Australian Bureau of Statistics
1301.6.55.001 - Tasmanian Statistical News, Jun 2010
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 08/06/2010
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2. The ability to understand statistical concepts
3. The ability to analyse, interpret and evaluate statistical information
4. The ability to communicate statistical information and understandings
In this issue, we will continue our focus on understanding statistical concepts. Proportions present data in a standardised way which allows simple but meaningful comparisons to be made. Proportions can be expressed as:
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; 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.
The percentage of a data set can be calculated by dividing a component value by the total value; and then multiplying that value by 100.
Percentage % = (Value / Total) X 100%
Of students attending a tutorial group, three were male and four were female. We want to know what percentage of the group was female.
To calculate this, divide the number of female students by the total number of students in the group, then multiply by 100.
(4 / 7) x 100 = 57.1%
Percentage represents the proportions of known values. By using a percentage to represent the data you provide the reader with an easy to read summary statistic. There can be downfalls of using the percentage. Percentages are not additive, as each percentage calculation is worked out on the new value.
Percentage change is a useful measure to identify change over time as an easy to read summary statistic. To calculate percentage change: new minus old, divided by old and multiply by 100.
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%
A rate is a measurement of one quantity in relation to another. For example, the ABS uses a rate to express the number of persons who are unemployed. It is the number of unemployed persons in relation to the labour force (employed + unemployed persons), not the total population.
In October 2008, Tasmania experienced its lowest unemployment rate on record. There were 242,000 employed persons and 9,300 unemployed persons, creating a total labour force of 251,300 persons. To calculate the unemployment rate, divide the number of unemployed by the total labour force then multiply by 100:
(9,300 / 251,300) x 100 = 3.7%
In this instance, the unemployment rate is expressed as a percentage because it is calculated as a proportion of 100. Other rates, such as the birth rate may be expressed as a proportion of 1000. That is, the number of births per 1000 of population.
Ratios are used to identify the meaning of actual data counts. For example, the sex ratio of births is the number of male live births per 100 female live births.
In 2007, there were 3,393 male live births in Tasmania, and 3,269 female live births. To calculate the sex ratio, divide male live births by female live births and multiply by 100.
(3,393 / 3,269) x 100 = 103.8
For further explanation of terms see Statistical Language! (ABS cat. no. 1332.0.55.002)
In upcoming issues of Tasmanian Statistical News we will discuss other statistical literacy concepts in more detail. Meanwhile, if you would like to know more about statistical literacy and its relevance to you, check out the article: What is statistical literacy and why is it important to be statistically literate? as featured in Tasmanian State and Regional Indicators (ABS cat. no. 1307.6) or visit the Understanding Statistics portal on the ABS website.
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This page last updated 6 September 2010