Find the Variance 9.58 , 9.69

$9.58$ ,

$9.69$

Step 1

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

$\overline{x} = \frac{9.58 + 9.69}{2}$

Step 2

Add

$9.58$ and

$9.69$ .

$\overline{x} = \frac{19.27}{2}$

Step 3

Divide

$19.27$ by

$2$ .

$\overline{x} = 9.635$

Step 4

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$\overline{x} = 9.635$

Step 5

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 6

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

$s = \frac{{(9.58 - 9.635)}^{2} + {(9.69 - 9.635)}^{2}}{2 - 1}$

Step 7

Simplify the result.

Simplify the numerator.

Subtract

$9.635$ from

$9.58$ .

$s = \frac{{(- 0.055)}^{2} + {(9.69 - 9.635)}^{2}}{2 - 1}$

Raise

$- 0.055$ to the power of

$2$ .

$s = \frac{0.003025 + {(9.69 - 9.635)}^{2}}{2 - 1}$

Subtract

$9.635$ from

$9.69$ .

$s = \frac{0.003025 + {0.055}^{2}}{2 - 1}$

Raise

$0.055$ to the power of

$2$ .

$s = \frac{0.003025 + 0.003025}{2 - 1}$

Add

$0.003025$ and

$0.003025$ .

$s = \frac{0.00605}{2 - 1}$

Simplify the expression.

Subtract

$1$ from

$2$ .

$s = \frac{0.00605}{1}$

Divide

$0.00605$ by

$1$ .

$s = 0.00605$

Step 8

Approximate the result.

$s^{2} \approx 0.006$

Find the Variance 9.58 , 9.69

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