Find the Mean 110 , 110 , 112 , 113 , 112 , 110 , 115 , 115 , 114 , 111 , 114 , 112 , 114 , 115 , 115 , 115 , 114 , 115 , 115 , 115 , 115 , 116 , 116 , 118 , 120 , 122 , 118 , 118 , 117 , 115

$110$ , $110$ , $112$ , $113$ , $112$ , $110$ , $115$ , $115$ , $114$ , $111$ , $114$ , $112$ , $114$ , $115$ , $115$ , $115$ , $114$ , $115$ , $115$ , $115$ , $115$ , $116$ , $116$ , $118$ , $120$ , $122$ , $118$ , $118$ , $117$ , $115$

Step 1

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

$\frac{110 + 110 + 112 + 113 + 112 + 110 + 115 + 115 + 114 + 111 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Step 2

Simplify the numerator.

Add $110$ and $110$ .

$\frac{220 + 112 + 113 + 112 + 110 + 115 + 115 + 114 + 111 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $220$ and $112$ .

$\frac{332 + 113 + 112 + 110 + 115 + 115 + 114 + 111 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $332$ and $113$ .

$\frac{445 + 112 + 110 + 115 + 115 + 114 + 111 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $445$ and $112$ .

$\frac{557 + 110 + 115 + 115 + 114 + 111 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $557$ and $110$ .

$\frac{667 + 115 + 115 + 114 + 111 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $667$ and $115$ .

$\frac{782 + 115 + 114 + 111 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $782$ and $115$ .

$\frac{897 + 114 + 111 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $897$ and $114$ .

$\frac{1011 + 111 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $1011$ and $111$ .

$\frac{1122 + 114 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $1122$ and $114$ .

$\frac{1236 + 112 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $1236$ and $112$ .

$\frac{1348 + 114 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $1348$ and $114$ .

$\frac{1462 + 115 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $1462$ and $115$ .

$\frac{1577 + 115 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $1577$ and $115$ .

$\frac{1692 + 115 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $1692$ and $115$ .

$\frac{1807 + 114 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $1807$ and $114$ .

$\frac{1921 + 115 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $1921$ and $115$ .

$\frac{2036 + 115 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $2036$ and $115$ .

$\frac{2151 + 115 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $2151$ and $115$ .

$\frac{2266 + 115 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $2266$ and $115$ .

$\frac{2381 + 116 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $2381$ and $116$ .

$\frac{2497 + 116 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $2497$ and $116$ .

$\frac{2613 + 118 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $2613$ and $118$ .

$\frac{2731 + 120 + 122 + 118 + 118 + 117 + 115}{30}$

Add $2731$ and $120$ .

$\frac{2851 + 122 + 118 + 118 + 117 + 115}{30}$

Add $2851$ and $122$ .

$\frac{2973 + 118 + 118 + 117 + 115}{30}$

Add $2973$ and $118$ .

$\frac{3091 + 118 + 117 + 115}{30}$

Add $3091$ and $118$ .

$\frac{3209 + 117 + 115}{30}$

Add $3209$ and $117$ .

$\frac{3326 + 115}{30}$

Add $3326$ and $115$ .

$\frac{3441}{30}$

Step 3

Cancel the common factor of $3441$ and $30$ .

Factor $3$ out of $3441$ .

$\frac{3 (1147)}{30}$

Cancel the common factors.

Factor $3$ out of $30$ .

$\frac{3 \cdot 1147}{3 \cdot 10}$

Cancel the common factor.

$\frac{3 \cdot 1147}{3 \cdot 10}$

Rewrite the expression.

$\frac{1147}{10}$

Step 4

Divide.

$114.7$

Find the Mean 110 , 110 , 112 , 113 , 112 , 110 , 115 , 115 , 114 , 111 , 114 , 112 , 114 , 115 , 115 , 115 , 114 , 115 , 115 , 115 , 115 , 116 , 116 , 118 , 120 , 122 , 118 , 118 , 117 , 115

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