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1 1-1 Overview 1- 2 Types of Data 1- 3 Abuses of Statistics 1- 4Design of Experiments Chapter 1 Introduction to Statistics

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2 Statistics (Definition) A collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data 1-1 Overview

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3 Definitions Population The complete collection of all data to be studied. Sample The subcollection data drawn from the population.

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4 Example Identify the population and sample in the study A quality-control manager randomly selects 50 bottles of Coca-Cola to assess the calibration of the filing machine.

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5 Statistics Broken into 2 areas Descriptive Statistics Inferencial Statistics Definitions

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6 Descriptive Statistics Describes data usually through the use of graphs, charts and pictures. Simple calculations like mean, range, mode, etc., may also be used. Inferencial Statistics Uses sample data to make inferences (draw conclusions) about an entire population Test Question

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7 Parameter vs. Statistic Quantitative Data vs. Qualitative Data Discrete Data vs. Continuous Data 1-2 Types of Data

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8 Parameter a numerical measurement describing some characteristic of a population population parameter Definitions

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9 Statistic a numerical measurement describing some characteristic of a sample sample statistic Definitions

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10 Examples Parameter 51% of the entire population of the US is Female Statistic Based on a sample from the US population is was determined that 35% consider themselves overweight.

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11 Definitions Quantitative data Numbers representing counts or measurements Qualitative (or categorical or attribute) data Can be separated into different categories that are distinguished by some nonnumeric characteristics

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12 Examples Quantitative data The number of FLC students with blue eyes Qualitative (or categorical or attribute) data The eye color of FLC students

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13 We further describe quantitative data by distinguishing between discrete and continuous data Definitions Quantitative Data Discrete Continuous

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14 Discrete data result when the number of possible values is either a finite number or a ‘countable’ number of possible values 0, 1, 2, 3,... Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale or interval that covers a range of values without gaps, interruptions, or jumps Definitions 2 3

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15 Discrete The number of eggs that hens lay; for example, 3 eggs a day. Continuous The amounts of milk that cows produce; for example, 2.343115 gallons a day. Examples

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16 Univariate Data »Involves the use of one variable (X) »Does not deal with causes and relationship Bivariate Data »Involves the use of two variables (X and Y) »Deals with causes and relationships Definitions

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17 Univariate Data How many first year students attend FLC? Bivariate Data Is there a relationship between then number of females in Computer Programming and their scores in Mathematics? Example

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18 1. Center: A representative or average value that indicates where the middle of the data set is located 2. Variation: A measure of the amount that the values vary among themselves or how data is dispersed 3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed) 4. Outliers: Sample values that lie very far away from the vast majority of other sample values 5. Time: Changing characteristics of the data over time Important Characteristics of Data

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19 Uses of Statistics Almost all fields of study benefit from the application of statistical methods Sociology, Genetics, Insurance, Biology, Polling, Retirement Planning, automobile fatality rates, and many more too numerous to mention.

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20 Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions 1-3 Abuses of Statistics

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21 Abuses of Statistics Bad Samples Inappropriate methods to collect data. BIAS (on test) Example: using phone books to sample data. Small Samples (will have example on exam) We will talk about same size later in the course. Even large samples can be bad samples. Loaded Questions Survey questions can be worked to elicit a desired response

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22 Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions Abuses of Statistics

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23 Bachelor High School Degree Diploma Salaries of People with Bachelor’s Degrees and with High School Diplomas $40,000 30,000 25,000 20,000 $40,500 $24,400 35,000 $40,000 20,000 10,000 0 $40,500 $24,400 30,000 Bachelor High School Degree Diploma (a)(b) (test question)

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24 We should analyze the numerical information given in the graph instead of being mislead by its general shape.

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25 Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions Abuses of Statistics

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26 Double the length, width, and height of a cube, and the volume increases by a factor of eight What is actually intended here? 2 times or 8 times?

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27 Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions Abuses of Statistics

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28 Precise Numbers There are 103,215,027 households in the US. This is actually an estimate and it would be best to say there are about 103 million households. Distorted Percentages 100% improvement doesn’t mean perfect. Deliberate Distortions Lies, Lies, all Lies Abuses of Statistics

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29 Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions Abuses of Statistics

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30 Abuses of Statistics Partial Pictures “Ninety percent of all our cars sold in this country in the last 10 years are still on the road.” Problem: What if the 90% were sold in the last 3 years?

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31 1-4 Design of Experiments

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32 Experiment apply some treatment (Action) Event observe its effects on the subject(s) (Observe) Example: Experiment: Toss a coin Event: Observe a tail Definition

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33 Designing an Experiment Identify your objective Collect sample data Use a random procedure that avoids bias Analyze the data and form conclusions

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34 Random (type discussed in this class) Systematic Convenience Stratified Cluster Methods of Sampling

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35 Random Sample members of the population are selected in such a way that each has an equal chance of being selected (if not then sample is biased) Simple Random Sample (of size n ) subjects selected in such a way that every possible sample of size n has the same chance of being chosen Definitions

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36 Random Sampling - selection so that each has an equal chance of being selected

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37 Systematic Sampling Select some starting point and then select every K th element in the population

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38 Convenience Sampling use results that are easy to get

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39 Stratified Sampling subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)

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40 Cluster Sampling - divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters

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41 Sampling Error the difference between a sample result and the true population result; such an error results from chance sample fluctuations. Nonsampling Error sample data that are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly). Definitions

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42 Factorial Notation 8! = 8x7x6x5x4x3x2x1 Order of Operations 1.( ) 2.POWERS 3.MULT. & DIV. 4.ADD & SUBT. 5.READ LIKE A BOOK Keep number in calculator as long a possible Using Formulas

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