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Chapter 2 Describing, Exploring, and Comparing Data Section 2.1 - Overview Terms: Center Variation Distribution Outliers Time Section 2.2 – Frequency Distributions Terms: Frequency Frequency Distribution (lower and upper class limits, class boundaries, class midpoints, class width) Relative Frequency Relative Frequency Distribution Cumulative Frequency Cumulative Frequency Distribution Cumulative Relative Frequency Open-Ended Intervals Section 2.3 – Visualizing Data Read this section on your own. Section 2.4 – Measures of Center Notation: n x N x n x 22 23.8 N Terms: Mean (arithmetic mean) Median Mode Bimodal Multimodal Midrange Weighted Mean Skewed Skewed to the left Skewed to the right Symmetric Example – Exercise #3 17.7 19.6 19.6 20.6 21.4 24 25.2 27.5 28.9 29.1 29.9 33.5 37.7 40 42 Example – Exercise #5 14 16 17 18 20 21 23 24 25 27 28 30 31 34 37 38 Section 2.5 – Measures of Variation Notation: s s2 σ σ2 Terms: Range Standard Deviation of a Sample Standard Deviation of a Population Sample Variance Population Variance Coefficient of Variation Mean Absolute Deviation (MAD) Empirical Rule For data sets having a distribution that is approximately bell-shaped, the following properties apply About ______ of all values fall within _____ standard deviation(s) of the mean About ______ of all values fall within _____ standard deviation(s) of the mean About ______ of all values fall within _____ standard deviation(s) of the mean Chebyshev’s Theorem The proportion (or fraction) of any set of data lying within K standard deviations of the mean 1 is always at least 1 2 , where K is any positive number greater than 1. K If K = 2, then at least _____ of all values fall within 2 standard deviations of the mean. If K = 3, then at least _____ of all values fall within 3 standard deviations of the mean. Section 2.6 – Measures of Relative Standing Terms: Standard Score (z Score) Sample z xx s Quartiles Percentiles Interquartile Range (IQR) Semi-interquartile Range Midquartile Population z x