Find the Variance 23 , 0 , 0

$23$ ,

$0$ ,

$0$

Step 1

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

$\overline{x} = \frac{23 + 0 + 0}{3}$

Step 2

Simplify the numerator.

Add

$23 + 0$ and

$0$ .

$\overline{x} = \frac{23 + 0}{3}$

Add

$23$ and

$0$ .

$\overline{x} = \frac{23}{3}$

Step 3

Divide.

$\overline{x} = 7.\overline{6}$

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.

$\overline{x} = 7.7$

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.

$s = \frac{{(23 - 7.7)}^{2} + {(0 - 7.7)}^{2} + {(0 - 7.7)}^{2}}{3 - 1}$

Step 7

Simplify the result.

Simplify the numerator.

Subtract

$7.7$ from

$23$ .

$s = \frac{{15.3}^{2} + {(0 - 7.7)}^{2} + {(0 - 7.7)}^{2}}{3 - 1}$

Raise

$15.3$ to the power of

$2$ .

$s = \frac{234.09 + {(0 - 7.7)}^{2} + {(0 - 7.7)}^{2}}{3 - 1}$

Subtract

$7.7$ from

$0$ .

$s = \frac{234.09 + {(- 7.7)}^{2} + {(0 - 7.7)}^{2}}{3 - 1}$

Raise

$- 7.7$ to the power of

$2$ .

$s = \frac{234.09 + 59.29 + {(0 - 7.7)}^{2}}{3 - 1}$

Subtract

$7.7$ from

$0$ .

$s = \frac{234.09 + 59.29 + {(- 7.7)}^{2}}{3 - 1}$

Raise

$- 7.7$ to the power of

$2$ .

$s = \frac{234.09 + 59.29 + 59.29}{3 - 1}$

Add

$234.09$ and

$59.29$ .

$s = \frac{293.38 + 59.29}{3 - 1}$

Add

$293.38$ and

$59.29$ .

$s = \frac{352.67}{3 - 1}$

Simplify the expression.

Subtract

$1$ from

$3$ .

$s = \frac{352.67}{2}$

Divide

$352.67$ by

$2$ .

$s = 176.335$

Step 8

Approximate the result.

$s^{2} \approx 176.335$

Find the Variance 23 , 0 , 0

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