What is Population
Population is the entire pool from which a statistical sample is drawn. In statistics, population may refer to people, objects, events, hospital visits, measurements, etc. A population can, therefore, be said to be an aggregate observation of subjects grouped together by a common feature.
BREAKING DOWN Population
A population can be defined by any number of characteristics within a group, which statisticians use to draw conclusions about the subjects in a study. A population can be vague or specific. Examples of population defined vaguely include number of newborn babies in North America, total number of tech startups in Asia, average height of all CFA exam candidates in the world, mean weight of U.S. taxpayers and so on. Population can also be defined more specifically — number of newborn babies in North America with brown eyes, the number of startups in Asia that failed in less than three years, the average height of all female CFA exam candidates, mean weight of all U.S. taxpayers over 30 years of age, among others.
Most times, statisticians and researchers want to know the characteristics of every entity in a population, so as to draw the most precise conclusion possible. This is impossible most times, however, since population sets tend to be quite large. For example, if a company wanted to know whether each of its 50,000 customers serviced during the year were satisfied, it might be challenging, costly and impractical to call each of the clients on the phone to conduct a survey. Since the characteristics of every individual in a population cannot be measured due to constraints of time, resources and accessibility, a sample of the population is taken.
A sample is a random selection of members of a population. It is a smaller group drawn from the population that has the characteristics of the entire population. The observations and conclusions made against the sample data are attributed to the population. The information obtained from the statistical sample allows statisticians to develop hypotheses about the larger population. In statistical equations, population is usually denoted with an uppercase 'N' while the sample is usually denoted with a lowercase 'n.'
For example, let's say a denim apparel manufacturer wants to check the quality of the stitching on its blue jeans before shipping them off to retail stores. It is not cost effective to examine every single pair of blue jeans the manufacturer produces (the population). Instead, the manufacturer looks at just 50 pairs (a sample) to draw a conclusion about whether the entire population is likely to have been stitched correctly.
A parameter is data based on an entire population. Statistics such as averages and standard deviations, when taken from populations, are referred to as population parameters. The population mean and population standard deviation are represented by the Greek letters µ and σ, respectively. The standard deviation is the variation in the population inferred from the variation in the sample. When the standard deviation is divided by the square root of the number of observations in the sample, the result is referred to as the standard error of the mean. While a parameter is a characteristic of a population, a statistic is a characteristic of a sample. Inferential statistics enables you to make an educated guess about a population parameter based on a statistic computed from a sample randomly drawn from that population.