Coefficient of
Variation
measures of central tendency
Coefficient of Variation
• Whenever two samples have the same units of measure,
the variance and standard deviation for each can be
compared directly.
• Karl Pearson devised the coefficient of variation to compare
the deviations of two different groups such as the heights
of men and women.
Coefficient of Variation
•The higher the coefficient of variation, the higher the variability of the data set
This means that, when comparing two or more data sets, the one with the highest coefficient of variability can be
said to have the highest variation.
Example
• The average age of people who live in entire Camarines Sur is 45 with
a standard deviation of 3. The average age of people who live in
entire Camarines Norte is 50 with a standard deviation of 5. Compare
the variations.
• Solution
:
3
CVar =
CVar =
45
5
50
= 0.066667 * 100 =
= 0.1 * 100 =
6.67 % ages of people in Cam Sur
10 % ages of people in Cam Norte
Conclusion : The age of people who live in Camarines Norte is more viable than the ages of people
who live in Camarines Sur.
•The mean for the number of pages in a
selected Filipino books is 132, with a
variance of 23; the mean for the number
of pages in a selected English book is
182, with a variance of 62. Compare the
variations.
Example
• The mean for the number of pages in a selected Filipino books is 132,
with a variance of 23; the mean for the number of pages in a selected
English book is 182, with a variance of 62. Compare the variations.
• Solution :
3.6 % pages of Filipino books
4.3 % pages of English books
Conclusion : The number of pages in selected English Books is more variable than the number of
pages in Filipino books since the coefficients of variation is larger for English Books