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5.1: 回顾和预览

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5.2: Introduction to z Scores

7,560 Views

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01:10 min

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April 30, 2023

Overview

在统计中，使用多种工具来解释数据。集中趋势的度量表示数据的特征，例如平均值、中位数和众数。此外，标准差和范围等方差度量用于从平均值中查找数据的分布。相对位置测量数据位置之间的距离。常用的相对排名度量是百分位数、z 分数和四分位数。

百分位数是一种分形，它将数据划分为具有大致相同数量的值的组。Percentile 将数据分为 100 个组，每个组中的值约为 1%。

Z 分数是位置的度量，因为它们根据相对于平均值的标准差来描述值的位置。z 分数为 2 表示数据值比平均值高 2 个标准差，负 3 z 分数表示值比平均值低 3 个标准差。

四分位数是将数据划分为季度的数字。要查找四分位数，首先，找到中位数或第二个四分位数。第一个四分位数 Q₁ 是数据下半部分的中间值，第三个四分位数 Q₃ 是数据上半部分的中间值或中位数。

本文改编自 Openstax， Introductory Statistics， Section 2.3 Measures of the location of the data 和 2.7 Measures of the spread of the数据

Transcript

统计学家使用多种工具来解释数据。集中趋势的度量（如平均值、中位数和众数）标识最能代表数据的单个值。

要了解值与平均值的传播距离，可以使用变化的度量，例如范围和标准差。

最后，要解释数据的每个值相对于其他数据点，可以使用相对排名的度量。

例如，学生在课堂测试中获得 85% 的分数。通过将此分数与同学的分数进行比较，可以知道学生的表现是优秀还是差。这种相对比较可以通过使用三种常用的相对地位度量（百分位数、z 分数或四分位数）中的任何一个来进行。

百分位数将数据划分为数百人的组，并测量数据在这些组中的位置。z 分数是用于查找异常值的标准分数。四分位数将一组数字汇总为四组，使用箱线图进行可视化。

Key Terms and definitions

Measures of Central Tendency - Represent characteristics of data like mean, median, mode.
Measures of Variance - Determine the data spread from the mean, such as standard deviation and range.
Relative Standing Measures - Measure the distance between data locations, like percentile, z-score, and quartiles.
Percentiles - Type of fractile that partition data into hundred equal parts/groups.
Quartiles - These are values which divide data into quarters or four equal parts.

Learning Objectives

Define Measures of Central Tendency - Explain what they are and their functions (e.g., mean, median, mode).
Contrast Regular Distribution vs Variance - Explain key differences (e.g., range and standard deviation).
Explore Relative Standing Measures - Describe their role in data interpretation (e.g., percentile).
Explain Z-Score - A measure of position that describes the location of a value in terms of standard deviations relative to the mean.
Apply Quartiles in Data Analysis - Show how data is divided into quarters for analysis.

Questions that this video will help you answer

What are Measures of Central Tendency and their significance in data interpretation?
How does Percentile partition data?
What is the role of a Z-Score in measurement of position?

This video is also useful for

Students - Understand How measures in statistics support data analysis and interpretation.
Educators - Provides a step by step guide for statistical concepts boosting teaching efficiency.
Researchers - Crucial understanding for scientific study or statistical analysis.
Science Enthusiasts - Offer insights and broader interest and curiosity value in statistical analysis.

5.1: 回顾和预览

7,560 Views

Overview

Transcript

Key Terms and definitions​

Learning Objectives

Questions that this video will help you answer

This video is also useful for

Tags

回顾和预览

<em>z</em> Scores 简介

<em>z</em> 分数和异常值

百分比

四分位数

5 个数字摘要

箱线图

什么是异常值？

修改后的箱线图

Key Terms and definitions