Pre-Algebra Examples

$- 1 \frac{1}{3}$ , $2 \frac{5}{6}$

Step 1

The five-number summary is a descriptive statistic that provides information about a set of observations. It consists of the following statistics:

1. Minimum (Min) - the smallest observation

2. Maximum (Max) - the largest observation

3. Median $M$ - the middle term

4. First Quartile $Q_{1}$ - the middle term of values below the median

5. Third Quartile $Q_{3}$ - the middle term of values above the median

Step 2

Arrange the terms in ascending order.

$- 1 \frac{1}{3}, 2 \frac{5}{6}$

Step 3

The minimum value is the smallest value in the arranged data set.

Step 4

The maximum value is the largest value in the arranged data set.

Step 5

Find the median.

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Step 5.1

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

$\frac{- 1 \frac{1}{3} + 2 \frac{5}{6}}{2}$

Step 5.2

Remove parentheses.

$\frac{- 1 \frac{1}{3} + 2 \frac{5}{6}}{2}$

Step 5.3

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

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Step 5.3.1

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

$\frac{- (1 + \frac{1}{3}) + 2 \frac{5}{6}}{2}$

Step 5.3.2

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

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Step 5.3.2.1

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

$\frac{- (\frac{3}{3} + \frac{1}{3}) + 2 \frac{5}{6}}{2}$

Step 5.3.2.2

Combine the numerators over the common denominator.

$\frac{- \frac{3 + 1}{3} + 2 \frac{5}{6}}{2}$

Step 5.3.2.3

Add $3$ and $1$ .

$\frac{- \frac{4}{3} + 2 \frac{5}{6}}{2}$

Step 5.4

Convert $2 \frac{5}{6}$ to an improper fraction.

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Step 5.4.1

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

$\frac{- \frac{4}{3} + 2 + \frac{5}{6}}{2}$

Step 5.4.2

Add $2$ and $\frac{5}{6}$ .

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Step 5.4.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{- \frac{4}{3} + 2 \cdot \frac{6}{6} + \frac{5}{6}}{2}$

Step 5.4.2.2

Combine $2$ and $\frac{6}{6}$ .

$\frac{- \frac{4}{3} + \frac{2 \cdot 6}{6} + \frac{5}{6}}{2}$

Step 5.4.2.3

Combine the numerators over the common denominator.

$\frac{- \frac{4}{3} + \frac{2 \cdot 6 + 5}{6}}{2}$

Step 5.4.2.4

Simplify the numerator.

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Step 5.4.2.4.1

Multiply $2$ by $6$ .

$\frac{- \frac{4}{3} + \frac{12 + 5}{6}}{2}$

Step 5.4.2.4.2

Add $12$ and $5$ .

$\frac{- \frac{4}{3} + \frac{17}{6}}{2}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- \frac{4}{3} \cdot \frac{2}{2} + \frac{17}{6}}{2}$

Step 5.5.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.5.2.1

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$\frac{- \frac{4 \cdot 2}{3 \cdot 2} + \frac{17}{6}}{2}$

Step 5.5.2.2

Multiply $3$ by $2$ .

$\frac{- \frac{4 \cdot 2}{6} + \frac{17}{6}}{2}$

Step 5.5.3

Combine the numerators over the common denominator.

$\frac{\frac{- 4 \cdot 2 + 17}{6}}{2}$

Step 5.5.4

Simplify the numerator.

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Step 5.5.4.1

Multiply $- 4$ by $2$ .

$\frac{\frac{- 8 + 17}{6}}{2}$

Step 5.5.4.2

Add $- 8$ and $17$ .

$\frac{\frac{9}{6}}{2}$

Step 5.5.5

Cancel the common factor of $9$ and $6$ .

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Step 5.5.5.1

Factor $3$ out of $9$ .

$\frac{\frac{3 (3)}{6}}{2}$

Step 5.5.5.2

Cancel the common factors.

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Step 5.5.5.2.1

Factor $3$ out of $6$ .

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

Step 5.5.5.2.2

Cancel the common factor.

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

Step 5.5.5.2.3

Rewrite the expression.

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

Step 5.6

Multiply the numerator by the reciprocal of the denominator.

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

Step 5.7

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

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Step 5.7.1

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

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

Step 5.7.2

Multiply $2$ by $2$ .

$\frac{3}{4}$

Step 5.8

Convert the median $\frac{3}{4}$ to decimal.

$0.75$

Step 6

The lower half of data is the set below the median.

$- 1 \frac{1}{3}$

Step 7

The upper half of data is the set above the median.

$2 \frac{5}{6}$

Step 8

The five most important sample values are sample minimum, sample maximum, median, lower quartile, and upper quartile.

$M = 0.75$

$Q_{1} = - 1 \frac{1}{3}$

$Q_{3} = 2 \frac{5}{6}$