What Are We Summarizing?Slide 2Slide 3Qualitative VariablesSummarizing Qualitative VariablesQuantitative VariablesSummarizing Quantitative VariablesCautionSlide 9Slide 10Slide 11Slide 12Continuous VariablesDiscrete VariablesDiscrete vs. ContinuousSlide 16What Are We Summarizing?Lecture 13Sections 4.1 – 4.2Mon, Feb 4, 2008What Are We Summarizing?How can we summarize data taken from a sample?We want to reduce the data down to a single number (a statistic).What Are We Summarizing?How best to summarize…Political affiliation?Body weight?Steak preference (rare, medium, etc.)?Number of children?Temperature throughout the day?What is the difference?Qualitative VariablesQualitative variable.The values of a qualitative variable may or may not have a natural order.Examples: Political affiliation.Steak preference.Summarizing Qualitative VariablesTypically, we use percentages or proportions to summarize qualitative variables.40% of the subjects are Democrats.50% of the people prefer their steak medium.Quantitative VariablesQuantitative variable.The values of a quantitative variable always have a natural order.Examples:A person’s weight.Number of children.Temperature.Summarizing Quantitative VariablesTypically, we use averages to summarize quantitative variables.The people in the sample weigh an average of 156.2 lbs.The people in the sample have an average of 2.3 children.The average temperature for the day was 82.7 degrees F.CautionSome qualitative variables may appear to be quantitative.Rate your own level of sexual desire:(1) Way below average(2) Below average(3) Average(4) Above average(5) Way above averageCautionIf a person selects #3, does that mean that his sexual desire is average?CautionIf two people select #3, does that mean that they have the same level of sexual desire?CautionIf one person selects #2 and another person selects #4, does that mean that the second person has twice the sexual desire as the first person?Quantitative VariablesA quantitative variable may be continuous or discrete.Continuous VariablesContinuous variable.Typically these are measured quantities: length, time, area, weight, etc.Discrete VariablesDiscrete variable.Typically these are count dataA verbal description usually contains the phrase “the number of.”Discrete vs. ContinuousSome data may mistakenly be thought to be discrete.TimeWeightClearly, all measurements must be rounded off. But that does not make the quantity itself discrete.Discrete vs. ContinuousWhat about heart rate, measured in beats per minute?It is the basic nature of the quantity that matters, not how we choose to record our
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