Unit 1: Introduction to Statistics PDF

Unit 1: Introduction STAT101: Statistics in The Modern World Department of Statistics UAE University STAT101 (UAEU) Unit 1: Introduction UAE University 1 / 12  O...

Unit 1: Introduction STAT101: Statistics in The Modern World Department of Statistics UAE University STAT101 (UAEU) Unit 1: Introduction UAE University 1 / 12  Outline 1 Introduction to Statistics 2 Types of Data 3 Sources of Data STAT101 (UAEU) Unit 1: Introduction UAE University 2 / 12  Introduction to Statistics Introduction to Statistics Statistics is a subject that plays an essential role in every area of our lives and world. It is a powerful tool for seeing our world in a more detailed fashion and for making informed decisions, although its poten- tial misuses caution us to avoid thoughtless acceptance of statistical conclusions. The recent and expected future development of computer speed and capacity increase the use of statistics with a larger scope and effect. Statistics is a tool with wide applicability. Statistics has limits that need to be acknowledged and respected, but its potential for helping us find meaning in our data driven world is enormous and growing. Trying to understand the economy, the weather, education, politics, risk, measurement, society, marketing, science, sports, medicine, and nearly every other aspect of our world fundamentally involves our ability to work with data in a meaningful way. STAT101 (UAEU) Unit 1: Introduction UAE University 3 / 12  Introduction to Statistics What is Statistics? Statistics is a science that deals with collecting and analyzing data, drawing conclusions, and making decisions. There are two main areas of Statistics: 1 Descriptive statistics: provides tabular and graphical techniques and nu- merical measures for describing data. 2 Inferential statistics: provides procedures for analyzing data and making decisions. Statistics is the study of data: (A) Politics, including elections, world conflict, economics, and business, cen- trally involves data and their interpretation. (B) Sports, education, the arts, medicine, and science fundamentally rely on statistical techniques. We can think of the study of statistics as dealing with two basic ques- tions: 1 How do we organize, describe, and summarize a collection of data when we know all the data? 2 How do we infer information about the whole population when we have data about only some members of the population? STAT101 (UAEU) Unit 1: Introduction UAE University 4 / 12  Introduction to Statistics Statistics and Data The trouble with data is that they can be misleading or meaningless. Data by themselves do not have meaning. Deducing the meaning from data is a necessary step. Perhaps the most famous quotation about statistics is from Mark Twain, which be attributed to Benjamin Disraeli, namely, “There are three kinds of lies: lies, damned lies, and statistics.” There is an apt rejoinder to Twain’s quote, namely, “It is easy to lie with statistics, but it is easier to lie without them.” Check this interesting Newsweek article (Lies, Damned Lies And...) on the important role of statistics in scientific research. The two most fundamental words in the study of statistics, statistics and data, share a grammatical issue. Are they singular or plural? Data is the plural of datum, a single piece of information. Statistics can be singular or plural, depending on the meaning. For ex- ample, statistics is the study of data or statistics are bits of information. STAT101 (UAEU) Unit 1: Introduction UAE University 5 / 12  Types of Data Types of Data Statistical data are available in all sorts of shapes and sizes. Information (data) concerning the human population can be classified as follows: 1 Qualitative data: labels or names used to identify attributes of the sample elements. The labels can be numbers with no real numerical meaning. Examples: nationality, religion, occupation, place of birth, home address, family status, gender, etc. 2 Quantitative data: numbers (with real meaning), representing measurements, obtained from the sample elements. Examples: socio-economic aspects like income, wealth and expenditure or biological information like age, height, weight, number of children, etc. The specific information on which we wish to focus is called the ’Statistical Characteristic’ or Variable and is denoted by the symbol x. STAT101 (UAEU) Unit 1: Introduction UAE University 6 / 12  Sources of Data Sources of Data Primary Data: Data are collected at source with a specific purpose in mind. The data are collected using survey, census, interview, direct observation or experiment that