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Dictionary, Census of Population, 2021

Appendix 2.3

Derived statistics

**Release date:**November 17, 2021

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 2021, 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).

The Gini coefficient, or Gini index, is a measure of inequality that indicates how equally income is distributed for a given population. It measures how much an income distribution deviates from perfect equality. Values of the Gini coefficient can range from 0 to 1. A value of 0 indicates that income is equally divided among the population, with all units receiving exactly the same amount of income. At the opposite extreme, a Gini coefficient of 1 denotes a perfectly unequal distribution, where one unit has all of the income in the economy. The Gini coefficient can be used to compare the equity of income allocation across different populations or within the same population over time. A decrease in the value of the Gini coefficient can generally be interpreted as reflecting a decrease in inequality, and vice versa.

For the census, Gini coefficients are calculated for three types of adjusted household income—market income, total income and after‑tax income—to provide different perspectives. It should be noted that for the calculation of the Gini coefficients, negative income is converted to 0. Adjusted income is computed by dividing the household income by a factor equal to the square root of the household size (known as the equivalence scale). This adjustment for different household sizes takes into account economies of scale. It reflects the fact that the needs of a household increase, but at a decreasing rate, as the number of members increases.

## 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:

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:

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