1. Measures of Dispersion
Jacek Wallusch _________________________________ Statistics for International Business
Lecture 2:
Measures of Dispersion

2. Getting Started ____________________________________________________________________________________________
risk, uncertainty
Steven Obanno: Do you believe in God Mister Le Chiffre?
Le Chiffre: No, I believe in a reasonable rate of return.
Steven Obanno: I want no risk in my portfolio.
Le Chiffre: Agreed.
Probability distribution and uncertainty and risk – this topic will be reconsidered soon
Statistics: 2
Steven Obanno and Le Chiffre, Cassino Royale

3. frequency of a class devided by the sample size.
Getting Started ____________________________________________________________________________________________
frequency distribution
Frequency Distribution:
tabular summary of a set of data showing the frequency (or number) of items in each of several non-overlapping classes.
Relative Frequency Distribution:
frequency of a class devided by the sample size.
Statistics: 2
A histogram displays the frequencies or relative frequencies (vertical axis) and the variable of interest (horizontal axis). File: redskins.xls

4. Cumulative frequency:
Getting Started ____________________________________________________________________________________________
frequency distribution
Items:
Frequency:
Relative frequency:
Cumulative frequency:
Cumulative relative frequency: A a B b
a + b
Sum:
a + b = T
Statistics: 2
T – sample size

5. Getting Started ____________________________________________________________________________________________
dispersion
Ogive
Statistics: 2
Ogive and gothic architecture

6. Example: Washington Redskins and yearly salaries
Getting Started ____________________________________________________________________________________________
dispersion
Ogive
cumulative relative frequency
Example: Washington Redskins and yearly salaries
salary clusters
Statistics: 2
Ogive depicts the cumulative distribution or cumulative relative frequency distribution

7. Getting Started ____________________________________________________________________________________________
dispersion
Ogive and mean value
Statistics: 2
Dotted, dashed line – cumulative relative frequency, solid line – mean value (arithmetic)

8. to measure disparities
Measures of Dispersion ____________________________________________________________________________________________
usage
Application:
to measure volatility
to measure disparities
histogram (spread around the mean)
ogive (cumulative distribution)
variance and/or standard deviation
Statistics: 2

9. Measures of Dispersion ____________________________________________________________________________________________
variance
population variance
estimate the mean value;
estimate the deviations from the mean value;
estimate the sum of squared deviations
sample variance
Statistics: 2
T – number of observations, m – population mean

10. estimate the square root of variance
Measures of Dispersion ____________________________________________________________________________________________
standard deviation
stadard deviation of a population
estimate the square root of variance
standard deviation of a sample
population vs. sample: estimate the population st.dev. for Redskins’ defence
Statistics: 2
standard deviation is measured in the same units as the original data

11. Getting Started ____________________________________________________________________________________________
dispersion
Regional disparities
Statistics: 2
Interpret the histograms first. Then, estimate the sample standard deviation.

12. estimate the population standard deviation for the Redskins’ defence
Measures of Dispersion ____________________________________________________________________________________________
standard deviation
Population vs. Sample:
estimate the population standard deviation for the Redskins’ defence
Statistics: 2
standard deviation is measured in the same units as the original data

13. a ratio of the interquartile range to the median
Volatility ____________________________________________________________________________________________
measuring variation
Coefficient of variation:
normalised measure of dispersion, a ratio of the standard deviation to the average
Quartile coefficient of variation:
a ratio of the interquartile range to the median
Statistics: 2
REMARKS [1] normalised measure: suitable for variables expressed in different units;
[2] suitable for variables expressed on ratio scale;

14. Dispersion ____________________________________________________________________________________________
detecting outliers
z-score:
estimate the mean value;
estimate the standard deviation;
divide the deviation from the mean by the standard deviation;
outliers:
suggested z-score for no outliers
Statistics: 2
Outlier: an observation numerically distant from the
other observations in a sample

15. Dispersion ____________________________________________________________________________________________
z-Score
z-score for the defensive players
Statistics: 2
database: Redskins.xls