Question

Detail, with very specific examples of each item, the meaning of the following concepts related to statistical data gathering: Be sure that the concept is first defined, IN YOUR OWN WORDS, and that you use a concrete example (including visual examples) to illustrate your understanding of the statistical concept: Population and Sample

Answer 1

A population is an infinite or finite group of all possible elements of a random variable. It is a wider set of people to whom the results of a research are generalized. It is important to note that a population usually has innumerable people, which acts as a hindrance to a convenient study. Therefore, a study is generally conducted on a limited or finite number of individuals, which leads to the formation of a smaller set or subset called sample.

A sample is a representative set or group, drawn from it's parent called the population. It is important to note that more than one sample can be drawn from the same population. A properly selected sample is the one, which draws most of the information about the parent population parameters. A sample should be appropriate to the level that it permits derivation of true inferences about the parent. A proper sample is also the one in which every individual drawn from the population has a non-zero chance or equal chance of being included in it.

The mean of a population is represented by the symbol μ, whereas the mean of a sample is represented by the symbol x. Mean or standard deviation, which are known to be the measurable characteristics of a population are called parameters. A measurable characteristic of a sample is known as a statistic.

Example- A population can be the students of an entire school, but the sample will be limited number of students chosen for a study from that school via a sampling technique. A population can be bus drivers of an entire state. But the sample will be limited number of bus drivers chosen for a study from that state via a sampling technique. A population can be the dancers of an institute. But the sample will be limited number of dancers chosen for a study from that institute via a sampling technique. So, it can be interpreted that population is the ocean, whereas sample is an aquarium.