Statistics Examples

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

Step 1

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

$\frac{2 + 4 + 6 + 8 + 10 + 12}{6}$

Step 2

Cancel the common factor of $2 + 4 + 6 + 8 + 10 + 12$ and $6$ .

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Step 2.1

Factor $2$ out of $2$ .

$\frac{2 (1) + 4 + 6 + 8 + 10 + 12}{6}$

Step 2.2

Factor $2$ out of $4$ .

$\frac{2 \cdot 1 + 2 \cdot 2 + 6 + 8 + 10 + 12}{6}$

Step 2.3

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

$\frac{2 \cdot (1 + 2) + 6 + 8 + 10 + 12}{6}$

Step 2.4

Factor $2$ out of $6$ .

$\frac{2 \cdot (1 + 2) + 2 (3) + 8 + 10 + 12}{6}$

Step 2.5

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

$\frac{2 \cdot (1 + 2 + 3) + 8 + 10 + 12}{6}$

Step 2.6

Factor $2$ out of $8$ .

$\frac{2 \cdot (1 + 2 + 3) + 2 (4) + 10 + 12}{6}$

Step 2.7

Factor $2$ out of $2 \cdot (1 + 2 + 3) + 2 (4)$ .

$\frac{2 \cdot (1 + 2 + 3 + 4) + 10 + 12}{6}$

Step 2.8

Factor $2$ out of $10$ .

$\frac{2 \cdot (1 + 2 + 3 + 4) + 2 (5) + 12}{6}$

Step 2.9

Factor $2$ out of $2 \cdot (1 + 2 + 3 + 4) + 2 (5)$ .

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5) + 12}{6}$

Step 2.10

Factor $2$ out of $12$ .

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5) + 2 (6)}{6}$

Step 2.11

Factor $2$ out of $2 \cdot (1 + 2 + 3 + 4 + 5) + 2 (6)$ .

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6)}{6}$

Step 2.12

Cancel the common factors.

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Step 2.12.1

Factor $2$ out of $6$ .

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6)}{2 (3)}$

Step 2.12.2

Cancel the common factor.

$\frac{2 \cdot (1 + 2 + 3 + 4 + 5 + 6)}{2 \cdot 3}$

Step 2.12.3

Rewrite the expression.

$\frac{1 + 2 + 3 + 4 + 5 + 6}{3}$

Step 3

Simplify the numerator.

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Step 3.1

Add $1$ and $2$ .

$\frac{3 + 3 + 4 + 5 + 6}{3}$

Step 3.2

Add $3$ and $3$ .

$\frac{6 + 4 + 5 + 6}{3}$

Step 3.3

Add $6$ and $4$ .

$\frac{10 + 5 + 6}{3}$

Step 3.4

Add $10$ and $5$ .

$\frac{15 + 6}{3}$

Step 3.5

Add $15$ and $6$ .

$\frac{21}{3}$

Step 4

Divide $21$ by $3$ .

$7$