Finite Math Examples

$166$ , $182$ , $177$ , $94$ , $120$ , $200$ , $175$

Step 1

Use the formula to find the geometric mean.

$\sqrt[7]{166 \cdot 182 \cdot 177 \cdot 94 \cdot 120 \cdot 200 \cdot 175}$

Step 2

Multiply $166$ by $182$ .

$\sqrt[7]{30212 \cdot 177 \cdot 94 \cdot 120 \cdot 200 \cdot 175}$

Step 3

Multiply $30212$ by $177$ .

$\sqrt[7]{5347524 \cdot 94 \cdot 120 \cdot 200 \cdot 175}$

Step 4

Multiply $5347524$ by $94$ .

$\sqrt[7]{502667256 \cdot 120 \cdot 200 \cdot 175}$

Step 5

Multiply $502667256$ by $120$ .

$\sqrt[7]{60320070720 \cdot 200 \cdot 175}$

Step 6

Multiply $60320070720$ by $200$ .

$\sqrt[7]{12064014144000 \cdot 175}$

Step 7

Multiply $12064014144000$ by $175$ .

$\sqrt[7]{2111202475200000}$

Step 8

Rewrite $2111202475200000$ as $2^{7} \cdot 16493769337500$ .

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Step 8.1

Factor $128$ out of $2111202475200000$ .

$\sqrt[7]{128 (16493769337500)}$

Step 8.2

Rewrite $128$ as $2^{7}$ .

$\sqrt[7]{2^{7} \cdot 16493769337500}$

Step 9

Pull terms out from under the radical.

$2 \sqrt[7]{16493769337500}$

Step 10

Approximate the result.

$154.6032272$

Step 11

The geometric 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.

$154.6$