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Recap of Individuals, Variables, and Distributions in Math

This recap covers the concepts of individuals, variables, categorical and quantitative variables, distributions, skewness, measures of center and spread, graphical procedures, and measures of dispersion. Homework exercises are also provided.

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Recap of Individuals, Variables, and Distributions in Math

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  1. Math 341 January 24, 2007

  2. 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.}

  3. 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.

  4. 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

  5. Length of Stay

  6. Fifth-grade IQ Scores

  7. 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.

  8. Graphical Procedures • Categorical Data • Bar Chart • Pie Chart • Quantitative Data • 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 1.7 on page 14.

  9. Section 1.3 • 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} - sensitive to outliers. • Median – middle value • Mode – most frequent occurring value.

  10. Homework Exercises: Sec 1: 4, 7, 8, 9. (pp. 10-11) Sec 2: 10, 11, 15, 18, 20, 25*, 29. (pp.23-28) Sec 3: 34, 36, 41, 42. (pp.34-36)

  11. Section 1.4 • Consider 3 samples • {1,2,5,5,8,9} • {3,4,5,5,6,7} • {5,5,5,5,5,5} • Measures of Dispersion (Spread) • Range • Variance • Standard Deviation • Five-number summary

  12. Thank you!

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