**APPENDIX 1** ANALYSING WEALTH DISTRIBUTION

**INTRODUCTION**

There are several ways to illustrate aspects of the distribution of wealth and to measure the extent of inequality. In this publication, four main types of indicators used are: means and medians, frequency distributions, percentile ratios and net worth shares. This appendix describes how these indicators are derived.

**MEAN AND MEDIAN**

Mean household net worth (total net worth divided by the number of households) and median household net worth (the midpoint when all households are ranked in ascending order of net worth) are simple indicators that can be used to show differences between subgroups of the population. Many tables in this publication include mean and median household net worth data.

The publication also includes information on mean and median household income. In most tables the income measure used is gross household income, and the means and medians are calculated with respect to the number of households. However, when the income measure used is equivalised disposable household income, mean and median income are calculated with respect to the number of persons. This enables people in large households to have the same contribution to the mean/median as people living alone, and is possible because equivalised disposable household income is an indicator of the economic resources available to each individual in a household.

The method for calculating means is described under 'Estimation' in the Explanatory Notes.

**FREQUENCY DISTRIBUTION**

A frequency distribution can be used to illustrate the location and spread of net worth within a population. It groups the population into classes by net worth and gives the number or proportion of households in each net worth range. A graph of the frequency distribution is a good way to portray the essence of a wealth distribution. Graph S1 in the Summary of Findings shows the proportion of households within $100,000 net worth ranges.

Frequency distributions can provide considerable detail about variations in the population being described, but it is difficult to describe the differences between two frequency distributions. They are therefore often accompanied by other summary statistics, such as the mean and median. Taken together, the mean and median can provide an indication of the shape of the frequency distribution. As can be seen in Graph S1 in the Summary of Findings, the distribution of net worth tends to be asymmetrical, with a small number of households having relatively high net worth and a larger number of households having relatively low net worth. The greater the asymmetry, the greater will be the difference between the mean and the median.

**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 wealth, 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, they 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 net worth quintiles and gross income quintiles. These quintiles each comprise the same number of households. In some tables, data presented are classified into equivalised disposable household income quintiles or equivalised disposable household net worth quintiles. Because equivalised disposable household income and equivalised disposable household net worth 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 disposable household income quintiles 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 30 and 31 in the Explanatory Notes).

**Upper values and medians**

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. The median of a whole population is P50, the median of the 3rd quintile is also P50, the median of the first quintile is P10, etc.

**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 net worth 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 (the median).

**Net worth shares**

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

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