Statistics New Zealand

Policy on Rounding of Numbers

--------------------------------------------------------------------------------------

INTRODUCTION

13.01.01

When making statistical calculations it is often necessary to round the numbers. It may not be possible, practicable, or reasonable (spurious accuracy), to record such numbers to the last digit. In publications, statistical series are often rounded to make them easily understood and readily comparable with other data. Such practices are quite acceptable providing an adequate level of accuracy is retained.

PROCEDURE

13.02.01

In these rules "rounding" means replacing a given number by another number called the "rounded number". This rounded number is selected from the sequence of integral multiples of a chosen rounding interval. Some examples will explain the terminology:

Example 1:

A rounding interval of 0.1 ie, we wish to round numbers to one decimal place. Then integral multiples of this interval are 0.1, 0.2, 0.3, 0.4 etc.

Example 2:

A rounding interval of 10 ie, we wish to round numbers to the nearest multiple of ten. Then integral multiples of this interval are 10, 20, 30, 40 etc.

13.02.02

If there is only one integral multiple nearest the given number, then that is accepted as the rounded number.

Example 1: Rounding interval 0.1

12.223 is rounded to 12.2

12.251 is rounded to 12.3

13.275 is rounded to 12.3

Example 2: Rounding interval 10

1222.3 is rounded to 1220

1347.6 is rounded to 1350

1489.1 is rounded to 1490

* NB: Random rounding is a confidentiality preserving technique, one of several possible, and should not be confused with the form of rounding discussed in this chapter.

13.02.03

If there are two successive integral multiples equally near the given number, then the even integral multiple is selected as the rounded number.

Example 1: Rounding interval 0.1

13.4500 is rounded to 13.4

13.5500 is rounded to 13.6

13.6500 is rounded to 13.6

Example 2: Rounding interval 10

1715.0 is rounded to 1720

1745.0 is rounded to 1740

1765.0 is rounded to 1760

13.02.04

The rule in 13.02.03 avoids any long-run bias in the rounded numbers that exists in some alternative methods of rounding. This standard rule tends to round up half the time and round down half the time.

13.02.05

Rounding in more than one stage by the application of the rules given may lead to errors. Rounding, therefore, must always be done in one step. For example, if we are rounding to one decimal place 12.251 should be rounded to 12.3 and not first to 12.25 and then to 12.2.

ROUNDING BY CALCULATOR

13.03.01

The electronic desk calculators used in the department have attachments for the rounding of numbers. Unfortunately, none of these attachments automatically round in accordance with rule 13.02.03 above. The decimal indicator should therefore be set to at least two digits more than that required and the number rounded mentally.

EDP SPECIFICATIONS

13.04.01

The above rules will also be used in all EDP specifications systems and the EDP authorities have been notified of this. However, it is desirable that all specifications for particular EDP systems should refer to these rules where rounding is used. Responsibility for this rests with the subject matter section.

13.04.02

When rounding of numbers is used, a discrepancy can occur between the total shown and the total of the individual items in the table e.g.,

41.9 + 20.4 + 6.7 + 8.2 + 5.0 + 1.6 + 16.1 = 100.0 (Rounded Total)

= 99.9 (Actual Total)

In most circumstances the standard explanation is needed so that the reader is assured that no error has been made in the figures presented.

The following statement is to be included at the foot of all tables or in the "Terms and Definitions" set out at the beginning of statistical publications:

Rounding

Figures have been rounded, and discrepancies may occur between sums of component items and totals. All percentages have been calculated using unrounded figures.