Statistics 简明教程
Statistics - Harmonic Mean
What is Harmonic Mean?
调和平均数也是一个数学平均数，但其应用受到限制。它通常用来求以两个不同计量单位的比率表示的变量的平均值，例如速度以千米/小时或英里/秒等为单位。
Harmonic Mean is also a mathematical average but is limited in its application. It is generally used to find average of variables that are expressed as a ratio of two different measuring units e. g. speed is measured in km/hr or miles/sec etc.
Formula
其中——
Where −
-
${H.M.}$ = Harmonic Mean
-
${W}$ = Weight
-
${X}$ = Variable value
Example
Problem Statement:
Problem Statement:
求项 4、7、12、19、25 的加权调和平均数，其权重分别为 1、2、1、1、1。
Find the weighted H.M. of the items 4, 7,12,19,25 with weights 1, 2,1,1,1 respectively.
Solution:
Solution:
${X}$ |
${W}$ |
$\frac{W}{X}$ |
4 |
1 |
0.2500 |
7 |
2 |
0.2857 |
12 |
1 |
0.0833 |
19 |
1 |
0.0526 |
25 |
1 |
0.0400 |
$\sum W$ |
$\sum \frac{W}{X}$= 0.7116 |
根据上面提到的公式，调和平均数 $G.M.$ 将是：
Based on the above mentioned formula, Harmonic Mean $G.M.$ will be:
∴ 加权调和平均数 = 8.4317
∴ Weighted H.M = 8.4317
我们将讨论计算 Harmonic Mean 的方法，适用于三类序列：
We’re going to discuss methods to compute the Harmonic Mean 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 |