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Introduction to Statistics: Concepts and Applications

This chapter provides an overview of statistics, including the role of statistics in everyday life, descriptive and inferential statistics, and different types of variables and data. It also introduces the art and science of statistics, highlighting its importance in collecting, organizing, and presenting data, as well as drawing inferences and making predictions.

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Introduction to Statistics: Concepts and Applications

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  1. What is Statistics? Chapter 1

  2. 1 1. 2. 3. 4. 1 - 2 Chapter Goals When you have completed this chapter, you will be able to: Explainwhat ismeant by statistics. Identify the role of statistics in the development of knowledge and everyday life. Explain what is meant bydescriptive statistics andinferential statistics. Distinguish between a qualitative variable and a quantitative variable. and...

  3. 1 5. 6. 7. 8. 1 - 3 Chapter Goals Distinguishbetween a discrete variable and a continuous variable. Collect datafrom published and unpublished sources. Distinguishamong the nominal, ordinal, interval, and ratio levelsof measurement. Identifyabuses of statistics. and...

  4. 1 9. 1 - 4 Chapter Goals Gain an overview of the art and science of statistics. We recommend that you read this chapter at least twice, once at the beginning and once at the end of your course!

  5. …it is the art and scienceof… • collecting • organizing • presenting data • drawing inferencesfrom a sample of information about an entire population as well as • predicting and developing policy analysis What isMeant by Statistics?

  6. in everyday life Role played by Statistics

  7. Who usesStatistics? Those using Statistical techniques include : Marketers Investors Economists Accountants Sports people Consumers Statisticians Hospitals Quality Controllers Educators Politicians Physicians

  8. Weather Forecasters Who usesStatistics?

  9. Sports Who usesStatistics?

  10. Types of Statistics

  11. Types of Statistics Methods of…collectingorganizingpresenting and analyzingdata Science of…making inferences about a population, based onsample information. Descriptive Inferential

  12. Identify the following… Descriptive Inferential A. A Gallup poll found that 83% of the people in a survey knew which country won the gold medal in Men’s Hockey in 2002. B. The accounting department of a firm will select a sample of invoices to check for accuracy of all the invoices of the company. C. Wine tasters sip a few drops of wine to make a decision with respect to all the wine waiting to be released for sale.

  13. The Method of Experimentation We start off with particular observationsfrom the real world and draw conclusionsabout thegeneral patterns in the real world! 1. Definethe experimental goal or a working hypothesis 2. Design an experiment 3. Collect data 4. Estimate the values/relations 5.Draw inferences 6. Predict and prepare policy analysis Chapters 8 and 12 Chapters 3 and 4 Chapters 5,7,8 and 9

  14. Real World Real World The Method of Experimentation Deductive Method Inductive Method Statistical Techniques Definitions &Assumptions Experimental Design & Data Collection Rules of Logic Objective or Working-Hypothesis Implications or Hypotheses

  15. A Study A study was undertaken to estimate the average height of penguins in Antarctica. Let’s review the steps they would take to prepare the estimate.

  16. What Information do we need? the POPULATION

  17. A population is acollection of all possibleindividuals, objects,or measurements of interest

  18. From POPULATION Take a …which are deemed to be representative of the Sample POPULATION Say, 101 What we now need is…

  19. Take a Measurement for each one in the sample Record 101 Sample Raw Data

  20. ? Goal What Now Displaying Data Results …to put the data into a readable and understandable format!

  21. More on these in chapter 2… Two methods that can be used to ‘see’ what the data conveys are Tables and Graphs/Charts

  22. Tables e.g. 101 More on these in chapter 2… … are an efficient method of displaying data and depicting data accurately.

  23. Pie Line Bar Scatter Histogram More on these in chapter 2… Charts Graphs

  24. More in chapter 8 … Why take a sample instead of studying every member of the population? Costs of surveying the entire population may be too large or prohibitive Destruction of elements during investigation Accuracy of results

  25. Why Study Statistics? • Data are everywhere • Statistical techniques are used to make many decision that affect our lives • No matter what your future line of work, you will make decisions that involve data. An understanding of statistical methods will help you make these decisions more effectively.

