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

2. Getting Started ____________________________________________________________________________________________
computers
Software:
MS Excel 2016 (English version)
GRETL (multiple language versions)
RStudio (English version)
Statistics: 1

3. Getting Started ____________________________________________________________________________________________
indices
Index vs. Raw Data
Aggregate:
Starting Value:
End Value: M1
67 865 M2 M3
Raw data can be deceptive: which aggregate has grown faster?
Statistics: 1
Monetary Aggregates M1, M2, and M3 in Poland

4. Getting Started ____________________________________________________________________________________________
indices
Fixed –base and Chain index
Statistics: 1
First month = 100 or previous month = 100

5. Where is your (favourite player’s) salary located?
Measures of Location ____________________________________________________________________________________________
mean
Why measures of location?
Where is your (favourite player’s) salary located?
Statistics: 1

6. Where is your (favourite player’s) salary located?
Measures of Location ____________________________________________________________________________________________
histogram
Measuring the (relative) frequencies
Where is your (favourite player’s) salary located?
Statistics: 1

7. Measures of Location ____________________________________________________________________________________________
mean
arithmetic mean
sum up the elements (from 1 to T);
divide the sum by the number of observations;
when to use
no outliers
Statistics: 1
T – number of observations, x – variable of interest

8. counting the frequencies
Measures of Location ____________________________________________________________________________________________
mean
using the arithmetic mean
Example 1: Her Majesty Queen Elizabeth II official state visits,
Excel and basic data mining:
counting the frequencies
=right
=countif, =countifs
Statistics: 1
Excel: sheet TheQueen

9. Measures of Location ____________________________________________________________________________________________
mean
using the mean value
problem:
Defence wins championships, Offence sells tickets. Who gets better paid, then?
offence:
USD for 31 players
defence:
USD for 36 players
Estimate the mean salary and interpret the results.
Which formation is more expansive and why?
Statistics: 1
Example: National Football League, Washington Redskins;

10. Measures of Location ____________________________________________________________________________________________
mean
geometric mean
estimate the product of all observations;
estimate the root of degree T of the product;
when to use
outliers, proportions, multiplications (e.g. interest rates, rates of return etc.)
Statistics: 1
T – number of observations, x – variable of interest

11. exponentiation and log-linearisation may sometimes by useful
Measures of Location ____________________________________________________________________________________________
mean
interesting fact
exponentiation and log-linearisation may sometimes by useful
Statistics: 1
T – number of observations, x – variable of interest

12. RUR into PLN: rate of return
Measures of Location ____________________________________________________________________________________________
mean
using the geometric mean
RUR into PLN: rate of return
Excel and basic data mining:
retrieving the forex values for sepcific dates
=vlookup
Statistics: 1
Foreign Exchange Rate (FOREX)

13. Redskins payroll again:
Measures of Location ____________________________________________________________________________________________
mean
trimmed mean
Redskins payroll again:
get rid of the smallest and largest cases;
re-estimate the mean value;
Trimmed mean: ROUND IT TO THE NEAREST INTEGER
Data Base: sheet Redskins
remove the countries with largest and smallest labour cost, and re-estimate the mean
Statistics: 1
5% trimmed mean: remove 0.05 x T smallest and largest cases from the sample: 0.05 x 69  3

14. Measures of Location ____________________________________________________________________________________________
mean
weighted average
example: market share
assume/estimate the weights;
multiply the values by their weights;
if the denominator is equal to 1, the weighted average reduces to the expression appearing in the numerator
Statistics: 1
– weights

15. Measures of Location ____________________________________________________________________________________________
exercises
1. Calculate your own CPI
a. name 5 consumer products and services;
b. assign the weights;
c. calculate the weighted average;
2. CPI and weights
compare the weights assigned to groups of consumer products and services around Europe
Statistics: 1
sheet: CPI weights

16. odd number of observations even number of observations
Measures of Location ____________________________________________________________________________________________
median
median
odd number of observations
even number of observations
Trimmed mean: ROUND IT TO THE NEAREST INTEGER
Data Base: Redskins.xls
Statistics: 1
odd: 1,3,5,7,9 etc even: 2,4,6,8 etc

17. a value that occurs with the highest frequency
Measures of Location ____________________________________________________________________________________________
mode
mode
a value that occurs with the highest frequency
Calculate the modes for defence and offence, and re-interpret Mr. Snyder's dilemma. Interpret the results considering the fact that the minimum wage for the NFL rookie is equal to $ USD (season 2015).
Trimmed mean: ROUND IT TO THE NEAREST INTEGER
Data Base: Redskins.xls
Statistics: 1
Applied Polish for Statisticians: WYST.NAJCZĘŚCIEJ (MS Excel)

18. a percentile calculated for i being equal to
Measures of Location ____________________________________________________________________________________________
percentile
percentile
a number within the sample corresponding to the rank calculated as follows:
quartiles
a percentile calculated for i being equal to
25, 50, 75, or 100
Statistics: 1
Applied Polish for Statisticians: KWARTYL (MS Excel)

19. of the Washington Redskins’ 1. total; 2. defensive; 3. offensive
Measures of Location ____________________________________________________________________________________________
exercise
percentile quartiles
calculate the
35th percentile st. quartile
of the Washington Redskins’
1. total; 2. defensive; 3. offensive
salaries
Statistics: 1