2.7 CALCULATION OF POPULATION COUNTS, MEANS, MEDIANS AND OTHER ESTIMATES
COUNTS
Counts of income units or households are derived by summing the weights assigned to each income unit or household record of interest. Counts of persons can also be obtained this way if only persons over 15 years of age are required. However, there are not separate records for persons under the age of 15, and therefore counts of persons including those under 15 years have to be derived by first multiplying each household weight by the number of persons in the household and then summing the products.
MEANS
The mean, or average, value of a data item (such as household expenditure on footwear) is usually calculated by selecting all the survey records for the population of interest (such as all households in Victoria), multiplying the value of the data item in each record by the weight of the record and summing the resultant products, and then dividing the total by the sum of the weights of the records. However, for some purposes means are required with respect to all people in the population, including those under the age of 15. As for the derivation of population counts, it is then necessary to use household records, multiplying the household weights by the number of persons. As described under means and medians in section 1.6 'Gini coefficient and other measures of income distribution', so-called person weighted measures are often used to summarise equivalised household income.
MEDIANS
Medians divide the population of interest into halves. To identify the median record, the population is first ranked in ascending order according to the data item of interest. Except for person weighted measures of household variables, the weights of the records are then accumulated until half the population is accounted for. The record at which this occurs is the median record, and its value for the data item of interest is the median value. For person weighted measures of household variables, the household weights are multiplied by the number of persons in the household before accumulation.
OTHER ESTIMATES
An analagous approach is used for other quantile measures.
Calculation of the Gini coefficient is included in Appendix 3 'Gini coefficient and other single statistic summaries of income distribution'.
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