Find the Median 10 , 6 , 15 , 14 , 8 , 21 , 10 , 5 , 19 , 18 , 4 , 5 , 166 , 122 , 10 , 9

$10$ , $6$ , $15$ , $14$ , $8$ , $21$ , $10$ , $5$ , $19$ , $18$ , $4$ , $5$ , $166$ , $122$ , $10$ , $9$

Step 1

Arrange the terms in ascending order.

$4, 5, 5, 6, 8, 9, 10, 10, 10, 14, 15, 18, 19, 21, 122, 166$

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.

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

Step 3

Remove parentheses.

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

Step 4

Cancel the common factor of $10 + 10$ and $2$ .

Factor $2$ out of $10$ .

$\frac{2 \cdot 5 + 10}{2}$

Factor $2$ out of $10$ .

$\frac{2 \cdot 5 + 2 \cdot 5}{2}$

Factor $2$ out of $2 \cdot 5 + 2 \cdot 5$ .

$\frac{2 \cdot (5 + 5)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 + 5}{1}$

Divide $5 + 5$ by $1$ .

$5 + 5$

Step 5

Add $5$ and $5$ .

$10$

Step 6

Convert the median $10$ to decimal.

$10$