Dictionary, Census of Population, 2016Appendix 4.0 Derived StatisticsDictionary, Census of Population, 2016Appendix 4.0 Derived Statistics

Release date: September 13, 2017

Median income and average income are two statistics commonly computed on income variables to measure central tendency.

These statistics can be derived for total income, after-tax income, employment income, wages and salaries, or any other particular source of income on a variety of universes: individuals, families, persons not in families and households.

Typically, for total income and after-tax income, median and average incomes of individuals are calculated for those with income (positive or negative); median and average incomes of households are calculated for all units, whether or not they had income; median and average incomes of families are calculated for all units, whether or not they had income; median and average incomes of persons not in families are calculated for all units, whether or not they had income.

However, for the income components, median and average incomes are sometimes calculated for units with income (positive or negative) only for all universes.

In 2016, as part of the measures to ensure non-disclosure of individual characteristics, the average income statistic is only available from the sampled population, i.e., information from the long-form census questionnaire. The median income statistic is the measure of central tendency and is available for 100% of the population (short-form census questionnaire).

Median income

The median income of a specified group is the amount that divides the income distribution of that group into two halves, i.e., the incomes of half of the units in that group are below the median, while those of the other half are above the median.

When median income is computed from the census short-form questionnaire, no weighting is required because each unit represents itself. When median income is computed from the census long-form questionnaire, certain units would represent multiple units (known as weight) due to sampling.

For an income size distribution, the median is usually estimated as follows:

$M = L m + c m ( d/ f m ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaacaWGnbGaaGzbVlaaysW7imaacqWF9a qpcaaMf8UaamitamaaBaaaleaacaWGTbaabeaakiaaykW7cqWFRaWk caaMc8Uaam4yamaaBaaaleaacaWGTbaabeaakiaaykW7daqadaqaai aadsgacaGGVaGaamOzamaaBaaaleaacaWGTbaabeaaaOGaayjkaiaa wMcaaaaa@4593@$, where

$M = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaacaWGnbGaaGzbVlaaysW7imaacqWF9a qpcaaMf8oaaa@36D6@$Median value

$L m = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaacaWGmbWaaSbaaSqaaiaad2gaaeqaaO GaaGzbVJWaaiab=1da9iaaywW7aaa@3670@$Lower boundary of the income group in which

$N 2 = ∑ W i 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaacaaMf8UaaGjbVlaaywW7daWcaaqaai aad6eaaeaacaaIYaaaaiaaykW7caaMe8ocdaGae8xpa0JaaGjbVpaa laaabaWaaabqaeaacaWGxbaaleqabeqdcqGHris5aOWaaSbaaSqaai aadMgaaeqaaaGcbaGaaGOmaaaaaaa@4132@$  falls, where

Number of (weighted) units in the specified group for which the distribution is being shown

Weight of each unit in the specified group, for the short-form census questionnaire, the weight is equal to 1 for each unit.

$c m = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaacaWGJbWaaSbaaSqaaiaad2gaaeqaaO GaaGzbVJWaaiab=1da9iaaywW7aaa@3687@$Size (range) of the median income group

$d = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaacaWGKbGaaGzbVlaaysW7imaacqWF9a qpcaaMf8oaaa@36ED@$Number of units in the specified group necessary from the median income group to reach the middle

i.e.,

$f m = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaacaWGMbWaaSbaaSqaaiaad2gaaeqaaO GaaGzbVJWaaiab=1da9iaaywW7aaa@368A@$Frequency or (weighted) total number of units in the median income group

In a similar fashion, decile income values (the 9 dollar amounts which divide the income recipients in 10 equal groups), quintiles (5 equal groups) and quartiles (4 equal groups) can also be derived for the population with income.

Average income

Average income of a specified group is calculated by dividing the aggregate income of that group by the number of units in that group.

This statistic is calculated for any specified group as follows:

$Y ¯ = ∑ ( Y i W i ) ∑ W i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaadaqdaaqaaiaadMfaaaGaaGzbVlaays W7imaacqWF9aqpcaaMf8+aaSaaaeaadaaeabqaamaabeaabaGaamyw amaaBaaaleaacaWGPbaabeaakmaabiaabaGaam4vamaaBaaaleaaca WGPbaabeaaaOGaayzkaaaacaGLOaaaaSqabeqaniabggHiLdaakeaa daaeabqaaiaadEfadaWgaaWcbaGaamyAaaqabaaabeqab0GaeyyeIu oaaaaaaa@42B0@$, where

$Y ¯ = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaadaqdaaqaaiaadMfaaaGaaGzbVlaays W7imaacqWF9aqpcaaMf8oaaa@36F3@$ Average income of the group specified

$Y i = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuWqHXwAIjxAaeXatLxBI9gBaebbnrfifHhDYfgasaacH8qrps0l bba9q8WrFfeaY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabiGacmGa daWaaiqacaGaaiaaeaaakeaacaWGzbWaaSbaaSqaaiaadMgaaeqaaO GaaGzbVlaaysW7imaacqWF9aqpcaaMf8oaaa@3806@$ Actual income of each unit in the group specified

Weight of each unit in the group specified

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