Statistics 简明教程

Statistics - Mean Deviation

这被称为平均偏差,定义为某个分布中偏差(忽略其符号)除以该分布中的项目数量。平均值可以是平均值、中位数或众数。理论上,中位数是最佳平均选择,因为忽略符号后偏差与中位数之和最小。然而,从实际角度而言,算术平均值是用于计算平均偏差的最常用平均值,并且用符号 ${MD}$ 表示。

Referred to as average deviation, it is defined as the sum of the deviations(ignoring signs) from an average divided by the number of items in a distribution The average can be mean, median or mode. Theoretically median is d best average of choice because sum of deviations from median is minimum, provided signs are ignored. However, practically speaking, arithmetic mean is the most commonly used average for calculating mean deviation and is denoted by the symbol ${MD}$.

我们将讨论计算三种类型数列的 Mean Deviation 的方法:

We’re going to discuss methods to compute the Mean Deviation for three types of series:

Individual Data Series

当数据是以个体为基础给出时。以下是关于个体序列的一个例子:

When data is given on individual basis. Following is an example of individual series:

Items

5

10

20

30

40

50

60

70

Discrete Data Series

当数据与其频率一起给出时。以下是离散序列的一个例子:

When data is given alongwith their frequencies. Following is an example of discrete series:

Items

5

10

20

30

40

50

60

70

Frequency

2

5

1

3

12

0

5

7

Continuous Data Series

当数据根据范围及其频率给出时。以下是连续序列的一个例子:

When data is given based on ranges alongwith their frequencies. Following is an example of continous series:

Items

0-5

5-10

10-20

20-30

30-40

Frequency

2

5

1

3

12