# Australian Bureau of Statistics

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 Making sense of statistics

Percentages explained

> Proportions
> Percentages
> How to calculate percentage change
> Rates and ratios

Proportions

Proportions present data in a standardised way which allows simple but meaningful comparisons to be made. Proportions can be expressed as:

• percentages
• rates
• ratios

Percentages

Percentage is the term used to express a number as a fraction of one hundred. It is symbolised using the percent sign %.

Percentage is commonly used to represent statistical data and provides an easy to read summary statistic; it is considered an important tool to illustrate the proportion of something. The percentage total of a data set should always add up to 100 except in special circumstances. (Percentages larger than the value of 100 often occur in financial situations, say for instance if a item originally costing \$1 was sold for \$1 then the profit would be 0%, if the same item was sold for \$2 then the profit would be 100%, and selling it for \$3 would be a 200% profit.)

To calculate a percentage, divide a component value by the total value; and then multiply that value by 100.

(Value / Total) x 100 = %

 Example Of students attending a tutorial group, three are male and four are female. We want to know what percentage of the group is female. To calculate this, divide the number of female students (4) by the total number of students (7) in the group, then multiply by 100. (4 / 7) x 100 = 57.1% More than half (57.1%) of the students attending the tutorial group are female.

Cautionary note

One downfall of using percentages is that they may not necessarily be added together. The basis of the percentages may be different. Each percentage calculation must be worked out independently, based on the actual numbers, to ensure you have the correct interpretation.

How to calculate percentage change

Percentage change is a useful measure to identify change over time as an easy to read summary statistic.

To calculate percentage change: new value minus old value, divided by old value and multiply by 100.

 Example According to the 1996 Census the population of Tasmania was 464,546. In 2006 it was 476,481. During that 10 year period Tasmania's population increased by 11,935 persons. This represented a percentage change of 2.6%. {(476,481 - 464,546) / 464,546} x 100 = 2.6% or {(Year 2006 - Year 1996) / Year 1996 x 100 = 2.6%

Rates and Ratios

Proportions can also be expressed as rates and ratios. For more information, see

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