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AP Statistics Tuesday, 26 August 2014 OBJECTIVE TSW learn (1) the reasons for studying statistics, and (2) vocabulary. FORM DUE (only if it is signed) –Information Sheet (wire basket) I will take batteries and battery money at the beginning of class. The Student Will

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Due Dates for Assignments News Article Tomorrow, Friday, 29 August 2014 Sec. 1.3 Tomorrow, Friday, 29 August 2014 Sec. 1.4 Tuesday, 02 September 2014

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Survey Fill out the survey (anonymously). Turn it in to the black tray when you finish.

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Chapter 1 The Role of Statistics

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Chapter 1: The Role of Statistics Sec. 1.1: Three Reasons to Study Statistics

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Three Reasons to Study Statistics 1.Become an informed “Information Consumer” Extract information from charts and graphs Follow numerical arguments Know the basics of how data should be gathered, summarized and analyzed to draw statistical conclusions

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Three Reasons to Study Statistics 2.Understand and Make Decisions Decide if existing information is adequate Collect more information in an appropriate way Summarize the available data effectively Analyze the available data Draw conclusions, make decisions, and assess the risks of an incorrect decision

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Three Reasons to Study Statistics 3.Evaluate Decisions That Affect Your Life Help understand the validity and appropriateness of processes and decisions that effect your life

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Chapter 1: The Role of Statistics Sec. 1.2: The Nature and Role of Variability

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What is Statistics? Statistics is the science of Collecting data Analyzing data Drawing conclusions from data

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Major Branches of Statistics 1.Descriptive Statistics Organizing, Summarizing Information Graphical techniques Numerical techniques 2.Inferential Statistics Estimation Decision making

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Descriptive statistics The methods of organizing and summarizing data

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Inferential Statistics Involves making generalizations from a sample to a population

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Important Terms 1. Population – The entire collection of individuals or objects about which information is desired is called the population.

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A census is a collection of data from every member of the population, allows a question about the population to be definitively answered. may be expensive, impractical, or sometimes impossible. Important Terms

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2. Sample – A sample is a subset of the population, selected for study in some prescribed manner. Using sample data rather than population data is more practical than a census. Gives variable results with some possibility of a wrong conclusion being adopted. Important Terms

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Discussion on Important Terms Generally it not reasonable, feasible or even possible to survey a population so that descriptions and decisions about the population are made based on using a sample. The study of statistics deals with understanding how to obtain samples and work with the sample data to make statistically justified decisions.

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3. Variable – A variable is any characteristic whose value may change from one individual to another Examples: Brand of television Height of a building Number of students in a class Important Terms

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4. Data results from making observations either on a single variable or simultaneously on two or more variables. 5. A univariate data set consists of observations on a single variable made on individuals in a sample or population Important Terms

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Univariate - data that describes a single characteristic of the population Important Terms

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6. A bivariate data set consists of observations on two variables made on individuals in a sample or population. 7. A multivariate data set consists of observations on two or more variables made on individuals in a sample or population. Important Terms

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Bivariate - data that describes two characteristics of the population Multivariate - data that describes more than two characteristics (beyond the scope of this course) Important Terms

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Classify as categorical or numerical gender age hair color smoker systolic blood pressure number of girls in class categorical numerical categorical numerical

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Data Sets A univariate data set is categorical (or qualitative) if the individual observations are categorical responses. A univariate data set is numerical (or quantitative) if the individual observations are numerical responses where numerical operations generally have meaning.

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Categorical Variables or qualitative identifies basic differentiating characteristics of the population

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Examples of Categorical Data The brand of TV owned by the six people that work in a small office RCA Magnavox Zenith Phillips GERCA …

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The hometowns of the 6 students in the first row of seats Mendon Victor Bloomfield Victor Pittsford Bloomfield Examples of Categorical Data

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The zipcodes* (of the hometowns) of the 6 students in the first row of seats. *Since numerical operations with zipcodes make no sense, the zipcodes are categorical rather than numeric.

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Numerical Variables or quantitative observations or measurements take on numerical values makes sense to average these values

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Types of Numerical Data Numerical data is discrete if the possible values are isolated points on the number line. Numerical data is continuous if the set of possible values form an entire interval on the number line.

