Statistics Examples

$2$ , $4$ , $6$ , $8$ , $10$ , $12$

Step 1

Use the formula to find the geometric mean.

$\sqrt[6]{2 \cdot 4 \cdot 6 \cdot 8 \cdot 10 \cdot 12}$

Step 2

Multiply $2$ by $4$ .

$\sqrt[6]{8 \cdot 6 \cdot 8 \cdot 10 \cdot 12}$

Step 3

Multiply $8$ by $6$ .

$\sqrt[6]{48 \cdot 8 \cdot 10 \cdot 12}$

Step 4

Multiply $48$ by $8$ .

$\sqrt[6]{384 \cdot 10 \cdot 12}$

Step 5

Multiply $384$ by $10$ .

$\sqrt[6]{3840 \cdot 12}$

Step 6

Multiply $3840$ by $12$ .

$\sqrt[6]{46080}$

Step 7

Rewrite $46080$ as $2^{6} \cdot 720$ .

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Step 7.1

Factor $64$ out of $46080$ .

$\sqrt[6]{64 (720)}$

Step 7.2

Rewrite $64$ as $2^{6}$ .

$\sqrt[6]{2^{6} \cdot 720}$

Step 8

Pull terms out from under the radical.

$2 \sqrt[6]{720}$

Step 9

Approximate the result.

$5.98759033$

Step 10

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.

$6$

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