Sample

Border police looking for illegal drugs with a specially trained dog: If they check every tenth car, they are taking an unbiased sample.

In statistics a sample is part of a population. The sample is carefully chosen. It should represent the whole population fairly, without bias. The reason samples are needed is that populations may be so large that counting all the individuals may not be possible or practical.

Therefore, solving a problem in statistics usually starts with sampling.[1] Sampling is about choosing which data to take for later analysis. As an example, suppose the pollution of a lake should be analysed for a study. Depending on where the samples of water were taken, the studies can have different results. As a general rule, samples need to be random. This means the chance or probability of selecting one individual is the same as the chance of selecting any other individual.

In practice, random samples are always taken by means of a well-defined procedure. A procedure is a set of rules, a sequence of steps written down on paper and followed to the letter. Even so, some bias may remain in the sample. Consider the problem of designing a sample to predict the result of an election poll. All known methods have their problems, and the results of an election are often different from predictions based on a sample. If you collect opinions by using telephones, or by meeting people in the street, the sample always has bias. Therefore, in cases like this a completely neutral sample is never possible.[2] In such cases a statistician will think about how to measure the amount of bias, and there are ways to estimate this.

A similar situation occurs when scientists measure a physical property, say the weight of a piece of metal, or the speed of light.[3] If we weigh an object with sensitive equipment we will get minutely different results. No system of measurement is ever perfect. We get a series of estimates, each one being a measurement. These are samples, with a certain degree of error. Statistics is designed to describe error, and carry out analysis on this kind of data.

There are different kinds of samples:

• A complete sample includes all the elements that have a given property.
• An unbiased or representative sample is produced by taking a complete sample and selecting elements from it, in a process that does not depend on the properties of the elements.

Stratified sampling

If a population has obvious sub-populations, then each of the sub-populations needs to be sampled. This is called stratified sampling. Stratified sampling is also known as stratified random sample. Stratified sampling is often represented as proportion, such as percent (%).