Lesson in Statistics and Probability Grade 11

1. Lesson 8: Measures of Variation
LESSON OUTLINE:
1. Introduction: The Case of the Returns on Stocks
2. Absolute Measures of Dispersion: Range, Interquartile
Range, Variance, Standard Deviation and Coefficient of
Variation
3. Relative Measure of Dispersion: Coefficient of Variation

2. LEARNING OUTCOME(S): At the end of
the lesson, the learner is able to:
• Calculate some measures of dispersion;
• Think of the strengths and limitations of these
measures; and
• Provide a sound interpretation of these
measures.

3. A. Introduction: The Case of the Returns on
Stocks.
Stocks -are shares of ownership in a company.
When people buy stocks they become part
owners of the company, whether in terms of
profits or losses of the company.
-the history of performance of a particular stock
maybe a useful guide to what may be expected of
its performance in the foreseeable future. This is
of course, a very big assumption, but we have to
assume it anyway.

4. The following data representing the rates of
return for two stocks, which we will call Stock A
and Stock B.

5. Rate of Return -is defined as the increase in value
of the portfolio (including any dividends or other
distributions) during the year divided by its
value at the beginning of the year.
Example
If the parents of Juana dela Cruz invests 50,000
pesos in a stock at the beginning of the year, and
the value of the stock goes up to 60,000 pesos,
thus having an increase in value of 10,000 pesos,
then the rate of return here is 10,000/50,000 =
0.20

6. Let us compute some measures of locations that
we learned in previous lessons to describe the
data given above

7. Two types of measures of variability or
dispersion
1.Absolute measure of dispersion
-provides a measure of variability of
observations or values within a data set.
Includes the range, interquartile range, variance,
and standard deviation.
2. relative measure of dispersion
-which is the other type of measure of dispersion
is used to compare variability of data sets of
different variables or variables measured in
different units of measurement.

8. B. Absolute Measures of Dispersion: Range,
Interquartile Range, Variance, and
Standard Deviation
Range -is a simple measure of variation defined as
the difference between the maximum and
minimum values. The range depends on the
extremes; it ignores information about what
goes in between the smallest (minimum) and
largest (maximum) values in a data set. The
larger the range, the larger is the dispersion of
the data set.

10. Interquartile range or IQR
-is the difference between the 3rd and the 1st
quartiles. Hence, it gives you the spread of the
middle 50% of the data set. Like the range, the
higher the value of the IQR, the larger is the
dispersion of the data set. Based on the
computations we did in the previous lesson, the
3rd quartile or Q3 is the 113th observation and is
equal to 38 while Q1 or P25 is the 38th
observation and is equal to 25. Hence,
IQR = 38 – 25 = 13.

11. Variance -is a measure of dispersion that accounts
for the average squared deviation of each
observation from the mean. Since we square the
difference of each observation from the mean,
the unit of measurement of the variance is the
square of the unit used in measuring each
observation.
-we usually denoted this expression as
Standard Deviation -is computed which is the
positive square of the variance

12. C. Relative Measure of Dispersion:
Coefficient of Variation
Coefficient of variation (CV)
-is used as measure of relative dispersion. It is
usually expressed as percentage and is computed
as CV = ×100%. CV is a measure of
dispersion relative to the mean of the data set.
With and having same unit of measurement, CV
is unit less or it does not depend on the unit of
measurement. Hence, it is used compare the
variability across the different data sets.