Finite Math Examples

$2$ , $6$ , $18$ , $54$ , $162$ , $486$

Step 1

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

$\frac{2 + 6 + 18 + 54 + 162 + 486}{6}$

Step 2

Cancel the common factor of $2 + 6 + 18 + 54 + 162 + 486$ and $6$ .

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Step 2.1

Factor $2$ out of $2$ .

$\frac{2 (1) + 6 + 18 + 54 + 162 + 486}{6}$

Step 2.2

Factor $2$ out of $6$ .

$\frac{2 \cdot 1 + 2 \cdot 3 + 18 + 54 + 162 + 486}{6}$

Step 2.3

Factor $2$ out of $2 \cdot 1 + 2 \cdot 3$ .

$\frac{2 \cdot (1 + 3) + 18 + 54 + 162 + 486}{6}$

Step 2.4

Factor $2$ out of $18$ .

$\frac{2 \cdot (1 + 3) + 2 (9) + 54 + 162 + 486}{6}$

Step 2.5

Factor $2$ out of $2 \cdot (1 + 3) + 2 (9)$ .

$\frac{2 \cdot (1 + 3 + 9) + 54 + 162 + 486}{6}$

Step 2.6

Factor $2$ out of $54$ .

$\frac{2 \cdot (1 + 3 + 9) + 2 (27) + 162 + 486}{6}$

Step 2.7

Factor $2$ out of $2 \cdot (1 + 3 + 9) + 2 (27)$ .

$\frac{2 \cdot (1 + 3 + 9 + 27) + 162 + 486}{6}$

Step 2.8

Factor $2$ out of $162$ .

$\frac{2 \cdot (1 + 3 + 9 + 27) + 2 (81) + 486}{6}$

Step 2.9

Factor $2$ out of $2 \cdot (1 + 3 + 9 + 27) + 2 (81)$ .

$\frac{2 \cdot (1 + 3 + 9 + 27 + 81) + 486}{6}$

Step 2.10

Factor $2$ out of $486$ .

$\frac{2 \cdot (1 + 3 + 9 + 27 + 81) + 2 (243)}{6}$

Step 2.11

Factor $2$ out of $2 \cdot (1 + 3 + 9 + 27 + 81) + 2 (243)$ .

$\frac{2 \cdot (1 + 3 + 9 + 27 + 81 + 243)}{6}$

Step 2.12

Cancel the common factors.

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Step 2.12.1

Factor $2$ out of $6$ .

$\frac{2 \cdot (1 + 3 + 9 + 27 + 81 + 243)}{2 (3)}$

Step 2.12.2

Cancel the common factor.

$\frac{2 \cdot (1 + 3 + 9 + 27 + 81 + 243)}{2 \cdot 3}$

Step 2.12.3

Rewrite the expression.

$\frac{1 + 3 + 9 + 27 + 81 + 243}{3}$

Step 3

Simplify the numerator.

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Step 3.1

Add $1$ and $3$ .

$\frac{4 + 9 + 27 + 81 + 243}{3}$

Step 3.2

Add $4$ and $9$ .

$\frac{13 + 27 + 81 + 243}{3}$

Step 3.3

Add $13$ and $27$ .

$\frac{40 + 81 + 243}{3}$

Step 3.4

Add $40$ and $81$ .

$\frac{121 + 243}{3}$

Step 3.5

Add $121$ and $243$ .

$\frac{364}{3}$

Step 4

Divide.

$121.\overline{3}$

Step 5

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.

$121.3$