {1406.4}^{2}}{5 - 1}$

Raise $1406.4$ to the power of $2$ .

$s = \frac{216783.36 + 205752.96 + 154920.96 + 8760.96 + 1977960.96}{5 - 1}$

Add $216783.36$ and $205752.96$ .

$s = \frac{422536.32 + 154920.96 + 8760.96 + 1977960.96}{5 - 1}$

Add $422536.32$ and $154920.96$ .

$s = \frac{577457.28 + 8760.96 + 1977960.96}{5 - 1}$

Add $577457.28$ and $8760.96$ .

$s = \frac{586218.24 + 1977960.96}{5 - 1}$

Add $586218.24$ and $1977960.96$ .

$s = \frac{2564179.2}{5 - 1}$

Simplify the expression.

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Subtract $1$ from $5$ .

$s = \frac{2564179.2}{4}$

Divide $2564179.2$ by $4$ .

$s = 641044.8$

Approximate the result.

$s^{2} \approx 641044.8$

Find the Variance 3 , 15 , 75 , 375 , 1875

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