Find the Variance 24 , 84

$24$ , $84$

Step 1

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

$\overline{x} = \frac{24 + 84}{2}$

Step 2

Cancel the common factor of $24 + 84$ and $2$ .

Factor $2$ out of $24$ .

$\overline{x} = \frac{2 \cdot 12 + 84}{2}$

Factor $2$ out of $84$ .

$\overline{x} = \frac{2 \cdot 12 + 2 \cdot 42}{2}$

Factor $2$ out of $2 \cdot 12 + 2 \cdot 42$ .

$\overline{x} = \frac{2 \cdot (12 + 42)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\overline{x} = \frac{2 \cdot (12 + 42)}{2 (1)}$

Cancel the common factor.

$\overline{x} = \frac{2 \cdot (12 + 42)}{2 \cdot 1}$

Rewrite the expression.

$\overline{x} = \frac{12 + 42}{1}$

Divide $12 + 42$ by $1$ .

$\overline{x} = 12 + 42$

Step 3

Add $12$ and $42$ .

$\overline{x} = 54$

Step 4

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

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

Step 5

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

$s = \frac{{(24 - 54)}^{2} + {(84 - 54)}^{2}}{2 - 1}$

Step 6

Simplify the result.

Simplify the numerator.

Subtract $54$ from $24$ .

$s = \frac{{(- 30)}^{2} + {(84 - 54)}^{2}}{2 - 1}$

Raise $- 30$ to the power of $2$ .

$s = \frac{900 + {(84 - 54)}^{2}}{2 - 1}$

Subtract $54$ from $84$ .

$s = \frac{900 + 30^{2}}{2 - 1}$

Raise $30$ to the power of $2$ .

$s = \frac{900 + 900}{2 - 1}$

Add $900$ and $900$ .

$s = \frac{1800}{2 - 1}$

Simplify the expression.

Subtract $1$ from $2$ .

$s = \frac{1800}{1}$

Divide $1800$ by $1$ .

$s = 1800$

Step 7

Approximate the result.

$s^{2} \approx 1800$

Find the Variance 24 , 84

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