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## Math 145

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**Math 145**January 24, 2007**Descriptive Statistics**• 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. • Qualitative (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.} • Consider: #1.18 (p. 20), #1.21 (p.21)**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.**Graphical Procedures**• Categorical Data • Bar Chart • Pie Chart • Quantitative Data • Histogram • Stem-and-leaf plot (stemplot) • Dotplot • These plots describe the Distribution of a variable.**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**Describing a distribution**• Skewness • Symmetric • Skewed to the right (positively skewed) • Skewed to the left (negatively skewed) • Center/Spread • No of peaks (modes) • Unimodal, Bimodal, Multimodal. • Outliers • Extreme values.**Homework**Exercises: Chapter 1 : (pp. 19-23) #1, 2, 5, 11, 12, 16, 24, 28 Chapter 2: (pp. 36-40) #5, 6, 10. (pp. 50-53) #25, 30, 32.