Measurement in Statistics: Uses of Percentages

Vocabulary and formulas regarding the conversion and use of percentages in statistics, including change, difference, and comparison rules.

Percentage to Common Fraction Conversion

To convert a percentage to a common fraction, replace the $$ symbol with division by $100$ and simplify the fraction if necessary.

Percentage to Decimal Conversion

To convert a percentage to a decimal, drop the $$ symbol and move the decimal point two places to the left (divide by $100$).

Decimal to Percentage Conversion

To convert a decimal to a percentage, move the decimal point two places to the right (multiply by $100$) and add the $$ symbol.

Common Fraction to Percentage Conversion

To convert a common fraction to a percentage, first convert the common fraction to a decimal and then convert the decimal to a percentage.

Absolute Change

A value describing the actual increase or decrease from a reference value to a new value; calculated as $\text{absolute change} = \text{new value} - \text{reference value}$.

Relative Change

A percentage describing the size of the absolute change in comparison to the reference value; calculated as $\text{relative change} = \frac{\text{absolute change}}{\text{reference value}} \times 100\%$.

Reference Value

The number that is used as the basis for a comparison.

Compared Value

The value which we compare to the reference value.

Absolute Difference

The difference between the compared value and the reference value; calculated as $\text{absolute difference} = \text{compared value} - \text{reference value}$.

Relative Difference

A percentage describing the size of the absolute difference in comparison to the reference value; calculated as $\text{relative difference} = \frac{\text{absolute difference}}{\text{reference value}} \times 100\%$.

$P\%$ more than

A rule stating that if a new or compared value is $P\%$ more than the reference value, then it is $(100 + P)\%$ of the reference value.

$P\%$ less than

A rule stating that if a new or compared value is $P\%$ less than the reference value, then it is $(100 - P)\%$ of the reference value.

Percentage Points

A unit used to express an absolute change or difference when comparing two percentage values.

Percentage (%)

In the context of comparing percentages, an expression in percent usually indicates a relative change or difference.