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Math 145 September 11, 2006 Recap Individuals – are the objects described by a set of data. Individuals may be people, but they may also be animals or things. Variable – a characteristic of an individual. A variable can take different values for different individuals. Categorical variable – places an individual into one of several groups or categories. {Gender, Blood Type} Quantitative variable – takes numerical values for which arithmetic operations such as adding and averaging make sense. {Height, Income, Time, etc.} Quantitative Variables Discrete Variables – There is a gap between possible values. Counts (no. of days, no. of people, etc.) Age in years Continuous Variables – Variables that can take on values in an interval. Survival time, amount of rain in a month, distance, etc. Distribution - The distribution of a variable tells us what values it takes and how often it takes these values Categorical Data Table or Bar Chart Quantitative Data Frequency Table Histogram Stem-and-leaf plot Length of Stay 5 1 15 9 3 7 2 12 4 18 9 13 28 24 13 1 6 10 5 6 9 Describing a distribution Skewness Center/Spread No of peaks (modes) Symmetric Skewed to the right Skewed to the left Unimodal, Bimodal, Multimodal Outliers Consider # 1.15, 1.17, 1.18 on page 29. Graphical Procedures Categorical Data Quantitative Data Bar Chart Pie Chart Histogram Stem-and-leaf plot (stemplot) Time Plot (Time Series Data) A time plot of a variable plots each observation against the time at which it was measured. Consider example 1.11 on page 22. Homework Exercises: Sec 1: 1.1, 1.2, 1.3, 1.9, 1.11, 1.17, 1.19, 1.20 Section 1.2 Measures of Center Mean (Average) {2.5, 3.2, 3.2, 3.4, 3.6, 3.7, 3.9, 3.9, 4, 4.2, 4.2} Median Measures of Spread Range Standard Deviation Five-number summary Consider example 1.11 on page 22. Homework Exercises: Sec 1: 1.1, 1.2, 1.3, 1.9, 1.11, 1.17, 1.19, 1.20 Sec 2: 1.42, 1.45, 1.47, 1.55-1.57*, 1.60, 1.62 Sec3: 1.78, 1.80, 1.81, 1.82, 1.83, 1.85*, 1.87, 1.89, 1.90*, 1.93-95, 1.97, 1.110, 1.115 Thank you!