Appendix A Coefficient of variance

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Coefficient of variance
In chapter 5.2.1.1, we have made use of coefficient of variance (CV). The following is a short summary
of the CV as it is used in the main text and tables. The CV which is sometimes referred to as relative
standard deviation, is defined as the ratio of the standard error of the estimator to the expected value.
In our case, we aim to calculate a CV for the estimated average of monthly earnings.
N
Based on the general definition of an average as
x
i

x
i 1
N
i
, we can define the estimated average
k
for the population by using the earlier definition of the weights in chapter 12.1,
Xˆ 
 wa x
a 1
k
w
a 1
where
x
a
is the observed average monthly earnings in enterprise a in the sample and
a
w is the
a
calculated weight for enterprise a .
 x
k
The standard deviation: s 
a 1
a
 x ²
k 1
where k is the number of clusters, in our case
enterprises, in the sample.
The CV can therefore be calculated as
expressed as a percentage
percentage.
cv % 
cv 
s
. The CV as commented in chapter 5.2.1.1 is often
Xˆ
s
100% . In text and tables, our CV is not expressed as a
Xˆ
a