Statistical Population Sample

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A Statistical Population Sample is a proper subset of a statistical population from which a dataset is collected or selected for statistical analysis.



Typically, the population is very large, making a census or a complete enumeration of all the values in the population is either impractical or impossible. The sample usually represents a subset of manageable size. Samples are collected and statistics are calculated from the samples so that one can make inferences or extrapolations from the sample to the population. The data sample may be drawn from a population without replacement, in which case it is a subset of a population; or with replacement, in which case it is a multisubset.[2]

  • (Leard Statistics, 2016) ⇒ "Hypothesis Testing - Structure and the Research, Null and Alternative Hypothesis" Laerd Statistics, © 2013 Lund Research Ltd, n.d. Web. Retrieved October 11, 2016, from
    • QUOTE: (...) In statistics terminology, the students in the study are the sample and the larger group they represent (i.e., all statistics students on a graduate management degree) is called the population. Given that the sample of statistics students in the study are representative of a larger population of statistics students, you can use hypothesis testing to understand whether any differences or effects discovered in the study exist in the population. In layman's terms, hypothesis testing is used to establish whether a research hypothesis extends beyond those individuals examined in a single study.
Another example could be taking a sample of 200 breast cancer sufferers in order to test a new drug that is designed to eradicate this type of cancer. As much as you are interested in helping these specific 200 cancer sufferers, your real goal is to establish that the drug works in the population (i.e., all breast cancer sufferers).
As such, by taking a hypothesis testing approach, Sarah and Mike want to generalize their results to a population rather than just the students in their sample. However, in order to use hypothesis testing, you need to re-state your research hypothesis as a null and alternative hypothesis

Depending on the sampling method, a sample can have fewer observations than the population, the same number of observations, or more observations. More than one sample can be derived from the same population.
Other differences have to do with nomenclature, notation, and computations. For example, a measurable characteristic of a population, such as a mean or standard deviation, is called a parameter; but a measurable characteristic of a sample is called a statistic.

To understand the basic foundation for hypothesis testing and other types of inferential statistics, it’s important to understand how a sample and a population differ.
A population is a collection of people, items, or events about which you want to make inferences. It is not always convenient or possible to examine every member of an entire population. For example, it is not practical to count the bruises on all apples picked at an orchard. It is possible, however, to count the bruises on a set of apples taken from that population. This subset of the population is called a sample.
If the sample is random and large enough, you can use the information collected from the sample to make inferences about the population. For example, you could count the number of apples with bruises in a random sample and then use a hypothesis test to estimate the percentage of all the apples that have bruises.


  1. Peck, Roxy; Chris Olsen; Jay L. Devore (2008). Introduction to Statistics and Data Analysis (3 ed.). Cengage Learning. ISBN 0-495-55783-8. Retrieved 2009-08-04. 
  2. Template:Citation