Find the Mean 19 , 16 1/2 , 19 , 16 1/2 , 21

$19$ , $16 \frac{1}{2}$ , $19$ , $16 \frac{1}{2}$ , $21$

Step 1

Convert $16 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$19, 16 + \frac{1}{2}, 19, 16 \frac{1}{2}, 21$

Add $16$ and $\frac{1}{2}$ .

To write $16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$19, 16 \cdot \frac{2}{2} + \frac{1}{2}, 19, 16 \frac{1}{2}, 21$

Combine $16$ and $\frac{2}{2}$ .

$19, \frac{16 \cdot 2}{2} + \frac{1}{2}, 19, 16 \frac{1}{2}, 21$

Combine the numerators over the common denominator.

$19, \frac{16 \cdot 2 + 1}{2}, 19, 16 \frac{1}{2}, 21$

Simplify the numerator.

Multiply $16$ by $2$ .

$19, \frac{32 + 1}{2}, 19, 16 \frac{1}{2}, 21$

Add $32$ and $1$ .

$19, \frac{33}{2}, 19, 16 \frac{1}{2}, 21$

Step 2

Convert $16 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$19, \frac{33}{2}, 19, 16 + \frac{1}{2}, 21$

Add $16$ and $\frac{1}{2}$ .

To write $16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$19, \frac{33}{2}, 19, 16 \cdot \frac{2}{2} + \frac{1}{2}, 21$

Combine $16$ and $\frac{2}{2}$ .

$19, \frac{33}{2}, 19, \frac{16 \cdot 2}{2} + \frac{1}{2}, 21$

Combine the numerators over the common denominator.

$19, \frac{33}{2}, 19, \frac{16 \cdot 2 + 1}{2}, 21$

Simplify the numerator.

Multiply $16$ by $2$ .

$19, \frac{33}{2}, 19, \frac{32 + 1}{2}, 21$

Add $32$ and $1$ .

$19, \frac{33}{2}, 19, \frac{33}{2}, 21$

Step 3

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

$\frac{19 + \frac{33}{2} + 19 + \frac{33}{2} + 21}{5}$

Step 4

Simplify the numerator.

To write $19$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{19 \cdot \frac{2}{2} + \frac{33}{2} + 19 + \frac{33}{2} + 21}{5}$

Combine $19$ and $\frac{2}{2}$ .

$\frac{\frac{19 \cdot 2}{2} + \frac{33}{2} + 19 + \frac{33}{2} + 21}{5}$

Combine the numerators over the common denominator.

$\frac{\frac{19 \cdot 2 + 33}{2} + 19 + \frac{33}{2} + 21}{5}$

Simplify the numerator.

Multiply $19$ by $2$ .

$\frac{\frac{38 + 33}{2} + 19 + \frac{33}{2} + 21}{5}$

Add $38$ and $33$ .

$\frac{\frac{71}{2} + 19 + \frac{33}{2} + 21}{5}$

To write $19$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{71}{2} + 19 \cdot \frac{2}{2} + \frac{33}{2} + 21}{5}$

Combine $19$ and $\frac{2}{2}$ .

$\frac{\frac{71}{2} + \frac{19 \cdot 2}{2} + \frac{33}{2} + 21}{5}$

Combine the numerators over the common denominator.

$\frac{\frac{71 + 19 \cdot 2}{2} + \frac{33}{2} + 21}{5}$

Simplify the numerator.

Multiply $19$ by $2$ .

$\frac{\frac{71 + 38}{2} + \frac{33}{2} + 21}{5}$

Add $71$ and $38$ .

$\frac{\frac{109}{2} + \frac{33}{2} + 21}{5}$

Combine the numerators over the common denominator.

$\frac{\frac{109 + 33}{2} + 21}{5}$

Add $109$ and $33$ .

$\frac{\frac{142}{2} + 21}{5}$

To write $21$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{142}{2} + 21 \cdot \frac{2}{2}}{5}$

Combine $21$ and $\frac{2}{2}$ .

$\frac{\frac{142}{2} + \frac{21 \cdot 2}{2}}{5}$

Combine the numerators over the common denominator.

$\frac{\frac{142 + 21 \cdot 2}{2}}{5}$

Simplify the numerator.

Multiply $21$ by $2$ .

$\frac{\frac{142 + 42}{2}}{5}$

Add $142$ and $42$ .

$\frac{\frac{184}{2}}{5}$

Divide $184$ by $2$ .

$\frac{92}{5}$

Step 5

Divide.

$18.4$

Find the Mean 19 , 16 1/2 , 19 , 16 1/2 , 21

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