Find the Variance 6 8 1 9 4

$6$ $8$ $1$ $9$ $4$

Step 1

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

$\overline{x} = \frac{6 + 8 + 1 + 9 + 4}{5}$

Step 2

Simplify the numerator.

Add $6$ and $8$ .

$\overline{x} = \frac{14 + 1 + 9 + 4}{5}$

Add $14$ and $1$ .

$\overline{x} = \frac{15 + 9 + 4}{5}$

Add $15$ and $9$ .

$\overline{x} = \frac{24 + 4}{5}$

Add $24$ and $4$ .

$\overline{x} = \frac{28}{5}$

Step 3

Divide.

$\overline{x} = 5.6$

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.

$s = \frac{{(6 - 5.6)}^{2} + {(8 - 5.6)}^{2} + {(1 - 5.6)}^{2} + {(9 - 5.6)}^{2} + {(4 - 5.6)}^{2}}{5 - 1}$

Step 6

Simplify the result.

Simplify the numerator.

Subtract $5.6$ from $6$ .

$s = \frac{{0.4}^{2} + {(8 - 5.6)}^{2} + {(1 - 5.6)}^{2} + {(9 - 5.6)}^{2} + {(4 - 5.6)}^{2}}{5 - 1}$

Raise $0.4$ to the power of $2$ .

$s = \frac{0.16 + {(8 - 5.6)}^{2} + {(1 - 5.6)}^{2} + {(9 - 5.6)}^{2} + {(4 - 5.6)}^{2}}{5 - 1}$

Subtract $5.6$ from $8$ .

$s = \frac{0.16 + {2.4}^{2} + {(1 - 5.6)}^{2} + {(9 - 5.6)}^{2} + {(4 - 5.6)}^{2}}{5 - 1}$

Raise $2.4$ to the power of $2$ .

$s = \frac{0.16 + 5.76 + {(1 - 5.6)}^{2} + {(9 - 5.6)}^{2} + {(4 - 5.6)}^{2}}{5 - 1}$

Subtract $5.6$ from $1$ .

$s = \frac{0.16 + 5.76 + {(- 4.6)}^{2} + {(9 - 5.6)}^{2} + {(4 - 5.6)}^{2}}{5 - 1}$

Raise $- 4.6$ to the power of $2$ .

$s = \frac{0.16 + 5.76 + 21.16 + {(9 - 5.6)}^{2} + {(4 - 5.6)}^{2}}{5 - 1}$

Subtract $5.6$ from $9$ .

$s = \frac{0.16 + 5.76 + 21.16 + {3.4}^{2} + {(4 - 5.6)}^{2}}{5 - 1}$

Raise $3.4$ to the power of $2$ .

$s = \frac{0.16 + 5.76 + 21.16 + 11.56 + {(4 - 5.6)}^{2}}{5 - 1}$

Subtract $5.6$ from $4$ .

$s = \frac{0.16 + 5.76 + 21.16 + 11.56 + {(- 1.6)}^{2}}{5 - 1}$

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

$s = \frac{0.16 + 5.76 + 21.16 + 11.56 + 2.56}{5 - 1}$

Add $0.16$ and $5.76$ .

$s = \frac{5.92 + 21.16 + 11.56 + 2.56}{5 - 1}$

Add $5.92$ and $21.16$ .

$s = \frac{27.08 + 11.56 + 2.56}{5 - 1}$

Add $27.08$ and $11.56$ .

$s = \frac{38.64 + 2.56}{5 - 1}$

Add $38.64$ and $2.56$ .

$s = \frac{41.2}{5 - 1}$

Simplify the expression.

Subtract $1$ from $5$ .

$s = \frac{41.2}{4}$

Divide $41.2$ by $4$ .

$s = 10.3$

Step 7

Approximate the result.

$s^{2} \approx 10.3$

Find the Variance 6 8 1 9 4

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