Statistics Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $2$ and $1$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.2.3

Add $4$ and $3$ .

$\frac{1}{4}, \frac{1}{2}, \frac{1}{4}, \frac{3}{4}, 1, \frac{3}{2}, \frac{1}{2}, \frac{7}{4}, \frac{1}{2}, \frac{1}{2}$

Step 3

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

$\frac{\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4

Simplify the numerator.

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Step 4.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{1}{4} + \frac{1}{2} \cdot \frac{2}{2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.2

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

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Step 4.2.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{\frac{1}{4} + \frac{2}{2 \cdot 2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.2.2

Multiply $2$ by $2$ .

$\frac{\frac{1}{4} + \frac{2}{4} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{\frac{1 + 2}{4} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.4

Add $1$ and $2$ .

$\frac{\frac{3}{4} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{\frac{3 + 1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.6

Add $3$ and $1$ .

$\frac{\frac{4}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.7

Combine the numerators over the common denominator.

$\frac{\frac{4 + 3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.8

Add $4$ and $3$ .

$\frac{\frac{7}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.9

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

$\frac{\frac{7}{4} + \frac{4}{4} + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.10

Combine the numerators over the common denominator.

$\frac{\frac{7 + 4}{4} + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.11

Add $7$ and $4$ .

$\frac{\frac{11}{4} + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.12

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{11}{4} + \frac{3}{2} \cdot \frac{2}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.13

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

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Step 4.13.1

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

$\frac{\frac{11}{4} + \frac{3 \cdot 2}{2 \cdot 2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.13.2

Multiply $2$ by $2$ .

$\frac{\frac{11}{4} + \frac{3 \cdot 2}{4} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.14

Combine the numerators over the common denominator.

$\frac{\frac{11 + 3 \cdot 2}{4} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.15

Simplify the numerator.

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Step 4.15.1

Multiply $3$ by $2$ .

$\frac{\frac{11 + 6}{4} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.15.2

Add $11$ and $6$ .

$\frac{\frac{17}{4} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.16

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{17}{4} + \frac{1}{2} \cdot \frac{2}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.17

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

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Step 4.17.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{\frac{17}{4} + \frac{2}{2 \cdot 2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.17.2

Multiply $2$ by $2$ .

$\frac{\frac{17}{4} + \frac{2}{4} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.18

Combine the numerators over the common denominator.

$\frac{\frac{17 + 2}{4} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.19

Add $17$ and $2$ .

$\frac{\frac{19}{4} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.20

Combine the numerators over the common denominator.

$\frac{\frac{19 + 7}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.21

Add $19$ and $7$ .

$\frac{\frac{26}{4} + \frac{1}{2} + \frac{1}{2}}{10}$

Step 4.22

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{26}{4} + \frac{1}{2} \cdot \frac{2}{2} + \frac{1}{2}}{10}$

Step 4.23

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

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Step 4.23.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{\frac{26}{4} + \frac{2}{2 \cdot 2} + \frac{1}{2}}{10}$

Step 4.23.2

Multiply $2$ by $2$ .

$\frac{\frac{26}{4} + \frac{2}{4} + \frac{1}{2}}{10}$

Step 4.24

Combine the numerators over the common denominator.

$\frac{\frac{26 + 2}{4} + \frac{1}{2}}{10}$

Step 4.25

Add $26$ and $2$ .

$\frac{\frac{28}{4} + \frac{1}{2}}{10}$

Step 4.26

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{28}{4} + \frac{1}{2} \cdot \frac{2}{2}}{10}$

Step 4.27

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

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Step 4.27.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{\frac{28}{4} + \frac{2}{2 \cdot 2}}{10}$

Step 4.27.2

Multiply $2$ by $2$ .

$\frac{\frac{28}{4} + \frac{2}{4}}{10}$

Step 4.28

Combine the numerators over the common denominator.

$\frac{\frac{28 + 2}{4}}{10}$

Step 4.29

Add $28$ and $2$ .

$\frac{\frac{30}{4}}{10}$

Step 4.30

Cancel the common factor of $30$ and $4$ .

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Step 4.30.1

Factor $2$ out of $30$ .

$\frac{\frac{2 (15)}{4}}{10}$

Step 4.30.2

Cancel the common factors.

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Step 4.30.2.1

Factor $2$ out of $4$ .

$\frac{\frac{2 \cdot 15}{2 \cdot 2}}{10}$

Step 4.30.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 15}{2 \cdot 2}}{10}$

Step 4.30.2.3

Rewrite the expression.

$\frac{\frac{15}{2}}{10}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{2} \cdot \frac{1}{10}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Factor $5$ out of $15$ .

$\frac{5 (3)}{2} \cdot \frac{1}{10}$

Step 6.2

Factor $5$ out of $10$ .

$\frac{5 \cdot 3}{2} \cdot \frac{1}{5 \cdot 2}$

Step 6.3

Cancel the common factor.

$\frac{5 \cdot 3}{2} \cdot \frac{1}{5 \cdot 2}$

Step 6.4

Rewrite the expression.

$\frac{3}{2} \cdot \frac{1}{2}$

Step 7

Multiply $\frac{3}{2}$ by $\frac{1}{2}$ .

$\frac{3}{2 \cdot 2}$

Step 8

Multiply $2$ by $2$ .

$\frac{3}{4}$

Step 9

Divide.

$0.75$

Step 10

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.

$0.8$