3.11:

3.11: 中频

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

中间范围是集中趋势的度量之一。它是两个极值之间的中间值，通常定义为最大和最小数据值的算术平均值。

在这个婴儿睡眠时间的示例数据集中，可以通过将最大和最小小时数相加并将总和除以 2 来计算中间值。

虽然中间值相对容易计算，但它很少用于统计，因为它忽略了所有中间数据值，并且在测量中缺乏稳健性。

中频对极值也很敏感。在此示例中，最大或最小睡眠时间的变化可以改变中间值。此外，中间范围不能用于分类数据，例如排名或标签。

中间范围是对范围或最大值和最小值之间的差值的补充。例如，通过了解中间值和数据范围，可以计算此数据集中的最大值和最小值。

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

中间值集中趋势平均值数据集范围异常值无波动