# What methods are used to calculate aggregates for groups of countries?

In general, when indicators are ratios, aggregates are computed using weights corresponding to the denominator of the ratio. Because of missing data, aggregates for groups of economies should be treated as approximations of unknown totals or average values. The aggregation rules are intended to yield estimates for a consistent set of economies from one period to the next and for all indicators. Small differences between sums of subgroup aggregates and overall totals and averages may occur because of the approximations used. In addition, compilation errors and data reporting practices may cause discrepancies in theoretically identical aggregates such as world exports and world imports.

Five methods of aggregation are used in World Development Indicators:

• For group and world totals denoted
in the indicator metadata as * gap-filled
total*, missing data are imputed based on the relationship of the sum of
available data to the total in the year of the previous estimate. The
imputation process works forward and backward from 2010. Missing values in 2010 are imputed using one of several proxy variables for which complete data are
available in that year. The imputed value is calculated so that it (or its
proxy) bears the same relationship to the total of available data. Imputed values
are usually not calculated if missing data account for more than a third of the
total in the benchmark year. The variables used as proxies are GNI in U.S.
dollars; total population; exports and imports of goods and services in U.S.
dollars; and value added in agriculture, industry, manufacturing, and services
in U.S. dollars.

• For aggregates denoted in the indicator
metadata as * sums*, missing
values are not imputed. Sums are not computed if more than a third of the
observations in the series or a proxy for the series are missing in a given
year.

• For aggregates of ratios denoted as * weighted averages* of the ratios
(using the value of the denominator or, in some cases, another indicator as a
weight) and denoted as

*, the aggregate ratios are based on available data. Missing values are assumed to have the same average value as the available data. No aggregate is calculated if missing data account for more than a third of the value of weights in the benchmark year. In a few cases the aggregate ratio may be computed as the ratio of group totals after imputing values for missing data according to the above rules for computing totals. In a few cases growth rates may be computed from time series of group totals. Growth rates are not calculated if more than half the observations in a period are missing. For further discussion of methods of computing growth rates see below.*

__unweighted averages__• Aggregates denoted as * medians* in the indicator metadata
are medians of the values shown in the table. No value is shown if more than
half the observations for countries with a population of more than 1 million
are missing. Exceptions to the rules may occur. Depending on the judgment of
World Bank analysts, the aggregates may be based on as little as 50 percent of
the available data. In other cases, where missing or excluded values are judged
to be small or irrelevant, aggregates are based only on the data shown in the
tables.