Finite Math Examples

$9$ , $2$ , $5$ , $6$ , $8$ , $7$ , $8$ , $5$ , $4$

Step 1

Use the formula to find the geometric mean.

$\sqrt[9]{9 \cdot 2 \cdot 5 \cdot 6 \cdot 8 \cdot 7 \cdot 8 \cdot 5 \cdot 4}$

Step 2

Multiply $9$ by $2$ .

$\sqrt[9]{18 \cdot 5 \cdot 6 \cdot 8 \cdot 7 \cdot 8 \cdot 5 \cdot 4}$

Step 3

Multiply $18$ by $5$ .

$\sqrt[9]{90 \cdot 6 \cdot 8 \cdot 7 \cdot 8 \cdot 5 \cdot 4}$

Step 4

Multiply $90$ by $6$ .

$\sqrt[9]{540 \cdot 8 \cdot 7 \cdot 8 \cdot 5 \cdot 4}$

Step 5

Multiply $540$ by $8$ .

$\sqrt[9]{4320 \cdot 7 \cdot 8 \cdot 5 \cdot 4}$

Step 6

Multiply $4320$ by $7$ .

$\sqrt[9]{30240 \cdot 8 \cdot 5 \cdot 4}$

Step 7

Multiply $30240$ by $8$ .

$\sqrt[9]{241920 \cdot 5 \cdot 4}$

Step 8

Multiply $241920$ by $5$ .

$\sqrt[9]{1209600 \cdot 4}$

Step 9

Multiply $1209600$ by $4$ .

$\sqrt[9]{4838400}$

Step 10

Rewrite $4838400$ as $2^{9} \cdot 9450$ .

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Step 10.1

Factor $512$ out of $4838400$ .

$\sqrt[9]{512 (9450)}$

Step 10.2

Rewrite $512$ as $2^{9}$ .

$\sqrt[9]{2^{9} \cdot 9450}$

Step 11

Pull terms out from under the radical.

$2 \sqrt[9]{9450}$

Step 12

Approximate the result.

$5.53024842$

Step 13

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.

$5.5$