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Discrete (numerical) listable set of values usually counts of items

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Types of Discrete Data The number of costumers served at a diner lunch counter over a one-hour time period is observed for a sample of seven different one-hour time periods 13 22 31 18 41 27 32 The number of textbooks bought by students at a given school during a semester for a sample of 16 students 5 3 6 8 6 1 3 6 12 3 5 7 6 7 5 4

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Continuous (numerical) data can take on any values in the domain of the variable usually measurements of something

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Types of Continuous Data The height of students that are taking a Data Analysis course at a local university is studied by measuring the heights of a sample of 10 students. 72.1” 64.3” 68.2” 74.1” 66.3” 61.2” 68.3” 71.1” 65.9” 70.8” Note: Even though the heights are only measured accurately to 1 tenth of an inch, the actual height could be any value in some reasonable interval.

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The crushing strength of a sample of four jacks used to support trailers. 7834 lb 8248 lb 9817 lb 8141 lb Gasoline mileage (miles per gallon) for a brand of car is measured by observing how far each of a sample of seven cars of this brand of car travels on ten gallons of gasoline. 23.1 26.4 29.8 25.0 25.9 22.6 24.3 Types of Continuous Data

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Frequency Distributions A frequency distribution for categorical data is a table that displays the possible categories along with the associated frequencies or relative frequencies. The frequency for a particular category is the number of times the category appears in the data set.

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The relative frequency for a particular category is the fraction or proportion of the time that the category appears in the data set. It is calculated as Frequency Distributions

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When the table includes relative frequencies, it is sometimes referred to as a relative frequency distribution Frequency Distributions

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Classroom Data Example This slide along with the one that follows contains a data set obtained from a large section of students taking Data Analysis in the Winter of 1993 and will be utilized throughout in the examples.

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Frequency Distribution Example The data in the column labeled vision is the answer to the question, “What is your principle means of correcting your vision?” The results are tabulated below

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Bar Chart Procedure 1.Draw a horizontal line, and write the category names or labels below the line at regularly spaced intervals. 2.Draw a vertical line, and label the scale using either frequency (or relative frequency). Continued on next slide

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3. Place a rectangular bar above each category label. The height is the frequency (or relative frequency) and all bars have the same width Bar Chart Procedure

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Bar chart – Example (frequency)

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Bar chart – (Relative frequency)

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Another example

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Dotplots - Procedure 1.Draw a horizontal line and mark it with an appropriate measurement scale. 2.Locate each value in the data set along the measurement scale, and represent it by a dot. If there are two or more observations with the same value, stack the dots vertically

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Dotplots - Example Using the weights of the 79 students

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Dotplots – Example To compare the weights of the males and females we put the dotplots on top of each other, using the same scales.

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The Nature and Role of Variability Scenario #1 Suppose every student in this class had the exact same schedule, ate a ham sandwich and coke for lunch every day, and wanted to go to the One Direction concert. How many students would a researcher have to interview to draw conclusions about what students eat for lunch? Why?

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The Nature and Role of Variability This is an unrealistic situation. In actuality, variability is almost universal. We need to understand variability to be able to collect, analyze, and draw conclusions from data in a sensible way.

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The Nature and Role of Variability Scenario #2 The basketball team and the gymnastics team are practicing in 2 different locations. A tall woman (5 ft 11 in.) tells you she is looking for her sister. 1.Where would you send her? 2.What reasoning would you use to decide?

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The Nature and Role of Variability Scenario #2 The basketball team and the gymnastics team are practicing in 2 different locations. You find a pair of size 6 tennis shoes and you want to return them. 1.Would you first check with the basketball team or the gymnastics team? 2.Why?

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The Nature and Role of Variability Scenario #3 Over a 200-day period, five samples of water are drawn from a particular well each day, and the concentration of contaminants (ppm) is measured. The samples each day are averaged and recorded. On day 201, a chemical spill occurs at a factory plant 1 mile away. One month after the spill, one day’s sample reads 16 ppm. 1.Is this convincing evidence that water was affected by the chemical spill? 2.What if the sample was 18 ppm? 22 ppm? 3.What is your reasoning?

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The Nature and Role of Variability These scenarios show that you have to understand variability to reach a conclusion. Recognizing unusual values in the presence of variability is the essence of statistical procedures, and it allows you to quantify the chance of being incorrect when a conclusion is based on sample data.

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Due Dates for Assignments News Article Tomorrow, Friday, 29 August 2014 Sec. 1.3 Tomorrow, Friday, 29 August 2014 Sec. 1.4 Tuesday, 02 September 2014

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The Nature and Role of Variability Assignment (You may type or hand-write this, but your answers must be complete sentences.) 1.Look in the newspaper (you may have to go on-line if you do not get a newspaper) for an article that uses statistics to reach a conclusion. 2.In your own words, describe the situation and conclusion. 3.Based on the information in the article, is the conclusion reasonable? Why or why not? 4.Attach the newspaper article to your sheet. 5. This is due on Friday, 29 August 2014.

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