Standard deviation is a mathematical concept.
Many professionals are intimidated by this as it involves mathematical calculations; however, you should understand the significance of this important concept. Once you understand the practical application of standard deviation and know the calculations, you will not forget it.
Let’s dive in.
Standard Deviation
标准偏差是“平均值的平均值”。它告诉您数据如何传播。
The mean is the average of the given numbers.
First, let’s analyze a mathematical example of this concept.
标准偏差的示例
Your class has five students, and the height of each student is as follows:
First student = 150 cm
第二学生= 160厘米
Third student = 170 cm
Fourth student = 165 cm
Fifth student = 155 cm
计算标准偏差。
为了计算标准偏差，您需要均值和差异。
Mean = (150 + 160 + 170 + 165 + 155) / 5
= 160 cm
要找到差异，请从每个学生的身高中减去此“平均高度”，将其保持平衡，将它们添加在一起，并取平均值。
方差= [（150 - 160）2 +（160 - 160）2 +（170 - 160）2 +（165 - 160）2 +（155 - 160）2] / 5
= [100 + 0 + 100 + 25 + 25] / 5
= 250 /5
= 50
因此，差异为50。
标准偏差=方差的平方根
Standard Deviation = Square Root of 50
= 7.07
因此,站ard deviation is 7.07 cm.
您可能想知道这些数据有多么有用。
These data are essential because they give you the following information:
- 学生的平均身高为160厘米（平均）。
- The height of most of the students varies from 152.93 cm (160 – 7.07) to 167.07 cm (160 + 7.07).
The image above shows the standard deviation for five students. The vertical lines show the height of each student (e.g., 150 cm, 160 cm, etc.). The blue line is the average (or mean) line, and the maroon lines represent the standard deviation.
您会看到标准偏差线在平均线上和低于平均线上，大多数学生的高度位于这两条栗色线之间。
Put simply, you can say that the height of most students is between 152.93 cm to 167.07 cm.
Let’s revise the whole procedure once again:
- Calculate the average height of the students.
- 从每个学生的高度上减去平均高度，然后对其进行平整。
- 将它们加在一起，并取平均值。
- 现在取平方根。
重要的提示
我在示例中使用了基于人群的数据；这样，我的意思是班上只有五名学生。
However, if you select sample data, i.e., choosing a few random numbers from a large data pool, you will have to divide the variance by (N-1), where N is the number of samples. In other words, if the class has hundreds of students, and you select five, you will divide the variance by (5 – 1) or 4.
您可能想知道，如果我们将其占据平方根，为什么我们要平方数字。
There is a reason for this calculation; the positive and negative numbers cancel each other out if we add the difference.
Application of Standard Deviation
Standard deviation is used in analyzing data, and it is a vital tool for industries, especially for clothing manufacturing.
标准偏差提供有关哪种尺寸小，正常，中等，大或超大的信息。根据结果，制造商设置了裤子，衬衫，T恤等的大小。
概括
标准偏差是一种统计分析工具，可以通过分析数据样本来帮助行业了解整个人群的参数。尽管该技术涉及数学计算，但该概念很简单，标准偏差告诉您您的数据如何传播。基于此信息，您可以开发和销售产品。
I hope the standard deviation is clear to you. If you still have doubts, send me a message through the comments section, and I will reply to you.
Standard deviation is an essential concept from a PMP perspective. You may see a question from this topic on your exam.
