The center of a distribution is a fundamental concept in statistics that provides crucial insights into a dataset’s central tendency. It is a measure that helps us understand where the data tends to cluster or concentrate. One commonly used measure of central tendency is the mean, also known as the average. To calculate the mean, one needs to add up all the data points and then divide the sum by the number of data points.
Another measure of the center of distribution or central tendency is the median. Median is the middle value when the data is arranged in ascending or descending order. It’s a dynamic measure that is less affected by extreme values, making it useful when dealing with skewed distributions.
The mode, on the other hand, presents the most frequently occurring value in a dataset. Unlike the mean and median, the mode is not necessarily unique, as a dataset can have multiple modes or none at all.
Understanding the center of a distribution is essential for making sense of data and drawing meaningful conclusions. It provides a summary of where the data is concentrated and helps identify potential outliers or unusual patterns. Whether you’re analyzing exam scores, stock prices, or any other dataset, grasping the center of the distribution is a vital step toward better statistical understanding and decision-making.
List of recommended resources #
For a broad overview #
Central Tendency | Understanding the Mean, Median & Mode
This blog post by Pritha Bhandari on Scribbr provides a broad overview of the basic concepts of the measures of the center of distribution.
Video: Mean, Median, and Mode: Measures of Central Tendency
This short tutorial by Crash Course Statistics provides an overview of the measures of central tendency.
For in depth understanding #
Analyzing Data from a National Assessment of Educational Achievement
This book by Gerry Shiel and Fernando Cartwright provides step-by-step details on how to analyze data collected in a national assessment.The analyses undertaken within it cover the measures of central tendency and dispersion, and various other functions used on statistical data.
Central Tendency and Variability
Written by Herbert F. Weisberg, as part of the Quantitative Applications in the Social Sciences series, this book explains how to measure the center and variation of a distribution in a clear, expository style.
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 it is used by estimators.
Case study #
Air Pollution Reduces Economic Activity: Evidence from India
This paper, co-written by Patrick A. Behrer, Rishabh Choudhary and Dhruv Sharma makes particular use of the center of distribution measure of the median to analyze its findings of particulate pollution reducing the gross domestic product of the country.
An Assessment of Community-Led Lift Irrigation Systems in Jharkhand, India
This policy research working paper written for Agriculture Global Practice uses the measures of central tendency to analyze the data collected from farmers in Jharkhand for assessing the solar powered community lift irrigation systems.
