class_09_03 - Statistical Data Mining ORIE 474 Fall 2007...

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Statistical Data Mining ORIE 474 Fall 2007 Tatiyana V. Apanasovich 09/03/07 Visualizing Data
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3. Visualizing and Exploring Data Summarizing Data Tools for Displaying Single variables Relationships between two variables More than two variables Principal Component Analysis
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3.2 Summarizing Data Suppose that x(1),…,x(n) is a set of n data values Relevant sample statistics are: Location measures: Mean Median and Quartiles Mode Dispersion or variability measures: Standard deviation and variance Interquartile range and range Skewness
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3.2 Summarizing Data (cont’d) Ex: 100 data points sampled from a normal distribution with mean 0 and std. dev. 10
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Sample Mean Sample Mean: Ex: (whereas µ=0) Location measure Sample mean is the value that is “central” in the sense that it minimizes the sum of squared differences between it and the data: Proof: = i i x n ) ( 1 ˆ μ 36 . 1 ˆ = μ ( 29 ( 29 = = - = - = - i i i i i x n a na i x a i x da a i x d ) ( 1 0 ) ( ) ( 2 ) ( 2 ( 29 2 ) ( min ˆ - = i a a i x μ
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Sample Median and Mode Sample median = value that has an equal number of data points above or below it If, as in our example, n is even, it is usually defined as the halfway between the 2 middle values Ex: (whereas m=0)
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