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

Getting Started ____________________________________________________________________________________________ computers Software: MS Excel 2016 (English version) GRETL (multiple language versions) RStudio (English version) Statistics: 1 www.wallusch-datenbank.de

Getting Started ____________________________________________________________________________________________ indices Index vs. Raw Data Aggregate: Starting Value: End Value: M1 67 865 686 587 M2 140 038 1 140 951 M3 140 428 1 151 171 Raw data can be deceptive: which aggregate has grown faster? Statistics: 1 Monetary Aggregates M1, M2, and M3 in Poland

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

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

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

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

counting the frequencies Measures of Location ____________________________________________________________________________________________ mean using the arithmetic mean Example 1: Her Majesty Queen Elizabeth II official state visits, 1952-2015 Excel and basic data mining: counting the frequencies =right =countif, =countifs Statistics: 1 Excel: sheet TheQueen

Measures of Location ____________________________________________________________________________________________ mean using the mean value problem: Defence wins championships, Offence sells tickets. Who gets better paid, then? offence: 44 046 277 USD for 31 players defence: 42 434 366 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;

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

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

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)

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

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

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

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

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 $435 000 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)

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)

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