Find the Mean 1 3/4 , 2 1/2 , 2

$1 \frac{3}{4}$ , $2 \frac{1}{2}$ , $2$

Step 1

Convert $1 \frac{3}{4}$ to an improper fraction.

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

$1 + \frac{3}{4}, 2 \frac{1}{2}, 2$

Add $1$ and $\frac{3}{4}$ .

Write $1$ as a fraction with a common denominator.

$\frac{4}{4} + \frac{3}{4}, 2 \frac{1}{2}, 2$

Combine the numerators over the common denominator.

$\frac{4 + 3}{4}, 2 \frac{1}{2}, 2$

Add $4$ and $3$ .

$\frac{7}{4}, 2 \frac{1}{2}, 2$

Step 2

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

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

$\frac{7}{4}, 2 + \frac{1}{2}, 2$

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

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

$\frac{7}{4}, 2 \cdot \frac{2}{2} + \frac{1}{2}, 2$

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

$\frac{7}{4}, \frac{2 \cdot 2}{2} + \frac{1}{2}, 2$

Combine the numerators over the common denominator.

$\frac{7}{4}, \frac{2 \cdot 2 + 1}{2}, 2$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{7}{4}, \frac{4 + 1}{2}, 2$

Add $4$ and $1$ .

$\frac{7}{4}, \frac{5}{2}, 2$

Step 3

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

$\frac{\frac{7}{4} + \frac{5}{2} + 2}{3}$

Step 4

Simplify the numerator.

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{7}{4} + \frac{5}{2} \cdot \frac{2}{2} + 2}{3}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{2}$ by $\frac{2}{2}$ .

$\frac{\frac{7}{4} + \frac{5 \cdot 2}{2 \cdot 2} + 2}{3}$

Multiply $2$ by $2$ .

$\frac{\frac{7}{4} + \frac{5 \cdot 2}{4} + 2}{3}$

Combine the numerators over the common denominator.

$\frac{\frac{7 + 5 \cdot 2}{4} + 2}{3}$

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{\frac{7 + 10}{4} + 2}{3}$

Add $7$ and $10$ .

$\frac{\frac{17}{4} + 2}{3}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{17}{4} + 2 \cdot \frac{4}{4}}{3}$

Combine $2$ and $\frac{4}{4}$ .

$\frac{\frac{17}{4} + \frac{2 \cdot 4}{4}}{3}$

Combine the numerators over the common denominator.

$\frac{\frac{17 + 2 \cdot 4}{4}}{3}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{\frac{17 + 8}{4}}{3}$

Add $17$ and $8$ .

$\frac{\frac{25}{4}}{3}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{4} \cdot \frac{1}{3}$

Step 6

Multiply $\frac{25}{4} \cdot \frac{1}{3}$ .

Multiply $\frac{25}{4}$ by $\frac{1}{3}$ .

$\frac{25}{4 \cdot 3}$

Multiply $4$ by $3$ .

$\frac{25}{12}$

Step 7

Divide.

$2.08\overline{3}$

Step 8

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.

$2.1$

Find the Mean 1 3/4 , 2 1/2 , 2

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