The mean, often called the average, is a fundamental statistical concept used to summarize data and gain insights into a dataset’s central tendency. Mean is an important concept used in various fields, from finance to science, allowing us to make informed decisions and draw meaningful conclusions.

To calculate the mean, you add all the values in a dataset and divide by the number of data points. For instance, in a set of test scores {85, 90, 92, 88, 78}, the mean score is (85 + 90 + 92 + 88 + 78) / 5 = 86.6. It provides a single numerical value that represents the “typical” value in the dataset.

The mean is versatile and works well with both small and large datasets. It is used to understand household income, stock market returns, and even scientific data like temperatures or experimental results. However, it’s important to note that outliers, extreme values, can significantly impact the mean, potentially skewing its interpretation.

In statistics, ‘mean’ can refer to:

- The mean of the sampling distribution is the center of a probability distribution, especially with respect to the Central Limit Theorem. It is an average of a set of distributions.
- Sample mean is the average value in a sample.
- Population mean is the average value in a population.

Some other types of means in statistics and mathematics, among others, are:

- Geometric mean
- Arithmetic-Geometric mean
- Weighted mean
- Harmonic mean

## 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.

This webpage by Laerd Statistics provides a broad overview of the three main measures of central tendency – mean, mode and median.

What Is a Mean? Definition in Math and Formula for Calculation

This Investopedia article by Adam Hayes provides a broad overview of the different types of means in mathematics.

### For in depth understanding #

Probability, Statistics and Other Frightening Stuff

Chapter 2 of this book by Alan Jones provides an easy-to-access understanding of the measures of central tendency and how it is used by estimators.

Schaum’s Outline of Statistics

Chapter 3 of this book written by Dr. Murray R. Spiegel and Larry J. Stephens is devoted to the study of the measures of central tendency, particularly on arithmetic mean.

### Case study #

This Policy Research Working Paper by Dhir Jhingran and Deepa Sankar studies the case of the Indian government’s Elementary Education for All Mission to understand how this flagship program relates investments to spatial and social disparities. It uses several measures of central tendency to analyze its findings.

Born with a Silver Spoon : Inequality in Educational Achievement across the World

This paper by Carlos Felipe Balcazar, Ambar Narayan and Sailesh Tiwari assesses the inequality of opportunity prevalent in educational achievement using the Human Opportunity Index methodology on data from the Programme for International Student Assessment. The paper uses the statistical tool of mean to make inferences from the data collected.

## References #

Central Tendency | Understanding the Mean, Median & Mode

Mean Median Mode: What They Are, How to Find Them