Find the Median 13 , 30 , 16 , 19 , 20 , 22 , 25 , 31

$13$ , $30$ , $16$ , $19$ , $20$ , $22$ , $25$ , $31$

Step 1

Arrange the terms in ascending order.

$13, 16, 19, 20, 22, 25, 30, 31$

Step 2

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

$\frac{20 + 22}{2}$

Step 3

Remove parentheses.

$\frac{20 + 22}{2}$

Step 4

Cancel the common factor of $20 + 22$ and $2$ .

Factor $2$ out of $20$ .

$\frac{2 \cdot 10 + 22}{2}$

Factor $2$ out of $22$ .

$\frac{2 \cdot 10 + 2 \cdot 11}{2}$

Factor $2$ out of $2 \cdot 10 + 2 \cdot 11$ .

$\frac{2 \cdot (10 + 11)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 \cdot (10 + 11)}{2 (1)}$

Cancel the common factor.

$\frac{2 \cdot (10 + 11)}{2 \cdot 1}$

Rewrite the expression.

$\frac{10 + 11}{1}$

Divide $10 + 11$ by $1$ .

$10 + 11$

Step 5

Add $10$ and $11$ .

$21$

Step 6

Convert the median $21$ to decimal.

$21$