Definition 1 (A Dictionary of Mathematics, Glenn and Littler, 1984):
A subset of a population, whose size is dictated either by practical convenience or the requirements of statistical significance. Samples are investigated statistically on the assumption that measures based on them can yield valid inferences about the characteristics of the population.
Definition 2 (The Penguin Dictionary of Mathematics, Nelson, 2003):
A finite subset of a population. A sample containing n items is called a sample of size n.
Definition 3 (Oxford Study Mathematics Dictionary (4th edition), Tapson, 2008):
A sample is a set chosen from a population and used to represent that population in the statistical methods being applied. This is necessary where it is not possible to collect all the data from a very large population.
Example: In conducting an opinion poll to see how people would vote in an election, it is only possible to ask a sample of the population about their intentions and predict a result for the whole population from that.
Definition 4 (Complete AZ Mathematics Handbook (3rd edition), Berry, Graham, Sharp and Berry, 2003):
A sample is any subset of the population under study. For example, we wished to find the height average of all 18-year-old mailes in the UK. It would be impractical to measure every 18-year-old male in the UK, so a selected number (the sample) are chosen who can be considered representative of the whole population.
There are several ways of selecting samples, namely, cluster sampling, quota sampling, random sampling and stratified sampling.
Definition 5 (McGraw-Hill Dictionary of Mathematics, 2nd edition):
A selection of a certain collection from a larger collection.
A shortened form of Anglo-Norman French assample, from Old French essample, from Latin exemplum “an example”. The Latin compound is made up of ex “out of” and emptus, past participle of emere “to take.” The Indo-European root is em- “to take, to distribute.” If you have a group of things that are the same type or follow a common pattern, a sample is one of those things that you have “taken out” to represent the group. Although sample was already used in English in the 13th century, the full form of the word, example, didn’t appear till the 14th century. In statistics, a sample is a representative subset of a population.