Statistics 简明教程

Statistics - Venn Diagram

维恩图是一种可视化表示实体或对象组之间的关系的方法。维恩图由圆圈组成，其中每个圆圈代表一个整体集合。维恩图可以有无限个圆圈，但通常情况下，两个或三个圆圈是更好的选择，否则该图会变得过于复杂。

Venn diagram is a way to visually represents relationship between groups of entities or objects. Venn diagrams are comprised of circles where each circle represents a whole set. Venn diagram can have unlimited circles but generally two or three circles are preferred otherwise the diagram becomes too complex.

Steps to draw a Venn Diagram

考虑以下人群：

Consider the following sets of people:

步骤 1：画一个矩形并将其标记为球员。

Step 1: Draw a rectangle and label it as players.

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步骤 2：画两个圆圈并将其标记为板球和曲棍球。确保圆圈相互重叠。

Step 2: Draw two circles and label them as Cricket and Hockey. Make sure that circles are overlapping each other.

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步骤 3：在圆圈中写上相关姓名。通用名称应位于通用区域内。

Step 3: Write Names inside the circle as relevant. Common name(s) should fall within common region.

venn diagram

Union

并集 ($ \cup $) 代表一个集合，其中项目出现在所有类别中，但不会重复。

Union ($ \cup $) represents a set where items are present in all categories but are not repeated.

Example

Problem Statement:

Problem Statement:

绘制 $ C \cup H $ 的维恩图。

Draw a Venn diagram of $ C \cup H $.

Solution:

Solution:

步骤 1：确定只打板球或曲棍球的球员。按如下方式绘制：

Step 1: Determine players who are either playing cricket or hockey. Draw them as following:

$ C \cup H = \{ Ram, Shyam, Mohan, Rohan, Ramesh, Suresh, Naresh, Mahesh, Leela, Sunita \} $。

$ C \cup H = \{ Ram, Shyam, Mohan, Rohan, Ramesh, Suresh, Naresh, Mahesh, Leela, Sunita \} $.

c union h

Intersection

交集 ($ \cap $) 代表一个集合，其中项目出现在两个类别中。

Intersection ($ \cap $) represents a set where items are present in both categories.

Example

Problem Statement:

Problem Statement:

绘制 $C \cap H $ 的维恩图。

Draw a Venn diagram of $ C \cap H $.

Solution:

Solution:

步骤 1：确定既打板球又打曲棍球的球员。按如下方式绘制：

Step 1: Determine players who are playing cricket and hockey both. Draw them as following:

$ C \cap H = \{ Ramesh \} $。

$ C \cap H = \{ Ramesh \} $.

c intersection h

Difference

差集 ($ - $) 代表一个集合，其中项目仅出现在一个类别中，而不出现在另一个类别中。

Difference ($ - $) represents a set where items are present only in one category and not in other one.

Example

Problem Statement:

Problem Statement:

绘制 $C - H $ 的维恩图。

Draw a Venn diagram of $ C - H $.

Solution:

Solution:

步骤 1：确定仅打板球的球员。按如下方式绘制：

Step 1: Determine players who are playing cricket only. Draw them as following:

$ C - H = \{ Ram, Shyam, Mohan, Rohan, Suresh \} $。

$ C - H = \{ Ram, Shyam, Mohan, Rohan, Suresh \} $.

c minus h