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What is Statistics? Chapter 1

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

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1 1 - 3 Chapter Goals 5. Distinguish between a discrete variable and a continuous variable. 6. Collect data from published and unpublished sources. 7. Distinguish among the nominal, ordinal, interval, and ratio levels of measurement. 8. Identify abuses of statistics. and...

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1 1 - 4 Chapter Goals 9. 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!

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**Statistics? What is Meant by collecting organizing presenting data**

…it is the art and science of… collecting organizing presenting data drawing inferences from a sample of information about an entire population as well as predicting and developing policy analysis What is Meant by Statistics?

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Role played by Statistics in everyday life

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**Who uses Statistics? Those using Statistical techniques include :**

Marketers Investors Accountants Economists Sports people Consumers Statisticians Hospitals Quality Controllers Educators Politicians Physicians

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Who uses Statistics? Weather Forecasters

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Who uses Statistics? Sports

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Types of Statistics

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**Methods of… collecting organizing presenting**

Types of Statistics Descriptive Inferential Methods of… collecting organizing presenting and analyzing data Science of… making inferences about a population, based on sample information.

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**Identify the following…**

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. 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. Descriptive Inferential

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**The Method of Experimentation**

We start off with particular observations from the real world and draw conclusions about the general patterns in the real world! 1. Define the 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

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**Real World Real World The Method of Experimentation Deductive Method**

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

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**Let’s review the steps they would take to prepare the estimate.**

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.

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What Information do we need? the POPULATION

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**A population is a collection of all possible individuals, objects, or measurements of interest**

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**POPULATION Say, 101 Sample POPULATION**

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

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**Raw Data 101 Sample Take a Measurement for each one in the sample**

Record

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**readable and understandable**

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

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**Two methods that can be used to ‘see’ **

what the data conveys are Tables and Graphs/Charts More on these in chapter 2…

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**Tables e.g. 101 … are an efficient method of displaying data**

and depicting data accurately. e.g. 101 More on these in chapter 2…

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**Bar Pie Line Scatter Histogram Charts Graphs**

More on these in chapter 2…

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**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 More in chapter 8 …

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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.

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Types of Data

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**a characteristic of a population or sample**

Types of Data A Variable a characteristic of a population or sample that is of interest to us

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**Types of Data Variables**

Qualitative Quantitative Categorical Observations Numerical Observations

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**Variables Qualitative – or Attribute Female Country of Birth U.K.**

Germany Taiwan China India Japan Russia Eye Colour Blue Brown Hazel Green Red GenderMale Female

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**Variables Quantitative – Numeric Minutes to end of Class**

55 45 30 5 Number of Two-Door Garages in a Street 10 20 30 40 ... Number of Satisfied Maple Leafs Fans 20 30 40 … Number of Children in a Family 1 2 3 4 …

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**… can be classified as either**

Variables Quantitative Numerical Observations … can be classified as either Discrete or Continuous Characteristics … can only assume certain 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)

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**Variables Continuous Quantitative … can be classified as either**

Numerical Observations … can be classified as either Discrete or Continuous Characteristics … can assume any value within a specified range! Continuous e.g. - Pressure in a tire - Weight of a pork chop - Height of students in a class

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**Summary of Types of Variables**

Data Qualitative Categorical Observations Quantitative Numerical Observations Discrete Continuous (number of children) (time used for an exam)

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Collecting Data

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**Sources of Statistical Information**

Published Data Statistical Abstracts Weather Sports

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**Sources of Statistical Information**

Government of Canada & Provinces Internet

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**Sources of Statistical Information**

International Organization for Economic Co-operation and Development IMF

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**Sources of Statistical Information**

Commissioned surveys: 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 , in the street, and at shopping malls! How to collect data…

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Levels of Measurement

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Nominal Levels of Measurement Ordinal Interval Ratio

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**Candy By Colour only Levels of Measurement M & Ms Nominal**

Data can only be classified into categories or counted and cannot be arranged in any particular order M & Ms Example Category: Candy By Colour only Classification: (No natural order)

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**Levels of Measurement M & Ms Nominal Mutually Exclusive:**

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

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**During a taste test of 4 soft drinks:**

Levels of Measurement Ordinal …involves data arranged in some order, but the differences between data values cannot be determined or are meaningless! Example During a taste test of 4 soft drinks: Mello Yello was ranked number……..…. 1. Sprite number……………………………. 2. Seven Up number..…………………..…... 3. Orange Crush number ….……………….4.

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**Levels of Measurement Interval There is no natural zero point**

…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 Temperature on the Celsius scale.

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**Distance travelled by manufacturer’s representatives per month**

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

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Abuses of Statistics

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**“There are three kinds of lies…**

Benjamin Disraeli said… “There are three kinds of lies… Lies Damned Lies & Objects: Stats_2ProbSample-B.ppt (Probability) Action Button: Stat Samples_B.ppt (Penguins) for Probability pen-heights_2Rev.xls (for Penguins) Statistics!

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Figures don’t lie. Liars figure! Caution

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**… graphs can also be misleading**

Caution 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 For Example

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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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**Unemployment Crime Rate &**

Chart 1-11A 3200 3000 2800 2600 2400 2200 2000 (in thousands) Crime Rate Unemployment Rate (%)

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**Unemployment Crime Rate &**

Chart 1-11B 3000 2500 2000 1500 1000 500 3000 2500 2000 (in thousands) Crime Rate 1500 1000 500 Unemployment Rate (%)

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**Unemployment Crime Rate &**

Chart 1-11C 3200 3000 2800 2600 2400 2200 2000 (in thousands) Crime Rate Unemployment Rate (%)

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**Test your learning… Click on… www.mcgrawhill.ca/college/lind**

Online Learning Centre for quizzes extra content data sets searchable glossary access to Statistics Canada’s E-Stat data …and much more!

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**This completes Chapter 1.**

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ROBERT MORRIS UNIVERSITY

ROBERT MORRIS UNIVERSITY

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