Find the Mean 101 , 102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 , 110 , 111 , 112

$101$ , $102$ , $103$ , $104$ , $105$ , $106$ , $107$ , $108$ , $109$ , $110$ , $111$ , $112$

Step 1

The mean of a set of numbers is the sum divided by the number of terms.

$\frac{101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Step 2

Simplify the numerator.

Add $101$ and $102$ .

$\frac{203 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Add $203$ and $103$ .

$\frac{306 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Add $306$ and $104$ .

$\frac{410 + 105 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Add $410$ and $105$ .

$\frac{515 + 106 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Add $515$ and $106$ .

$\frac{621 + 107 + 108 + 109 + 110 + 111 + 112}{12}$

Add $621$ and $107$ .

$\frac{728 + 108 + 109 + 110 + 111 + 112}{12}$

Add $728$ and $108$ .

$\frac{836 + 109 + 110 + 111 + 112}{12}$

Add $836$ and $109$ .

$\frac{945 + 110 + 111 + 112}{12}$

Add $945$ and $110$ .

$\frac{1055 + 111 + 112}{12}$

Add $1055$ and $111$ .

$\frac{1166 + 112}{12}$

Add $1166$ and $112$ .

$\frac{1278}{12}$

Step 3

Cancel the common factor of $1278$ and $12$ .

Factor $6$ out of $1278$ .

$\frac{6 (213)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$\frac{6 \cdot 213}{6 \cdot 2}$

Cancel the common factor.

$\frac{6 \cdot 213}{6 \cdot 2}$

Rewrite the expression.

$\frac{213}{2}$

Step 4

Divide.

$106.5$