3.11:

3.11: Milieu de gamme

JoVE Core
Statistics

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JoVE Core Statistics

Midrange

3.13: Types of Skewness

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01:07 min

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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

Le milieu de gamme est l’une des mesures de la tendance centrale. C’est la valeur à mi-chemin entre les deux valeurs extrêmes et est généralement défini comme la moyenne arithmétique des valeurs de données maximale et minimale.

Dans cet exemple de jeu de données sur le temps de sommeil des nourrissons, le milieu peut être calculé en additionnant le nombre maximum et minimum d’heures et en divisant la somme par deux.

Bien que le milieu de gamme soit relativement facile à calculer, il est rarement utilisé en statistiques car il ignore toutes les valeurs de données intermédiaires et manque de robustesse dans la mesure.

Le médium est également sensible aux valeurs extrêmes. Dans cet exemple, une modification du nombre maximal ou minimal d’heures de sommeil peut modifier le milieu de gamme. De plus, le milieu de gamme ne peut pas être utilisé pour des données catégorielles telles que les rangs ou les étiquettes.

Le milieu de gamme est complémentaire à la plage ou à la différence entre les valeurs maximale et minimale. Par exemple, en connaissant la valeur moyenne et la plage de données, on peut calculer les valeurs maximale et minimale dans cet ensemble de données.

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

Milieu de gamme Tendance centrale Moyenne Ensemble de données Plage Valeur aberrante Sans fluctuation