Find the Variance 125 , -25 , 5 , -1

$125$ , $- 25$ , $5$ , $- 1$

Step 1

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

$\overline{x} = \frac{125 - 25 + 5 - 1}{4}$

Step 2

Simplify the numerator.

Subtract $25$ from $125$ .

$\overline{x} = \frac{100 + 5 - 1}{4}$

Add $100$ and $5$ .

$\overline{x} = \frac{105 - 1}{4}$

Subtract $1$ from $105$ .

$\overline{x} = \frac{104}{4}$

Step 3

Divide $104$ by $4$ .

$\overline{x} = 26$

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.

$s = \frac{{(125 - 26)}^{2} + {(- 25 - 26)}^{2} + {(5 - 26)}^{2} + {(- 1 - 26)}^{2}}{4 - 1}$

Step 6

Simplify the result.

Simplify the numerator.

Subtract $26$ from $125$ .

$s = \frac{99^{2} + {(- 25 - 26)}^{2} + {(5 - 26)}^{2} + {(- 1 - 26)}^{2}}{4 - 1}$

Raise $99$ to the power of $2$ .

$s = \frac{9801 + {(- 25 - 26)}^{2} + {(5 - 26)}^{2} + {(- 1 - 26)}^{2}}{4 - 1}$

Subtract $26$ from $- 25$ .

$s = \frac{9801 + {(- 51)}^{2} + {(5 - 26)}^{2} + {(- 1 - 26)}^{2}}{4 - 1}$

Raise $- 51$ to the power of $2$ .

$s = \frac{9801 + 2601 + {(5 - 26)}^{2} + {(- 1 - 26)}^{2}}{4 - 1}$

Subtract $26$ from $5$ .

$s = \frac{9801 + 2601 + {(- 21)}^{2} + {(- 1 - 26)}^{2}}{4 - 1}$

Raise $- 21$ to the power of $2$ .

$s = \frac{9801 + 2601 + 441 + {(- 1 - 26)}^{2}}{4 - 1}$

Subtract $26$ from $- 1$ .

$s = \frac{9801 + 2601 + 441 + {(- 27)}^{2}}{4 - 1}$

Raise $- 27$ to the power of $2$ .

$s = \frac{9801 + 2601 + 441 + 729}{4 - 1}$

Add $9801$ and $2601$ .

$s = \frac{12402 + 441 + 729}{4 - 1}$

Add $12402$ and $441$ .

$s = \frac{12843 + 729}{4 - 1}$

Add $12843$ and $729$ .

$s = \frac{13572}{4 - 1}$

Simplify the expression.

Subtract $1$ from $4$ .

$s = \frac{13572}{3}$

Divide $13572$ by $3$ .

$s = 4524$

Step 7

Approximate the result.

$s^{2} \approx 4524$

Find the Variance 125 , -25 , 5 , -1

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