Find the Median 350 , 380 , 390 , 390 , 420 , 460 , 460 , 470 , 500 , 530

$350$ , $380$ , $390$ , $390$ , $420$ , $460$ , $460$ , $470$ , $500$ , $530$

Step 1

Arrange the terms in ascending order.

$350, 380, 390, 390, 420, 460, 460, 470, 500, 530$

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.

$\frac{420 + 460}{2}$

Step 3

Remove parentheses.

$\frac{420 + 460}{2}$

Step 4

Cancel the common factor of $420 + 460$ and $2$ .

Factor $2$ out of $420$ .

$\frac{2 \cdot 210 + 460}{2}$

Factor $2$ out of $460$ .

$\frac{2 \cdot 210 + 2 \cdot 230}{2}$

Factor $2$ out of $2 \cdot 210 + 2 \cdot 230$ .

$\frac{2 \cdot (210 + 230)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 \cdot (210 + 230)}{2 (1)}$

Cancel the common factor.

$\frac{2 \cdot (210 + 230)}{2 \cdot 1}$

Rewrite the expression.

$\frac{210 + 230}{1}$

Divide $210 + 230$ by $1$ .

$210 + 230$

Step 5

Add $210$ and $230$ .

$440$

Step 6

Convert the median $440$ to decimal.

$440$