What Are We Summarizing Lecture 13 Sections 4 1 4 2 Mon Feb 4 2008 What 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 Variables Qualitative variable The values of a qualitative variable may or may not have a natural order Examples Political affiliation Steak preference Summarizing Qualitative Variables Typically we use percentages or proportions to summarize qualitative variables 40 of the subjects are Democrats 50 of the people prefer their steak medium Quantitative Variables Quantitative variable The values of a quantitative variable always have a natural order Examples A person s weight Number of children Temperature Summarizing Quantitative Variables Typically 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 Caution Some 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 average Caution If a person selects 3 does that mean that his sexual desire is average Caution If two people select 3 does that mean that they have the same level of sexual desire Caution If 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 Variables A quantitative variable may be continuous or discrete Continuous Variables Continuous variable Typically these are measured quantities length time area weight etc Discrete Variables Discrete variable Typically these are count data A verbal description usually contains the phrase the number of Discrete vs Continuous Some data may mistakenly be thought to be discrete Time Weight Clearly all measurements must be rounded off But that does not make the quantity itself discrete Discrete vs Continuous What 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 observations
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