Find the Variance 30 , 31 , 32 , 33 , 34

$30$ , $31$ , $32$ , $33$ , $34$

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

$\overline{x} = \frac{30 + 31 + 32 + 33 + 34}{5}$

Simplify the numerator.

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Add $30$ and $31$ .

$\overline{x} = \frac{61 + 32 + 33 + 34}{5}$

Add $61$ and $32$ .

$\overline{x} = \frac{93 + 33 + 34}{5}$

Add $93$ and $33$ .

$\overline{x} = \frac{126 + 34}{5}$

Add $126$ and $34$ .

$\overline{x} = \frac{160}{5}$

Divide $160$ by $5$ .

$\overline{x} = 32$

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.

$s = \frac{{(30 - 32)}^{2} + {(31 - 32)}^{2} + {(32 - 32)}^{2} + {(33 - 32)}^{2} + {(34 - 32)}^{2}}{5 - 1}$

Simplify the result.

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Simplify the numerator.

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Subtract $32$ from $30$ .

$s = \frac{{(- 2)}^{2} + {(31 - 32)}^{2} + {(32 - 32)}^{2} + {(33 - 32)}^{2} + {(34 - 32)}^{2}}{5 - 1}$

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

$s = \frac{4 + {(31 - 32)}^{2} + {(32 - 32)}^{2} + {(33 - 32)}^{2} + {(34 - 32)}^{2}}{5 - 1}$

Subtract $32$ from $31$ .

$s = \frac{4 + {(- 1)}^{2} + {(32 - 32)}^{2} + {(33 - 32)}^{2} + {(34 - 32)}^{2}}{5 - 1}$

Raise $- 1$ to the power of $2$ .

$s = \frac{4 + 1 + {(32 - 32)}^{2} + {(33 - 32)}^{2} + {(34 - 32)}^{2}}{5 - 1}$

Subtract $32$ from $32$ .

$s = \frac{4 + 1 + 0^{2} + {(33 - 32)}^{2} + {(34 - 32)}^{2}}{5 - 1}$

Raising $0$ to any positive power yields $0$ .

$s = \frac{4 + 1 + 0 + {(33 - 32)}^{2} + {(34 - 32)}^{2}}{5 - 1}$

Subtract $32$ from $33$ .

$s = \frac{4 + 1 + 0 + 1^{2} + {(34 - 32)}^{2}}{5 - 1}$

One to any power is one.

$s = \frac{4 + 1 + 0 + 1 + {(34 - 32)}^{2}}{5 - 1}$

Subtract $32$ from $34$ .

$s = \frac{4 + 1 + 0 + 1 + 2^{2}}{5 - 1}$

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

$s = \frac{4 + 1 + 0 + 1 + 4}{5 - 1}$

Add $4$ and $1$ .

$s = \frac{5 + 0 + 1 + 4}{5 - 1}$

Add $5$ and $0$ .

$s = \frac{5 + 1 + 4}{5 - 1}$

Add $5$ and $1$ .

$s = \frac{6 + 4}{5 - 1}$

Add $6$ and $4$ .

$s = \frac{10}{5 - 1}$

Reduce the expression by cancelling the common factors.

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Subtract $1$ from $5$ .

$s = \frac{10}{4}$

Cancel the common factor of $10$ and $4$ .

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Factor $2$ out of $10$ .

$s = \frac{2 (5)}{4}$

Cancel the common factors.

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Factor $2$ out of $4$ .

$s = \frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$s = \frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$s = \frac{5}{2}$

Approximate the result.

$s^{2} \approx 2.5$

Find the Variance 30 , 31 , 32 , 33 , 34

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