Find the Variance 84 , 294

$84$ , $294$

Step 1

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

$\overline{x} = \frac{84 + 294}{2}$

Step 2

Cancel the common factor of $84 + 294$ and $2$ .

Factor $2$ out of $84$ .

$\overline{x} = \frac{2 \cdot 42 + 294}{2}$

Factor $2$ out of $294$ .

$\overline{x} = \frac{2 \cdot 42 + 2 \cdot 147}{2}$

Factor $2$ out of $2 \cdot 42 + 2 \cdot 147$ .

$\overline{x} = \frac{2 \cdot (42 + 147)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\overline{x} = \frac{2 \cdot (42 + 147)}{2 (1)}$

Cancel the common factor.

$\overline{x} = \frac{2 \cdot (42 + 147)}{2 \cdot 1}$

Rewrite the expression.

$\overline{x} = \frac{42 + 147}{1}$

Divide $42 + 147$ by $1$ .

$\overline{x} = 42 + 147$

Step 3

Add $42$ and $147$ .

$\overline{x} = 189$

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.

$s = \frac{{(84 - 189)}^{2} + {(294 - 189)}^{2}}{2 - 1}$

Step 6

Simplify the result.

Simplify the numerator.

Subtract $189$ from $84$ .

$s = \frac{{(- 105)}^{2} + {(294 - 189)}^{2}}{2 - 1}$

Raise $- 105$ to the power of $2$ .

$s = \frac{11025 + {(294 - 189)}^{2}}{2 - 1}$

Subtract $189$ from $294$ .

$s = \frac{11025 + 105^{2}}{2 - 1}$

Raise $105$ to the power of $2$ .

$s = \frac{11025 + 11025}{2 - 1}$

Add $11025$ and $11025$ .

$s = \frac{22050}{2 - 1}$

Simplify the expression.

Subtract $1$ from $2$ .

$s = \frac{22050}{1}$

Divide $22050$ by $1$ .

$s = 22050$

Step 7

Approximate the result.

$s^{2} \approx 22050$

Find the Variance 84 , 294

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