Find the Median 64 , 61 , 66 , 64 , 58 , 63 , 68 , 64 , 60 , 57 , 65 , 63 , 69 , 64 , 64 , 68 , 61 , 65

$64$ , $61$ , $66$ , $64$ , $58$ , $63$ , $68$ , $64$ , $60$ , $57$ , $65$ , $63$ , $69$ , $64$ , $64$ , $68$ , $61$ , $65$

Step 1

Arrange the terms in ascending order.

$57, 58, 60, 61, 61, 63, 63, 64, 64, 64, 64, 64, 65, 65, 66, 68, 68, 69$

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.

$\frac{64 + 64}{2}$

Step 3

Remove parentheses.

$\frac{64 + 64}{2}$

Step 4

Cancel the common factor of $64 + 64$ and $2$ .

Factor $2$ out of $64$ .

$\frac{2 \cdot 32 + 64}{2}$

Factor $2$ out of $64$ .

$\frac{2 \cdot 32 + 2 \cdot 32}{2}$

Factor $2$ out of $2 \cdot 32 + 2 \cdot 32$ .

$\frac{2 \cdot (32 + 32)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 \cdot (32 + 32)}{2 (1)}$

Cancel the common factor.

$\frac{2 \cdot (32 + 32)}{2 \cdot 1}$

Rewrite the expression.

$\frac{32 + 32}{1}$

Divide $32 + 32$ by $1$ .

$32 + 32$

Step 5

Add $32$ and $32$ .

$64$

Step 6

Convert the median $64$ to decimal.

$64$