Tutorial:Rounding of numbers

Authors of statistical publications must balance accuracy with readability. Reporting overly precise numbers can obscure important information and create a misleading sense of accuracy. Therefore, rounding large numbers and long decimals enhances readability and prevents false precision.

Although Eurostat's common editorial guidelines address number rounding, more detailed guidance is needed due to growing inquiries from authors and contractors. The best rounding policy varies by publication context and statistical domain, making universal rules challenging. However, this document aims to harmonise practices and offer straightforward recommendations for publications aimed at non-specialists.

General recommendations

The general recommendations apply to all communication elements of statistical publications (texts, tables, graphs and maps):

Use only the number of digits which are necessary and make sense for the purpose of a clear communication.
Rounding of numbers should take place at the latest phase of data processing and analysis.
For target indicators always use the full precision of the indicator to assess whether the target has been met. The rounding should not change the situation of the countries towards the target (to achieve or exceed the target).
Big numbers are difficult to grasp. It may be reasonable to round them and use the words millions, billions, etc.
In case of doubt on the number of digits to be used, authors should consult the Dissemination unit.
A disclaimer should be added, when applicable, at the beginning or end of the publication describing the rounding policy and the reasons for possible inconsistencies. For instance:

Due to rounding, some totals may not correspond with the sum of the separate figures.

Specific recommendations

The specific recommendations are based on 3 increasing levels of approximation: while detailed figures from data sources (e.g. Eurobase) should not be changed when preparing graphs and maps (level 0), they should be partially rounded for compiling tables (level 1) and rounded even further when writing texts (level 2).

Summary

Level 0: Graphs and maps should be built using unrounded figures from the original dataset(s).

Examples: 12.34% and 56.789%, 1 234 and 56 789 persons

Level 1: For tables with percentages, the general rule is to round to one decimal. For tables with absolute numbers, identify the smallest number, decide how many digits to keep for this number, and then round all other entries to those digits.

Examples: 12.3% and 56.8%, 1 200 and 56 800 persons

Level 2: In text 2 significant (non-zero) digits are in general sufficient.

Examples: 12% and 57%, 1 200 and 57 000 persons

Details

The assessment whether a target has been met should be done on the basis of unrounded figures (and properly reflecting the accuracy of the data).

Level 1: Numbers and percentages in tables should undergo initial rounding, but this applies to text tables, not detailed annex tables. For percentages and proportions, round to one decimal place. If values often exceed 70%, use no decimals; however, for indicators like monthly changes, more decimals may be necessary. Rounding should not misrepresent a country's position regarding targets or thresholds.

For tables with absolute numbers, identify the shortest number in terms of digits and round others to match its significant digits, generally 2, to ensure consistency in totals, except for minor rounding discrepancies. Display decimals for exchange rates.

When displaying multiple indicators in one table, keep the number of significant digits consistent: one side for absolute figures and the other for relative quantities.

Level 2: Numbers and percentages in text should be more rounded than those in tables. Detailed figures are generally unnecessary in text analyses; consider adding a table if needed for clarity.

When precision is not crucial, group countries or units and use terms like "at least," "about," or "less than." Use unrounded numbers for grouping, then round them, adjusting the text if needed due to rounding overlaps.

For target indicators or thresholds, use maximum precision to accurately rank positions. Inconsistencies in digit precision for countries of different sizes are acceptable in text, as the focus is on communicating concepts.

Tables

Consider the following population data extracted from Eurobase:

Luxembourg shows the smallest figure; keeping two significant digits implies rounding to the “ten-thousands” position, i.e. to 340 000. By rounding all other numbers to this position we obtain the table:

The unrounded total is 137 836 166 which, according to the rounding scheme applied in the table, rounds to 137 840 000. This is exactly the sum of the rounded figures in the table!

Even though the proposed rounding scheme reduces the possibility of inconsistencies between the sum of rounded numbers and the rounded sum, small differences could still occur. In this case, it is important to report the disclaimer described above (general recommendations number 6).

Texts

Consider the same population dataset as above. By keeping two significant digits, population in Germany rounds to 61 000 000, in Belgium to 9 700 000 and in Luxembourg to 340 000. The significant positions clearly differ in these three numbers; however this is generally not a problem in texts.

Text describing a table: good example

The following is a good example of how to present analysis of numbers reported in a table. In the accompanying text, countries are regrouped and rounded figures are used.

Example of numbers in text with too many digits

Consider the following example of text:

The total number of available hospitals beds in the EU was 2.70 million in 2010, equivalent to one bed for every 185.8 persons or 538.2 hospitals beds per 100 000 inhabitants.

The figures in this text are too much detailed (up to four significant digits) and it is difficult for the reader to retain the main messages. Original numbers should be rounded to two digits only.

Solution

The total number of available hospital beds in the EU was 2.7 million in 2010, equivalent to around one bed for every 190 persons, or 540 hospitals beds per 100 000 inhabitants.

Note that the rounding above must be done on the most detailed available figures for increased consistency.

Rounding of numbers in tables: bad example

Reconsider the population dataset introduced in the first table. If instead of applying the above mentioned recommendation for tables, we had kept the same number of significant digits in all figures in the table, we would not have achieved the same level of coherence. For instance, with two significance digits we have

The rounded total is 140 000 000 and this is different from the sum of the rounded figures (138 040 000).