Find the Median 36 , 40 , 40 , 38 , 39 , 45 , 41 , 42

$36$ , $40$ , $40$ , $38$ , $39$ , $45$ , $41$ , $42$

Step 1

Arrange the terms in ascending order.

$36, 38, 39, 40, 40, 41, 42, 45$

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.

$\frac{40 + 40}{2}$

Step 3

Remove parentheses.

$\frac{40 + 40}{2}$

Step 4

Cancel the common factor of $40 + 40$ and $2$ .

Factor $2$ out of $40$ .

$\frac{2 \cdot 20 + 40}{2}$

Factor $2$ out of $40$ .

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

Factor $2$ out of $2 \cdot 20 + 2 \cdot 20$ .

$\frac{2 \cdot (20 + 20)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 \cdot (20 + 20)}{2 (1)}$

Cancel the common factor.

$\frac{2 \cdot (20 + 20)}{2 \cdot 1}$

Rewrite the expression.

$\frac{20 + 20}{1}$

Divide $20 + 20$ by $1$ .

$20 + 20$

Step 5

Add $20$ and $20$ .

$40$

Step 6

Convert the median $40$ to decimal.

$40$