PDB_Stat_100_Lecture_03_Printable

PDB_Stat_100_Lecture_03_Printable - STA 100 Lecture 3 Paul...

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STA 100 Lecture 3 Paul Baines Department of Statistics University of California, Davis January 7th, 2011

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Admin for the Day I Homework 1 posted, due Wednesday, Jan 12th in class I Electronic submissions are not valid: We must receive a paper copy I Handwritten or printed versions are both fine I If you complete your homework on computer (e.g., doc, pdf) then please also submit it to Smartsite via the Assignments tab I Smartsite submission not required if you handwrite your homework solutions I Detailed R and R Commander Instructions Online References for Today: Rosner, Ch 2.1-2.12 (7th Ed.)
Topics For Today 1. Exploratory Data Analysis: 2. Descriptive Statistics:

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Exploratory Summaries We have seen some graphs – lets look at other descriptive statistics.
Measures of Center Mean The ‘average’ value: ¯ x = 1 n n X i =1 x i (1) Median The middle value. Median ( x ) = x ( n +1 2 ) if n is odd 1 2 x ( n 2 ) + x ( n 2 +1 ) if n is even (2) where x ( i ) denotes the i th smallest value i.e., x (1) = min , x ( n ) = max . Mode The most common value.

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Beyond the Center The median naturally describes the center of a distribution. What other quantities might we want to describe? Definition Percentiles Definition 2.6, Rosner: Define the p th percentile by: 1. The ( k + 1) -th largest value, if np / 100 is not an integer (where k is the largest integer less than np / 100 ). 2. The average of the np / 100 -th and ( np / 100 + 1) -th largest values, if np / 100 is an integer. Example: X = (0,1,2,3,4,5,6,7,8,9,10) What is the (i) median, (ii) lower quartile, (iii) 10 th percentile? There is actually very little consesus on how to compute percentiles. In R : 9 methods. . . !
Computing Percentiles Step 1 Re-order the data in increasing order Step 2 Write down n (the number of data points) and p

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