Find the Variance 70.80 , 72.50 , 73.90

$70.8$ , $72.5$ , $73.9$

Step 1

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

$\overline{x} = \frac{70.8 + 72.5 + 73.9}{3}$

Step 2

Simplify the numerator.

Add $70.8$ and $72.5$ .

$\overline{x} = \frac{143.3 + 73.9}{3}$

Add $143.3$ and $73.9$ .

$\overline{x} = \frac{217.2}{3}$

Step 3

Divide $217.2$ by $3$ .

$\overline{x} = 72.4$

Step 4

Divide.

$\overline{x} = 72.4$

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.

$s = \frac{{(70.8 - 72.4)}^{2} + {(72.5 - 72.4)}^{2} + {(73.9 - 72.4)}^{2}}{3 - 1}$

Step 7

Simplify the result.

Simplify the numerator.

Subtract $72.4$ from $70.8$ .

$s = \frac{{(- 1.6)}^{2} + {(72.5 - 72.4)}^{2} + {(73.9 - 72.4)}^{2}}{3 - 1}$

Raise $- 1.6$ to the power of $2$ .

$s = \frac{2.56 + {(72.5 - 72.4)}^{2} + {(73.9 - 72.4)}^{2}}{3 - 1}$

Subtract $72.4$ from $72.5$ .

$s = \frac{2.56 + {0.1}^{2} + {(73.9 - 72.4)}^{2}}{3 - 1}$

Raise $0.1$ to the power of $2$ .

$s = \frac{2.56 + 0.01 + {(73.9 - 72.4)}^{2}}{3 - 1}$

Subtract $72.4$ from $73.9$ .

$s = \frac{2.56 + 0.01 + {1.5}^{2}}{3 - 1}$

Raise $1.5$ to the power of $2$ .

$s = \frac{2.56 + 0.01 + 2.25}{3 - 1}$

Add $2.56$ and $0.01$ .

$s = \frac{2.57 + 2.25}{3 - 1}$

Add $2.57$ and $2.25$ .

$s = \frac{4.82}{3 - 1}$

Simplify the expression.

Subtract $1$ from $3$ .

$s = \frac{4.82}{2}$

Divide $4.82$ by $2$ .

$s = 2.41$

Step 8

Approximate the result.

$s^{2} \approx 2.41$

Find the Variance 70.80 , 72.50 , 73.90

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