you or your company have conducted for the purpose of obtaining specific figures. Primary data can be relied on because you know where it came from and what was done to it. Secondary Data: Data are collected from external sources other than the user. The data may be available in books, in scientific journals, on tapes, on CDs, on the Internet, etc. Secondary data are cheap and easy to collect, but must be treated with caution. STAT101 (UAEU) Unit 1: Introduction UAE University 7 / 12  Sources of Data Stock Magnitudes Stock Magnitudes: may refer to a stock taking event at a specific point in time, e.g. a census establishing the number of inhabitants in country A, the number of unemployed in country B or the number of registered motor vehicles in country C. Examples: 1 Population by country (xi ) as measured at time ti 1 : UAE population in 2009 = xPi,2009 = 4, 619, 000. World population in 2009 = xi,2009 = 6, 828, 155, 000. 2 Registered motor vehicles by country (xi ) as measured at a stock taking point in time ti : P Registered motor vehicles worldwide in 1990 = xi,1990 = 582, 981, 777. Registered motor vehicles in USA in 2008= xi,2008 = 255, 917, 664 2 1 Source: World Resources Institute 2 Source: US Bureau of Transit Statistics STAT101 (UAEU) Unit 1: Introduction UAE University 8 / 12  Sources of Data Flow Magnitudes Flow Magnitudes: Data may refer to a period of time, e.g. the gross national product (GNP) produced in country A, normally refers to a calendar year of 365 or 366 days. The same applies to annual exports, imports or investment undertaken during a specific period. Example: Manufactured motor vehicles by country (xi ) as measured during the reference year ti 3 : Year Production P 2009 P xi,2009 = 51, 971, 328 2008 P xi,2008 = 52, 940, 559 2007 P xi,2007 = 54, 920, 317 2006 P xi,2006 = 49, 886, 549 2005 xi,2005 = 46, 862, 978 3 Source: Worldometers STAT101 (UAEU) Unit 1: Introduction UAE University 9 / 12  Sources of Data Primary and Secondary Magnitudes Primary Magnitudes: All data come in some kind of denomination, e.g. in currency, metric or imperial units of measurement like kilometers or miles, or in some other specific units such as hertz, gigawatt, volt, etc. Such figures, which are expressed in clearly defined units of account. The stock and flow magnitudes above are examples of such primary magnitudes. Examples: Fatalities resulting from road accidents in UAE, number of UAE University graduates, etc. Secondary Magnitudes: Ratios, percentages or index figures used for comparison purposes or to highlight relevant developments. Example: When comparing the road accidents in Europe, it is expected that large countries such as Germany, France, Spain and Italy would tend to show higher road accident figures than the smaller ones, Denmark, Ireland or Luxembourg. It is, therefore, more meaningful to compare these road accident flow magnitudes with other primary magnitudes, e.g. population per country or number of registered motor vehicles per country. STAT101 (UAEU) Unit 1: Introduction UAE University 10 / 12  Sources of Data Exercise Use the following table 1.1 (Unit1.xls) on deaths from road accidents, popu- lation size (millions) and registered passenger cars (millions) of some coun- tries in 2015 4. Answer the following questions: 1 Rank the countries regarding the number of deaths. Which five coun- tries have the highest absolute number of deaths. 2 Rank the countries regarding the mortatlity rates. Which five countries have the highest mortality rates. 3 Compare the ranks of the number of deaths with the ranks of the mortatlity rates. Comment on the difference. 4 Work out the averages mortatlity rates in Eurpean countries and MENA countries. Which countries have higher mortatlity rates resulting from road accidents? 5 Plot a Bar chart for the mortatlity rates of MENA countries. Comment on the graph. 4 Source: Insurannce News Around The World STAT101 (UAEU) Unit 1: Introduction UAE University 11 / 12  Sources of Data Exercise Table: Deaths in MENA countries and some other countries from road accidents in relation to population size (millions) and registered passenger cars (millions) in 2015. Country Population Number of cars Deaths Mortality rates in millions in millions deaths per millio Germany 81.4 48.4 3540 0.434 France 66.8 38.6 3461 0.518 Spain 46.4 27.4 1689 0.36 Italy 60.8 42.2 3428 0.563 United Kingdom 65.3 38.2 1806 0.277 Portugal 10.3 5.8 593 0.573 Belgium 11.3 6.4 732 0.648 Greece 10.8 6.2 1013 0.935 Netherlands 16.9 9.3 531 0.313 Denmark 5.6 2.8 178 0.31 Argentina 43.4 13.7 5619 1.294 STAT101 (UAEU) Unit 1: Introduction UAE University 12 / 12