In statistics, two fundamental concepts, ‘population’ and ‘sample,’ are essential in research and analysis.

## Population #

A population in statistics refers to the entire group or collection of individuals, objects, or data points that are the subject of interest for a study. Populations are often large and diverse, making studying every single element within them impractical.

## Sample #

Conversely, a sample is a subset of the population selected for research and data collection. It represents a manageable portion of the larger population. Selecting an unbiased and representative sample is crucial to ensure that the sample’s findings accurately reflect the population’s characteristics and trends. Various sampling methods, such as random sampling or stratified sampling, help researchers achieve this goal.

## Population Parameter vs. Sample Statistic #

Population parameters are numerical values that describe characteristics of an entire population, like the mean of all students’ test scores in a school. On the other hand, sample statistics are values calculated from a subset (sample) of the population, providing estimates of the population parameters, like the mean test score of a sample of students.

### Population Parameter: #

Mean: μ = (ΣX) / N, where ΣX is the sum of all values in the population and N is the size of the population

Standard Deviation: σ = √[(Σ(X-μ)²) / N], where X is a value in the population, μ is the population mean, and N is the size of the population

### Sample Statistic: #

Mean: x̄ = (Σx) / n, where Σx is the sum of all values in the sample and n is the size of the sample

Standard Deviation: s = √[(Σ(x-x̄)²) / (n-1)], where x is a value in the sample and x̄ is the sample mean

While the population represents the entire interest group, the sample is a practical subset used to draw meaningful conclusions and insights, making statistical analysis feasible and insightful.

## List of recommended resources #

### For a broad overview #

Sample: What It Means in Statistics, Types, and Examples

This Investopedia article by Will Kenton provides a brief overview of samples in statistics and an explanation of the various types of samples along with examples.

Sample Size and Power Calculations

This lecture by Ben Olken produced by the Poverty Action Lab and the Massachusetts Institute of Technology provides a brief overview of the various methods used for identifying the right sample size for randomized evaluations.

This paper by Ellen Taylor-Powell written as part of the Program Development and Evaluation, University of Wisconsin-Extension provides a guide on the different types of sampling techniques.

### For in depth understanding #

Sampling In Marketing Research

Chapter 7 of this book Marketing research and information systems provides a detailed study of how to collect data for research and how to select a truly representative population of interest.

The Survey Methods Workbook: From Design to Analysis

This book written by Alan Buckingham and Peter Saunders provides an in-depth explanation of data collection methods in research, from preparing a questionnaire to inferring population parameters from sample statistics.

### Case study #

This survey draws on a probability sample of 1,455 respondents, 711 of whom are based in rural areas, while 467 and 277 are living in urban and semi-urban areas respectively to monitor food insecurity and vulnerability in Yemen.

This paper, by Derek H. C. Chen of The World Bank and Kishore Gawande of Texas A&M University, investigates principal components as well as factor analytic methods to provide a clear political-economic meaning of the factors. It makes uses of the formulas of population parameter and variance to assess its data.

## References #

Population vs. Sample | Definitions, Differences & Examples

Population vs Sample: Uses and Examples