# lec8 - STATISTICS 13 STATISTICS Lecture 8 Oct. 11, 2010...

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STATISTICS 13 STATISTICS 13 STATISTICS 13 Lecture 8 Lecture 8 Oct. 11, 2010 Oct. 11, 2010

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Review Tchebysheff’s Theorem Measures of Relative Standing –Z-scores Pecentiles: Q1,m,Q2 •I QR
Five-number Summary Arrange the measurements in an increasing order Divide into four equal parts compute Q 1 , Q 2 (median), Q 3 Example (service year): (8, 17.5, 26.5, 31.75, 42) Gives a quick summary of the data distribution Measure of location (median) Measure of spread (IQR = Q 3 –Q 1 ) Can be used to draw a box plot (another graphical tool!) The Five-Number Summary : Min Q1 Median Q3 Max The Five-Number Summary : Min Q1 Median Q3 Max

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Constructing Box Plot Compute Q1,Q2 ( = m),Q 3 and the IQR Draw a horizontal line to represent the scale of measurements Represent the three quartiles as short vertical lines along the horizontal scale Join the end points horizontally to create a box Q 1 Q 3 m
Constructing Box Plot (cont.) Build fences Lower fence = Q 1 –1 .5±x±IQR Upper fence = Q 3 + 1.5 x IQR Measurements outside the fences are considered outliers and marked as ( * ) Q 1 m Q 3 * Lower fence Upper fence Outlier

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Constructing Box Plot (cont.) Draw “whiskers” connecting the fences to the minimum and the maximum among the measurements that are not outliers Q 1 m Q 3 * Min (among non-outliers) Max (among non-outliers) fence -- -fence -outlier
Example 1: Service Year years of service 40 35 30 25 20 15 10 Boxplot of years of service

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Example 2: Box Office Revenue 20000 15000 10000 5000 0 Boxplot of Revenue
Interpreting Box Plot Symmetric : median line in the center of box

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## This note was uploaded on 11/18/2010 for the course STA 13 taught by Professor Samaniego during the Spring '10 term at UC Davis.

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lec8 - STATISTICS 13 STATISTICS Lecture 8 Oct. 11, 2010...

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