Is "statistics" singular or plural?

• Statistics shows that people are having fewer children these days!
• Statistics show that people are having fewer children these days!

Which one is grammatical?

When considering the 'discipline of statistics' as a field of study or body of knowledge, it is singular:

Statistics shows that people are having fewer children these days!

When considering the figures from statistical data, as is often the case in comparative analysis, the figures themselves may be regarded as 'statistics', hence plural:

Statistics show that people are having fewer children these days!

Both are correct. It depends on the context and the author's intent.

The word statistics is used both as singular and as plural.

• The singular statistics is the science of collection, presentation, analysis and interpretation of numerical data.
• The plural statistics refers to numerical facts or observations collected with a definite purpose. Statistics in this sense have the following characteristics:
  1. Statistics are a sum total of observations.
  2. Statistics are expressed quantitatively and not qualitatively.
  3. Statistics are collected with a definite purpose.
  4. Statistics in an experiment are comparable and can be classified into various groups.