3.11:

3.11: Midrange

JoVE Core
Statistics

A subscription to JoVE is required to view this content. Sign in or start your free trial.

JoVE Core Statistics

Midrange

3.13: Types of Skewness

3,653 Views

•

01:07 min

•

April 30, 2023

Overview

A somewhat easy to compute quantitative estimate of a data set’s central tendency is its midrange, which is defined as the mean of the minimum and maximum values of an ordered data set.

Simply put, the midrange is half of the data set’s range. Similar to the mean, the midrange is sensitive to the extreme values and hence the prospective outliers. However, unlike the mean, the midrange is not sensitive to all the values of the data set that lie in the middle. Thus, it is prone to outliers and does not accurately represent the central tendency of the data set.

Due to these disadvantages, the midrange is not used much. Nonetheless, in a relatively fluctuation-free data set, it can be easily calculated to obtain a quick estimate of the central tendency.

Transcript

The midrange is one of the measures of central tendency. It is the value midway between the two extreme values and is typically defined as the arithmetic mean of the maximum and minimum data values.

In this sample dataset of the sleep time of infants, the midrange can be calculated by adding the maximum and minimum hours and dividing the sum by two.

Although the midrange is relatively easy to compute, it is rarely used in statistics as it ignores all intermediate data values and lacks robustness in measurement.

The midrange is also sensitive to extreme values. In this example, a change in the maximum or minimum hours of sleep can alter the midrange. Besides, the midrange cannot be used for categorical data such as ranks or labels.

The midrange is complementary to the range or the difference between the maximum and minimum values. For instance, by knowing the midrange value and the data range, one can compute the maximum and minimum values in this dataset.

Key Terms and definitions

Midrange - The average of the minimum and maximum values of a data set.
Outliers - Extreme values that can significantly affect numerical summaries.
Central Tendency - A measure that attempts to describe what is typical or central in a data set.
Sample Midrange - Sometimes preferred over mean, when estimating the population mean.
Statistics - The science of collecting, organizing, analyzing, interpreting, and presenting data.

Learning Objectives

Define Midrange – Explain what a midrange is (e.g., midrange).
Contrast Midrange vs Mean – Understand the difference in how each is calculated and their sensitivities (e.g., outliers).
Explore Outliers – Describe why these can significantly affect a midrange (e.g., extreme value).
Explain Use of Sample Midrange – Detail why sample midrange might be preferred as an estimator of the population mean.
Apply Central Tendency in Context – Describe how midrange serves as a measure of central tendency.

Questions that this video will help you answer

What is a midrange and how does it relate to measures of central tendency?
What makes the midrange susceptible to outliers?
Under what conditions might the sample midrange be preferred over the mean?

This video is also useful for

Statistics students – Helps understand the concept of midrange and its properties
Educators – Provides a clear framework for teaching the concept of midrange
Researchers in data analysis – Relevance for understanding and interpreting numerical summaries
Data Enthusiasts – Offers insights and sparks broader interest and curiosity in statistical measures

Tags

Midrange Central Tendency Mean Data Set Range Outliers Fluctuation-free