Find the Variance 340 , 75 , 123 , 259 , 151

$340$ , $75$ , $123$ , $259$ , $151$

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

$\overline{x} = \frac{340 + 75 + 123 + 259 + 151}{5}$

Simplify the numerator.

Add $340$ and $75$ .

$\overline{x} = \frac{415 + 123 + 259 + 151}{5}$

Add $415$ and $123$ .

$\overline{x} = \frac{538 + 259 + 151}{5}$

Add $538$ and $259$ .

$\overline{x} = \frac{797 + 151}{5}$

Add $797$ and $151$ .

$\overline{x} = \frac{948}{5}$

Divide.

$\overline{x} = 189.6$

Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.

$s^{2} = \sum_{i = 1}^{n} \frac{{(x_{i} - x_{a v g})}^{2}}{n - 1}$

Set up the formula for variance for this set of numbers.

$s = \frac{{(340 - 189.6)}^{2} + {(75 - 189.6)}^{2} + {(123 - 189.6)}^{2} + {(259 - 189.6)}^{2} + {(151 - 189.6)}^{2}}{5 - 1}$

Simplify the result.

Simplify the numerator.

Subtract $189.6$ from $340$ .

$s = \frac{{150.4}^{2} + {(75 - 189.6)}^{2} + {(123 - 189.6)}^{2} + {(259 - 189.6)}^{2} + {(151 - 189.6)}^{2}}{5 - 1}$

Raise $150.4$ to the power of $2$ .

$s = \frac{22620.16 + {(75 - 189.6)}^{2} + {(123 - 189.6)}^{2} + {(259 - 189.6)}^{2} + {(151 - 189.6)}^{2}}{5 - 1}$

Subtract $189.6$ from $75$ .

$s = \frac{22620.16 + {(- 114.6)}^{2} + {(123 - 189.6)}^{2} + {(259 - 189.6)}^{2} + {(151 - 189.6)}^{2}}{5 - 1}$

Raise $- 114.6$ to the power of $2$ .

$s = \frac{22620.16 + 13133.16 + {(123 - 189.6)}^{2} + {(259 - 189.6)}^{2} + {(151 - 189.6)}^{2}}{5 - 1}$

Subtract $189.6$ from $123$ .

$s = \frac{22620.16 + 13133.16 + {(- 66.6)}^{2} + {(259 - 189.6)}^{2} + {(151 - 189.6)}^{2}}{5 - 1}$

Raise $- 66.6$ to the power of $2$ .

$s = \frac{22620.16 + 13133.16 + 4435.56 + {(259 - 189.6)}^{2} + {(151 - 189.6)}^{2}}{5 - 1}$

Subtract $189.6$ from $259$ .

$s = \frac{22620.16 + 13133.16 + 4435.56 + {69.4}^{2} + {(151 - 189.6)}^{2}}{5 - 1}$

Raise $69.4$ to the power of $2$ .

$s = \frac{22620.16 + 13133.16 + 4435.56 + 4816.36 + {(151 - 189.6)}^{2}}{5 - 1}$

Subtract $189.6$ from $151$ .

$s = \frac{22620.16 + 13133.16 + 4435.56 + 4816.36 + {(- 38.6)}^{2}}{5 - 1}$

Raise $- 38.6$ to the power of $2$ .

$s = \frac{22620.16 + 13133.16 + 4435.56 + 4816.36 + 1489.96}{5 - 1}$

Add $22620.16$ and $13133.16$ .

$s = \frac{35753.32 + 4435.56 + 4816.36 + 1489.96}{5 - 1}$

Add $35753.32$ and $4435.56$ .

$s = \frac{40188.88 + 4816.36 + 1489.96}{5 - 1}$

Add $40188.88$ and $4816.36$ .

$s = \frac{45005.24 + 1489.96}{5 - 1}$

Add $45005.24$ and $1489.96$ .

$s = \frac{46495.2}{5 - 1}$

Simplify the expression.

Subtract $1$ from $5$ .

$s = \frac{46495.2}{4}$

Divide $46495.2$ by $4$ .

$s = 11623.8$

Approximate the result.

$s^{2} \approx 11623.8$

Find the Variance 340 , 75 , 123 , 259 , 151

Related Questions

Support LCMGCF.com by disabling your adblocker.