Statistics 简明教程

Statistics - Co-efficient of Variation

Coefficient of Variation

标准差是离散的绝对测量。当需要比较两个序列时，使用称为变异系数的离散相对测量。

Standard variation is an absolute measure of dispersion. When comparison has to be made between two series then the relative measure of dispersion, known as coeff.of variation is used.

变异系数CV由下式定义和给出：

Coefficient of Variation, CV is defined and given by the following function:

Formula

其中——

Where −

${CV}$ = Coefficient of Variation.
${\sigma}$ = standard deviation.
${X}$ = mean.

Example

Problem Statement:

从以下数据中。确定风险项目，更具风险：

From the following data. Identify the risky project, is more risky:

Year	1	2	3	4	5
Project X (Cash profit in Rs. lakh)	10	15	25	30	55
Project Y (Cash profit in Rs. lakh)	5	20	40	40	30

Solution:

为了确定风险项目，我们必须确定其中哪个项目在产生利润方面不够稳定。因此，我们计算变异系数。

In order to identify the risky project, we have to identify which of these projects is less consistent in yielding profits. Hence we work out the coefficient of variation.

Project X	Project y
${X}$	${X_i - \bar X}$ ${x}$
${x^2}$	${Y}$
${Y_i - \bar Y}$ ${y}$	${y^2}$
10	-17
289	5
-22	484
15	-12
144	20
-7	49
25	-2
4	40
13	169
30	3
9	40
13	169
55	28
784	30
3	9
${\sum X = 135}$
${\sum x^2 = 1230}$	${\sum Y = 135}$
	${\sum y^2 = 880}$

Project X

Project Y

由于项目 X 的离散变异系数高于项目 Y，因此，尽管平均利润相同，项目 X 的风险更高。

Since coeff.of variation is higher for project X than for project Y, hence despite the average profits being same, project X is more risky.