Coefficient Variation
Lecture 14
The concept of coefficient of variation was suggested by
Karl Pearson. The coefficient of variation is a relative measure of dispersion
and applicable to compare two more datasets, even if they have different units of measurement.
Definition
The coefficient of variation is the percentage ratio of the standard deviation to the mean.
Let us have two data sets, X and Y. dataset X is said to be consistent if
Example 4.8: Find the coefficient of variation
of the following data.
12, 13, 15, 18, 21
Solution:
Example 4.9: The mean and standard deviation of two
commodities are given below:
|
Commodities |
Mean |
Standard
Deviation |
|
A |
8
kg |
1.36 kg |
|
B |
2
kg |
0.45
kg |
Which commodity is consistent?
Solution:
The coefficient of variation for commodity A is smaller than the coefficient of variation for commodity B. Thus, commodity A is consistent.
Example 4.10: The performance of two students in the
last five class tests is given below:
|
Test |
1 |
2 |
3 |
4 |
5 |
|
X |
7 |
8 |
6 |
7 |
5 |
|
Y |
4 |
10 |
4 |
9 |
6 |
Which of the student’s is a better average, and which one is consistent performance?
Solution: Compute the mean and standard deviation for
each student.
Example 4.11: The coefficient of variation is 52% and the mean of the data is 12.5. Find the standard deviation
Solution:
Example 4.12: The standard deviation and coefficient
of variation of a data are 25 and 3.50, respectively. Find the mean.
Solution:
Example 4.13: The total score obtained by two students
X and Y in the five papers is 460 and 482 with a standard deviation of 2.10 and
3.60, respectively. Who is more consistent in performance?
Solution:
The mean and coefficient of variation of student X:
The mean and coefficient of variation of student Y:
The coefficient of variation
of student X is smaller than the coefficient of variation of student Y.
Thus, it is concluded that student X performance is more consistent.
- Read More: Skewness
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