Find the Variance 2 , 839 , 1 , 275

$2$ ,

$839$ ,

$1$ ,

$275$

Step 1

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

$\overline{x} = \frac{2 + 839 + 1 + 275}{4}$

Step 2

Simplify the numerator.

Add

$2$ and

$839$ .

$\overline{x} = \frac{841 + 1 + 275}{4}$

Add

$841$ and

$1$ .

$\overline{x} = \frac{842 + 275}{4}$

Add

$842$ and

$275$ .

$\overline{x} = \frac{1117}{4}$

Step 3

Divide.

$\overline{x} = 279.25$

Step 4

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$\overline{x} = 279.3$

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.

$s = \frac{{(2 - 279.3)}^{2} + {(839 - 279.3)}^{2} + {(1 - 279.3)}^{2} + {(275 - 279.3)}^{2}}{4 - 1}$

Step 7

Simplify the result.

Simplify the numerator.

Subtract

$279.3$ from

$2$ .

$s = \frac{{(- 277.3)}^{2} + {(839 - 279.3)}^{2} + {(1 - 279.3)}^{2} + {(275 - 279.3)}^{2}}{4 - 1}$

Raise

$- 277.3$ to the power of

$2$ .

$s = \frac{76895.29 + {(839 - 279.3)}^{2} + {(1 - 279.3)}^{2} + {(275 - 279.3)}^{2}}{4 - 1}$

Subtract

$279.3$ from

$839$ .

$s = \frac{76895.29 + {559.7}^{2} + {(1 - 279.3)}^{2} + {(275 - 279.3)}^{2}}{4 - 1}$

Raise

$559.7$ to the power of

$2$ .

$s = \frac{76895.29 + 313264.09 + {(1 - 279.3)}^{2} + {(275 - 279.3)}^{2}}{4 - 1}$

Subtract

$279.3$ from

$1$ .

$s = \frac{76895.29 + 313264.09 + {(- 278.3)}^{2} + {(275 - 279.3)}^{2}}{4 - 1}$

Raise

$- 278.3$ to the power of

$2$ .

$s = \frac{76895.29 + 313264.09 + 77450.89 + {(275 - 279.3)}^{2}}{4 - 1}$

Subtract

$279.3$ from

$275$ .

$s = \frac{76895.29 + 313264.09 + 77450.89 + {(- 4.3)}^{2}}{4 - 1}$

Raise

$- 4.3$ to the power of

$2$ .

$s = \frac{76895.29 + 313264.09 + 77450.89 + 18.49}{4 - 1}$

Add

$76895.29$ and

$313264.09$ .

$s = \frac{390159.38 + 77450.89 + 18.49}{4 - 1}$

Add

$390159.38$ and

$77450.89$ .

$s = \frac{467610.27 + 18.49}{4 - 1}$

Add

$467610.27$ and

$18.49$ .

$s = \frac{467628.76}{4 - 1}$

Simplify the expression.

Subtract

$1$ from

$4$ .

$s = \frac{467628.76}{3}$

Divide

$467628.76$ by

$3$ .

$s = 155876.25\overline{3}$

Step 8

Approximate the result.

$s^{2} \approx 155876.2533$

Find the Variance 2 , 839 , 1 , 275

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