Find the Variance 64 , 65 , 71 , 75 , 69

$64$ , $65$ , $71$ , $75$ , $69$

Step 1

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

$\overline{x} = \frac{64 + 65 + 71 + 75 + 69}{5}$

Step 2

Simplify the numerator.

Add $64$ and $65$ .

$\overline{x} = \frac{129 + 71 + 75 + 69}{5}$

Add $129$ and $71$ .

$\overline{x} = \frac{200 + 75 + 69}{5}$

Add $200$ and $75$ .

$\overline{x} = \frac{275 + 69}{5}$

Add $275$ and $69$ .

$\overline{x} = \frac{344}{5}$

Step 3

Divide.

$\overline{x} = 68.8$

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.

$s = \frac{{(64 - 68.8)}^{2} + {(65 - 68.8)}^{2} + {(71 - 68.8)}^{2} + {(75 - 68.8)}^{2} + {(69 - 68.8)}^{2}}{5 - 1}$

Step 6

Simplify the result.

Simplify the numerator.

Subtract $68.8$ from $64$ .

$s = \frac{{(- 4.8)}^{2} + {(65 - 68.8)}^{2} + {(71 - 68.8)}^{2} + {(75 - 68.8)}^{2} + {(69 - 68.8)}^{2}}{5 - 1}$

Raise $- 4.8$ to the power of $2$ .

$s = \frac{23.04 + {(65 - 68.8)}^{2} + {(71 - 68.8)}^{2} + {(75 - 68.8)}^{2} + {(69 - 68.8)}^{2}}{5 - 1}$

Subtract $68.8$ from $65$ .

$s = \frac{23.04 + {(- 3.8)}^{2} + {(71 - 68.8)}^{2} + {(75 - 68.8)}^{2} + {(69 - 68.8)}^{2}}{5 - 1}$

Raise $- 3.8$ to the power of $2$ .

$s = \frac{23.04 + 14.44 + {(71 - 68.8)}^{2} + {(75 - 68.8)}^{2} + {(69 - 68.8)}^{2}}{5 - 1}$

Subtract $68.8$ from $71$ .

$s = \frac{23.04 + 14.44 + {2.2}^{2} + {(75 - 68.8)}^{2} + {(69 - 68.8)}^{2}}{5 - 1}$

Raise $2.2$ to the power of $2$ .

$s = \frac{23.04 + 14.44 + 4.84 + {(75 - 68.8)}^{2} + {(69 - 68.8)}^{2}}{5 - 1}$

Subtract $68.8$ from $75$ .

$s = \frac{23.04 + 14.44 + 4.84 + {6.2}^{2} + {(69 - 68.8)}^{2}}{5 - 1}$

Raise $6.2$ to the power of $2$ .

$s = \frac{23.04 + 14.44 + 4.84 + 38.44 + {(69 - 68.8)}^{2}}{5 - 1}$

Subtract $68.8$ from $69$ .

$s = \frac{23.04 + 14.44 + 4.84 + 38.44 + {0.2}^{2}}{5 - 1}$

Raise $0.2$ to the power of $2$ .

$s = \frac{23.04 + 14.44 + 4.84 + 38.44 + 0.04}{5 - 1}$

Add $23.04$ and $14.44$ .

$s = \frac{37.48 + 4.84 + 38.44 + 0.04}{5 - 1}$

Add $37.48$ and $4.84$ .

$s = \frac{42.32 + 38.44 + 0.04}{5 - 1}$

Add $42.32$ and $38.44$ .

$s = \frac{80.76 + 0.04}{5 - 1}$

Add $80.76$ and $0.04$ .

$s = \frac{80.8}{5 - 1}$

Simplify the expression.

Subtract $1$ from $5$ .

$s = \frac{80.8}{4}$

Divide $80.8$ by $4$ .

$s = 20.2$

Step 7

Approximate the result.

$s^{2} \approx 20.2$

Find the Variance 64 , 65 , 71 , 75 , 69

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