Standard deviation is a statistical concept that provides insights into data dispersion and variability. It is the average amount of variability in the dataset. It measures the extent to which data points deviate from the mean.

## How to calculate standard deviation: #

Different formulas are used for calculating standard deviations depending on whether the data has been collected from a whole population or a sample.

### Population standard deviation #

When data has been collected from every member of the population that the researcher is interested in, an exact value for population standard deviation can be found.

The population standard deviation formula looks like this:

Formula:

where,

– σ represents the population standard deviation.

– Σ denotes summation.

– X denotes individual data points.

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

– N is the total number of data points.

### Sample standard deviation #

When data has been collected from a sample, the sample standard deviation is used to make estimates or inferences about the population standard deviation.

Sample standard deviation formula:

where,

– s represents the population standard deviation.

– Σ denotes summation.

– X denotes individual data points.

– x is the sample mean.

– n is the number of values in the sample.

### How to interpret standard deviation: #

Standard deviation provides a way to comprehend the spread of data. A small standard deviation suggests that most data points are close to the mean, indicating low variability. Conversely, a large standard deviation implies greater dispersion and higher variability.

## List of recommended resources #

### For a broad overview #

Calculating the Mean and Standard Deviation with Excel

This guide provides a simple step by step instruction of how to calculate the standard deviation and the central tendency of mean using Excel.

How to Calculate Standard Deviation (Guide) | Calculator & Examples

This article by Scribbr provides an easy-to-follow and concise guide on standard deviation, how to calculate it and its use as a measure of variability.

### For in depth understanding #

Schaum’s Outline of Statistics

Chapter 4 of this book by Dr. Murray R. Spiegel and Larry J. Stephens – The Standard Deviation and Other Measures of Dispersion – provides an in-depth study of standard deviation in statistics.

Statistical Evaluations in Exploration for Mineral Deposits

Chapter 6 of this book by Friedrich-Wilhelm Wellmer, explains how standard deviation or variance can be calculated from the sample selected for Wellmer’s study on mineral deposits.

### Case study #

Global Bank Lending under Climate Policy

This paper studies the response of bank foreign subsidiaries to climate policy in their host countries. The paper finds that the banks, through their foreign subsidiaries, expand their credit by 4.6 percent following an increase of one-standard deviation in the host country’s climate policy index.

The Longer Students Were Out of School, the Less They Learned

This paper by Harry Anthony Patrinos analyzes school closures during the COVID-19 pandemic using a unique database. Through his observations, Patrinos learns that means a 20 week closure, for example, would reduce learning outcomes by 0.20 standard deviation, almost one year of schooling.

## References #

https://www.investopedia.com/terms/s/standarddeviation.asp

https://statistics.laerd.com/statistical-guides/measures-of-spread-standard-deviation.php