Find the Mean 83 , 96 , 67 , 67 , 86 , 65 , 82 , 85 , 97 , 73 , 85 , 67 , 99 , 98 , 65 , 96 , 70 , 92 , 74 , 83 , 72 , 76

$83$ , $96$ , $67$ , $67$ , $86$ , $65$ , $82$ , $85$ , $97$ , $73$ , $85$ , $67$ , $99$ , $98$ , $65$ , $96$ , $70$ , $92$ , $74$ , $83$ , $72$ , $76$

Step 1

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

$\frac{83 + 96 + 67 + 67 + 86 + 65 + 82 + 85 + 97 + 73 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Step 2

Simplify the numerator.

Add $83$ and $96$ .

$\frac{179 + 67 + 67 + 86 + 65 + 82 + 85 + 97 + 73 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $179$ and $67$ .

$\frac{246 + 67 + 86 + 65 + 82 + 85 + 97 + 73 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $246$ and $67$ .

$\frac{313 + 86 + 65 + 82 + 85 + 97 + 73 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $313$ and $86$ .

$\frac{399 + 65 + 82 + 85 + 97 + 73 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $399$ and $65$ .

$\frac{464 + 82 + 85 + 97 + 73 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $464$ and $82$ .

$\frac{546 + 85 + 97 + 73 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $546$ and $85$ .

$\frac{631 + 97 + 73 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $631$ and $97$ .

$\frac{728 + 73 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $728$ and $73$ .

$\frac{801 + 85 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $801$ and $85$ .

$\frac{886 + 67 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $886$ and $67$ .

$\frac{953 + 99 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $953$ and $99$ .

$\frac{1052 + 98 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $1052$ and $98$ .

$\frac{1150 + 65 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $1150$ and $65$ .

$\frac{1215 + 96 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $1215$ and $96$ .

$\frac{1311 + 70 + 92 + 74 + 83 + 72 + 76}{22}$

Add $1311$ and $70$ .

$\frac{1381 + 92 + 74 + 83 + 72 + 76}{22}$

Add $1381$ and $92$ .

$\frac{1473 + 74 + 83 + 72 + 76}{22}$

Add $1473$ and $74$ .

$\frac{1547 + 83 + 72 + 76}{22}$

Add $1547$ and $83$ .

$\frac{1630 + 72 + 76}{22}$

Add $1630$ and $72$ .

$\frac{1702 + 76}{22}$

Add $1702$ and $76$ .

$\frac{1778}{22}$

Step 3

Cancel the common factor of $1778$ and $22$ .

Factor $2$ out of $1778$ .

$\frac{2 (889)}{22}$

Cancel the common factors.

Factor $2$ out of $22$ .

$\frac{2 \cdot 889}{2 \cdot 11}$

Cancel the common factor.

$\frac{2 \cdot 889}{2 \cdot 11}$

Rewrite the expression.

$\frac{889}{11}$

Step 4

Divide.

$80.\overline{81}$

Step 5

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$80.8$

Find the Mean 83 , 96 , 67 , 67 , 86 , 65 , 82 , 85 , 97 , 73 , 85 , 67 , 99 , 98 , 65 , 96 , 70 , 92 , 74 , 83 , 72 , 76

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