Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9CHAPTER 2• 2.1 - Basic Definitions and Properties Population Characteristics = “Parameters” Sample Characteristics = “Statistics” Random Variables (Numerical vs. Categorical)• 2.2, 2.3 - Exploratory Data Analysis Graphical Displays Descriptive Statistics• Measures of Center (mode, median, mean) • Measures of Spread (range, variance, standard deviation)Quantitative [measurement] length mass temperature pulse rate # puppies  shoe size2POPULATION – composed of “units” (people, rocks, toasters,...)“Random Variable” X = any numerical value that can be assigned to each unit of a population“Random” refers to the notion that this value is unknown until actually observed (usually as part of an outcome of an experiment to test a specific hypothesis). [Contrast this with the idea of a “nonrandom” variable with no empirical error, e.g., X = # cards in a deck = 52.]There are two general types.........Quantitative and QualitativeImportant Fact: To make certain calculations simpler, we assume that populations are “arbitrarily large” (or indeed, infinite).10 10½ 11What do we want to know about this population?Quantitative [measurement] length mass temperature pulse rate # puppies  shoe sizeCONTINUOUS(can take their values at any point in a continuous interval)DISCRETE(only take their values in disconnected jumps)3POPULATION – composed of “units” (people, rocks, toasters,...)“Random Variable” X = any numerical value that can be assigned to each unit of a population“Random” refers to the notion that this value is unknown until actually observed (usually as part of an outcome of an experiment to test a specific hypothesis). [Contrast this with the idea of a “nonrandom” variable with no empirical error, e.g., X = # cards in a deck = 52.]There are two general types.........Quantitative and QualitativeImportant Fact: To make certain calculations simpler, we assume that populations are “arbitrarily large” (or indeed, infinite).What do we want to know about this population?Qualitative [categorical] video game levels (1, 2, 3,...) income level (1 = low, 2 = mid, 3 = high) zip code ID # color (Red, Green, Blue)ORDINAL,RANKED1 2 3IMPORTANT CASE: Binary (or Dichotomous)• Gender (Male / Female)• “Pregnant?” (Yes / No)• Coin toss (Heads / Tails)• Treatment (Drug / Placebo) 1, “Success” 0, “Failure”X =4NOMINALPOPULATION – composed of “units” (people, rocks, toasters,...)“Random Variable” X = any numerical value that can be assigned to each unit of a population“Random” refers to the notion that this value is unknown until actually observed (usually as part of an outcome of an experiment to test a specific hypothesis). [Contrast this with the idea of a “nonrandom” variable with no empirical error, e.g., X = # cards in a deck = 52.]There are two general types.........Quantitative and QualitativeImportant Fact: To make certain calculations simpler, we assume that populations are “arbitrarily large” (or indeed, infinite).What do we want to know about this population?Qualitative [categorical] video game levels (1, 2, 3,...) income level (1 = low, 2 = mid, 3 = high) zip code ID # color (Red, Green, Blue)ORDINAL,RANKED1 2 3IMPORTANT CASE: Binary (or Dichotomous)• Gender (Male / Female)• “Pregnant?” (Yes / No)• Coin toss (Heads / Tails)• Treatment (Drug / Placebo) 1, “Success” 0, “Failure”X =5NOMINALPOPULATION – composed of “units” (people, rocks, toasters,...)“Random Variable” X = any numerical value that can be assigned to each unit of a population“Random” refers to the notion that this value is unknown until actually observed (usually as part of an outcome of an experiment to test a specific hypothesis). [Contrast this with the idea of a “nonrandom” variable with no empirical error, e.g., X = # cards in a deck = 52.]There are two general types.........Quantitative and QualitativeImportant Fact: To make certain calculations simpler, we assume that populations are “arbitrarily large” (or indeed, infinite).Another way… define X using “indicator variables”:�����1GreeBluRed1,= 0,0n, eI�����2GreeBluRed0,= 1,0n, eI�����3GreeBluRed0,= 0,1n, eIWhat do we want to know about this population?Note thatI1 + I2 + I3 = 1Example: Excel file of patient blood types Note that each patient row sums to 1, i.e.,O + A + B + AB = 1.Note that each patient row sums to 1, i.e.,O + A + B + AB = 1.X“Population Distribution of X”(somewhat idealized)“Population Distribution of X”(somewhat idealized)X  POPULATION – composed of “units” (people, rocks, toasters,...)Important Fact: To make certain calculations simpler, we assume that populations are “arbitrarily large” (or indeed, infinite).“Random Variable” X = any numerical value that can be assigned to each unit of a population“Random” refers to the notion that this value is unknown until actually observed (usually as part of an outcome of an experiment to test a specific hypothesis). [Contrast this with the idea of a “nonrandom” variable with no empirical error, e.g., X = # cards in a deck = 52.]There are two general types.........Quantitative and QualitativePopulation mean6Population “standard deviation” (“mu”) and  (“sigma”) are examples of parameters – nonrandom “population characteristics” whose exact values cannot be directly measured, but can (hopefully) be estimated from known “sample characteristics” – statistics. (“mu”) and  (“sigma”) are examples of parameters – nonrandom “population characteristics” whose exact values cannot be directly measured, but can (hopefully) be estimated from known “sample characteristics” – statistics.POPULATION – composed of “units” (people, rocks, toasters,...)= value of X for 1st individual 7x1= value of X for 2nd individual x2x3 x4 x5 x6 …etc….xn SAMPLE of size nHow do we infer information about the