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CALCULATION OF POPULATION COUNTS, MEANS AND MEDIANS
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 aged 15 years and over are required. However, there are not separate records for persons under the age of 15 years, 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.
The mean, or average, value of a data item is usually calculated by selecting all the survey records for the population of interest, 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. For example, the mean gross income of Queensland households is the weighted sum of the gross income of each such household divided by the sum of the weights relating to each such household.
However, for some purposes, means for a household variable may be required with respect to all people in a population group, including children aged under 15 years. Such measures (referred to as person weighted measures) are often used when analysing equivalised household income. Estimates of mean equivalised disposable household income in HECS published output are obtained by multiplying the equivalised disposable income of each household by the number of people in the household (including children) and by the weight of the household, summing across all households and then dividing by the estimated number of people in the population group. (The estimated number of people in the population group is calculated as outlined above in the section 'counts', by first multiplying each household weight by the number of persons in the household and then summing the products).
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.
An analogous approach is used for other quantile measures.
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