Variance is a fundamental statistical concept that measures the spread or dispersion of data points within a dataset. It plays an essential role in measuring the variability and reliability of data. Variance is typically denoted by the symbol σ2 (sigma squared) for populations and s^2 for samples.

To calculate variance, you follow a simple formula:

σ^2 = Σ(xi – μ)^2 / N

In this formula:

– σ^2 represents population variance.

– Σ denotes the sum.

– xi represents individual data points.

– μ is the mean (average) of the dataset.

– N is the total number of data points.

Variance serves several essential purposes in statistics:

- Measure of Spread: It quantifies how much individual data points deviate from the mean. A higher variance indicates a greater spread.
- Decision Making: Variance helps in decision-making processes, such as quality control in manufacturing or investment risk assessment.
- Comparing Datasets: Researchers use variance to compare the variability of two or more datasets, making it invaluable in scientific studies.
- Hypothesis Testing: Variance is vital in determining whether observed differences are statistically significant in statistical hypothesis testing.

Variance vs. Standard Deviation

Variance measures variability in squared units, while standard deviation measures variability in the original units of the data. Standard deviation is commonly used because it provides a more intuitive understanding of the spread of the data. In contrast, variance is helpful for mathematical calculations and is often used in statistical formulas.

## List of recommended resources #

### For a broad overview #

How to Calculate Variance | Calculator, Analysis & Examples

This Scribbr blog provides a broad understanding of variance and analysis of variance (ANOVA) in statistics.

This video tutorial by MIT OpenCourseWare as part of the Introduction to Probability course provides an introductory overview to the topic of variance in statistics.

Resource: STAT 502: Analysis of Variance and Design of Experiments

This PennState Eberly College of Science course provides an overview of the statistical tool of ANOVA – analysis of variance.

### For in depth understanding #

This book by Gudmund R. Iversen and Helmut Norpoth presents a conceptual understanding of variance analysis and outlines methods for analyzing variance that are used to study the effect of one or more nominal variables on a dependent, interval level variable.

A Student’s Guide to Data and Error Analysis

This easy-to-access, concise and practical guide brings the reader up-to-speed on the proper handling and presentation of scientific data and its inaccuracies. It also provides further reading material for advanced readers.

### Case study #

This paper explores the effects of family background on the conditional variance of children’s outcomes in the context of intergenerational educational mobility using data from three large developing countries – China, India, and Indonesia.

Variance and Skewness in Density Predictions: A World GDP Growth Forecast Assessment

This paper, written by Fabian Mendez-Ramos, introduces a Bayesian cross-entropy forecast (BCEF) procedure to assess the variance and skewness in density forecasting.

## References #

https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch12/5214891-eng.htm

https://www.investopedia.com/terms/v/variance.asp