Finite Math Examples

57

$57$ ,

5

$5$ ,

39

$39$

Step 1

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

\overline{x} = \frac{57 + 5 + 39}{3}

$\overline{x} = \frac{57 + 5 + 39}{3}$

Step 2

Simplify the numerator.

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Step 2.1

Add

57

$57$ and

5

$5$ .

\overline{x} = \frac{62 + 39}{3}

$\overline{x} = \frac{62 + 39}{3}$

Step 2.2

Add

62

$62$ and

39

$39$ .

\overline{x} = \frac{101}{3}

$\overline{x} = \frac{101}{3}$

\overline{x} = \frac{101}{3}

$\overline{x} = \frac{101}{3}$

Step 3

Divide.

\overline{x} = 33.\overline{6}

$\overline{x} = 33.\overline{6}$

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} = 33.7

$\overline{x} = 33.7$

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}

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

Step 6

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

s = \frac{{(57 - 33.7)}^{2} + {(5 - 33.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}

$s = \frac{{(57 - 33.7)}^{2} + {(5 - 33.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Subtract

33.7

$33.7$ from

57

$57$ .

s = \frac{{23.3}^{2} + {(5 - 33.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}

$s = \frac{{23.3}^{2} + {(5 - 33.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7.1.2

Raise

23.3

$23.3$ to the power of

2

$2$ .

s = \frac{542.89 + {(5 - 33.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}

$s = \frac{542.89 + {(5 - 33.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7.1.3

Subtract

33.7

$33.7$ from

5

$5$ .

s = \frac{542.89 + {(- 28.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}

$s = \frac{542.89 + {(- 28.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7.1.4

Raise

- 28.7

$- 28.7$ to the power of

2

$2$ .

s = \frac{542.89 + 823.69 + {(39 - 33.7)}^{2}}{3 - 1}

$s = \frac{542.89 + 823.69 + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7.1.5

Subtract

33.7

$33.7$ from

39

$39$ .

s = \frac{542.89 + 823.69 + {5.3}^{2}}{3 - 1}

$s = \frac{542.89 + 823.69 + {5.3}^{2}}{3 - 1}$

Step 7.1.6

Raise

5.3

$5.3$ to the power of

2

$2$ .

s = \frac{542.89 + 823.69 + 28.09}{3 - 1}

$s = \frac{542.89 + 823.69 + 28.09}{3 - 1}$

Step 7.1.7

Add

542.89

$542.89$ and

823.69

$823.69$ .

s = \frac{1366.58 + 28.09}{3 - 1}

$s = \frac{1366.58 + 28.09}{3 - 1}$

Step 7.1.8

Add

1366.58

$1366.58$ and

28.09

$28.09$ .

s = \frac{1394.67}{3 - 1}

$s = \frac{1394.67}{3 - 1}$

s = \frac{1394.67}{3 - 1}

$s = \frac{1394.67}{3 - 1}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Subtract

1

$1$ from

3

$3$ .

s = \frac{1394.67}{2}

$s = \frac{1394.67}{2}$

Step 7.2.2

Divide

1394.67

$1394.67$ by

2

$2$ .

s = 697.335

$s = 697.335$

s = 697.335

$s = 697.335$

s = 697.335

$s = 697.335$

Step 8

Approximate the result.

s^{2} \approx 697.335

$s^{2} \approx 697.335$