  26. Types of Data

  27. Types of Data A Variable a characteristic of a population orsample that is of interest to us

  28. Quantitative Qualitative Types of Data Variables Categorical Observations Numerical Observations

  29. Variables Qualitative – or Attribute Country of Birth U.K. Germany Taiwan China India Japan Russia Eye Colour Blue Brown Hazel Green Red GenderMale Female

  30. Variables Quantitative – Numeric Minutes to end of Class 55 45 30 5 0 Number of Two-Door Garages in a Street 10 20 30 40 ... Number of Satisfied Maple Leafs Fans 0 20 30 40 … Number of Children in a Family 1 2 3 4 …

  31. Quantitative Numerical Observations Variables … can be classified as either Discrete or Continuous Characteristics … can only assumecertain values and there are usually “gaps”between values Discrete e.g. - Number of bedrooms in a house - Number of hammers sold (1,2,3,…etc)

  32. Quantitative Numerical Observations Variables … can be classified as either Discrete or Continuous Characteristics … can assumeanyvaluewithin a specified range! Continuous e.g. - Pressure in a tire - Weight of a pork chop - Height of students in a class

  33. Quantitative Numerical Observations Qualitative Categorical Observations Summary of Types of Variables Data Discrete Continuous (number of children) (time used for an exam)

  34. Collecting Data

  35. Sources of Statistical Information Published Data Statistical Abstracts Weather Sports

  36. Sources of Statistical Information www.strategis.gc.ca www.bankofcanada.ca www.gc.ca Government of Canada & Provinces www.theweathernetwork.com Internet www.mcgrawhill.ca/college/lind

  37. Sources of Statistical Information International www.census.gov www.bls.gov/ www.un.org Organization for Economic Co-operation and Development www.oecd.org www.imf.org IMF www.worldbank.org/

  38. Sources of Statistical Information Commissioned surveys: How to collect data… To develop information for the survey that they are doing, pollsters often contact the selected ‘sample population’. For Example…At home, over the telephone, by mail, by email, in the street, and at shopping malls!

  39. Levels of Measurement

  40. Levels of Measurement Nominal Ordinal Interval Ratio

  41. M & Ms Nominal Levels of Measurement Data can only be classified into categories or counted and cannotbe arranged in any particular order Example Candy Category: By Colour only Classification: (No natural order)

  42. Nominal Levels of Measurement M & Ms Example Mutually Exclusive: …where an individual, object, or measurement is included in ONLY ONE CATEGORY Exhaustive: …where each individual, object, or measurement MUST APPEAR in one of the categories

  43. Ordinal Levels of Measurement …involves data arranged in some order, but the differencesbetween data valuescannot be determined or are meaningless! Example During a taste test of 4 soft drinks: Mello Yellowas ranked number……..…. 1. Sprite number……………………………. 2. Seven Up number..…………………..…... 3. Orange Crushnumber ….……………….4.

  44. Interval Temperature on the Celsius scale. Levels of Measurement …similar to the Ordinal Level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point Example

  45. Monthly income of surgeons Ratio Distance travelled by manufacturer’s representatives per month Levels of Measurement …the Interval Levelwithan inherent zero starting point. Differences and ratios are meaningful for this level of measurement. Examples

  46. Abuses of Statistics

  47. Benjamin Disraeli said… “There are three kinds of lies… Lies Damned Lies & Statistics!

  48. Caution Figures don’t lie. Liars figure!

  49. Caution For Example As you begin to study statistical methods, you are cautioned to take what you see published as “statistical facts”with a healthy grain of skepticism! … an average may not be representative of all the data … graphs can also be misleading … be sure to study the sampling methods

  50. Caution Review the following three slides and notice the effect that the different scales have on your interpretation of the pattern between Crime and Unemployment Rates.

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