Find the Variance 1.56 , 24

$1.56$ , $24$

Step 1

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

$\overline{x} = \frac{1.56 + 24}{2}$

Step 2

Add $1.56$ and $24$ .

$\overline{x} = \frac{25.56}{2}$

Step 3

Divide $25.56$ by $2$ .

$\overline{x} = 12.78$

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.

$\overline{x} = 12.8$

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.

$s = \frac{{(1.56 - 12.8)}^{2} + {(24 - 12.8)}^{2}}{2 - 1}$

Step 7

Simplify the result.

Simplify the numerator.

Subtract $12.8$ from $1.56$ .

$s = \frac{{(- 11.24)}^{2} + {(24 - 12.8)}^{2}}{2 - 1}$

Raise $- 11.24$ to the power of $2$ .

$s = \frac{126.3376 + {(24 - 12.8)}^{2}}{2 - 1}$

Subtract $12.8$ from $24$ .

$s = \frac{126.3376 + {11.2}^{2}}{2 - 1}$

Raise $11.2$ to the power of $2$ .

$s = \frac{126.3376 + 125.44}{2 - 1}$

Add $126.3376$ and $125.44$ .

$s = \frac{251.7776}{2 - 1}$

Simplify the expression.

Subtract $1$ from $2$ .

$s = \frac{251.7776}{1}$

Divide $251.7776$ by $1$ .

$s = 251.7776$

Step 8

Approximate the result.

$s^{2} \approx 251.7776$

Find the Variance 1.56 , 24

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