Finite Math Examples

$\frac{1}{3}$ , $- 3$

Step 1

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

$\frac{\frac{1}{3} - 3}{2}$

Step 2

Simplify the numerator.

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Step 2.1

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{1}{3} - 3 \cdot \frac{3}{3}}{2}$

Step 2.2

Combine $- 3$ and $\frac{3}{3}$ .

$\frac{\frac{1}{3} + \frac{- 3 \cdot 3}{3}}{2}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{\frac{1 - 3 \cdot 3}{3}}{2}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 3$ by $3$ .

$\frac{\frac{1 - 9}{3}}{2}$

Step 2.4.2

Subtract $9$ from $1$ .

$\frac{\frac{- 8}{3}}{2}$

Step 2.5

Move the negative in front of the fraction.

$\frac{- \frac{8}{3}}{2}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{8}{3} \cdot \frac{1}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$\frac{- 8}{3} \cdot \frac{1}{2}$

Step 4.2

Factor $2$ out of $- 8$ .

$\frac{2 (- 4)}{3} \cdot \frac{1}{2}$

Step 4.3

Cancel the common factor.

$\frac{2 \cdot - 4}{3} \cdot \frac{1}{2}$

Step 4.4

Rewrite the expression.

$\frac{- 4}{3}$

Step 5

Move the negative in front of the fraction.

$- \frac{4}{3}$

Step 6

Divide.

$- 1.\overline{3}$

Step 7

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.

$- 1.3$