**APPENDIX 1** ANALYSING INCOME DISTRIBUTIONS

**INTRODUCTION**

There are several ways to illustrate aspects of the distribution of income and its variability across society. In this publication, three main types of indicators used are: means, quantile measures and income shares. This appendix describes how these indicators are derived.

**MEANS**

Mean household income (average household income) is a simple indicator that can be used to show income differences between subgroups of the population.

Different income measures have been used in the tables. For the equivalised income measures, mean income is calculated with respect to the number of persons, even when the table is describing households. This enables people in large households to have the same contribution to the mean as people living alone. For other income measures, the means are calculated with respect to the number of households. For more information on equivalised income see __Appen____dix 2__.

**QUANTILE MEASURES**

When households (or any other units) are ranked from the lowest to the highest on the basis of some characteristic such as their household income they can then be divided into equally sized groups. The generic term for such groups is quantiles.

**Quintiles, deciles and percentiles**

When the population is divided into five equally sized groups, the quantiles are called quintiles. If there are 10 groups, the quantiles are deciles and division into 100 groups gives percentiles. Thus the first quintile will comprise the first two deciles and the first 20 percentiles.

This publication presents data classified into income quintiles and net worth quintiles. These quintiles each comprise the same number of households. In some tables, data presented are classified into equivalised disposable income quintiles and equivalised final income quintiles. Because equivalised income can be viewed as an indicator of the economic resources available to individuals in a household, these quintiles each comprise the same number of persons. When data are presented by equivalised income they are supplemented by data relating to the 2nd and 3rd deciles. These deciles are included to enable quintile style analysis to be carried out without undue impact from very low incomes which may not accurately reflect levels of economic wellbeing (see paragraphs 19 to 24 of the __Explan____atory Notes__).

**Upper values**

In some analyses, the statistic of interest is the boundary between quantiles. This is usually expressed in terms of the upper value of a particular percentile. For example, the upper value of the first quintile is also the upper value of the 20th percentile and is described as P20. The upper value of the ninth decile is P90.

**Percentile ratios**

Percentile ratios summarise the relative distance between two points on a distribution. To illustrate the full spread of a distribution, the percentile ratio needs to refer to points near the extremes of the distribution, for example, the P90/P10 ratio. The P80/P20 ratio better illustrates the magnitude of the range within which the incomes of the majority of the population fall. The P80/P50 and P20/P50 ratios focus on comparing the ends of the distribution with the midpoint.

**INCOME SHARES**

Income shares can be calculated and compared for each income quintile (or any other subgrouping) of a population. The aggregate income of the units in each quintile is divided by the overall aggregate income of the entire population to derive income shares.

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