L03_220.pdf - Percentiles STATA Box Plots Standardizing and Other Transformations Lecture 3 Reading Sections 5.7 5.14 Remember when you finish a chapter

L03_220.pdf - Percentiles STATA Box Plots Standardizing and...

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ECO220Y1Y, Lecture 3, Page 1 of 9 Percentiles, STATA, Box Plots, Standardizing, and Other Transformations Reading: Sections 5.7 – 5.14 1 Lecture 3 Remember, when you finish a chapter make sure not to miss the last couple of boxes: “What Can Go Wrong?” and “Ethics in Action” .0 23 .48 28 .3506 .0747 .0345 .0115 .00 57 .005 7 .0057 .0 057 0 .1 .2 .3 .4 .5 .6 Fraction 0 20 40 60 Inflation Rate, 2011 n = 174 countries, bin width = 5 Measures of Relative Standing: Percentiles 2 What is approx. median (50 th percentile)? 2.30 th percentile? 85.64 th percentile? World bank data, again 3 Reading STATA Output . su inflation_2011, detail inflation_2011 ------------------------------------------------------------- Percentiles Smallest 1% -2.517798 -4.895247 5% .9223603 -2.517798 10% 2.075173 -.3644478 Obs 174 25% 3.329906 -.2833333 Sum of Wgt. 174 50% 4.977675 Mean 6.646499 Largest Std. Dev. 6.77998 75% 8.253968 26.09021 90% 12.43155 33.22422 Variance 45.96813 95% 17.71178 47.27686 Skewness 3.773002 99% 47.27686 53.2287 Kurtosis 22.85972 Median? Sample size? Range?
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ECO220Y1Y, Lecture 3, Page 2 of 9 4 Trips Freq. Percent Cum. Trips Freq. Percent Cum. 0 294 35.85 35.85 19 1 0.12 95.85 1 76 9.27 45.12 20 3 0.37 96.22 2 66 8.05 53.17 21 2 0.24 96.46 3 58 7.07 60.24 22 4 0.49 96.95 4 47 5.73 65.98 23 1 0.12 97.07 5 47 5.73 71.71 24 4 0.49 97.56 6 36 4.39 76.10 25 2 0.24 97.80 7 30 3.66 79.76 26 4 0.49 98.29 8 28 3.41 83.17 27 2 0.24 98.54 9 15 1.83 85.00 28 3 0.37 98.90 10 9 1.10 86.10 30 1 0.12 99.02 11 16 1.95 88.05 34 1 0.12 99.15 12 25 3.05 91.10 35 1 0.12 99.27 13 9 1.10 92.20 36 1 0.12 99.39 14 5 0.61 92.80 41 1 0.12 99.51 15 9 1.10 93.90 43 1 0.12 99.63 16 5 0.61 94.51 44 1 0.12 99.76 17 6 0.73 95.24 45 1 0.12 99.88 18 4 0.49 95.73 50 1 0.12 100.00 cont’d Total 820 100.00 What is the median? What is the 75 th percentile? 5 0 .1 .2 .3 Density 0 5 10 20 30 40 50 Number Fishing Trips Discrete Histogram (bin width = 1) 6 Reading STATA Output . summarize Number_of_Trips, detail; Number_of_Trips ------------------------------------------------------------- Percentiles Smallest 1% 0 0 5% 0 0 10% 0 0 Obs 820 25% 0 0 Sum of Wgt. 820 50% 2 Mean 4.52439 Largest Std. Dev. 6.684273 75% 6 43 90% 12 44 Variance 44.6795 95% 17 45 Skewness 2.717188 99% 30 50 Kurtosis 13.01081 How can the 10 th percentile and the 25 th percentile both be zero?
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ECO220Y1Y, Lecture 3, Page 3 of 9 One Popular Use of Percentiles Quartiles: 1 st quartile: obs btwn 0 th and 25 th percentiles 2 nd quartile: obs btwn 25 th and 50 th percentiles 3 rd quartile: obs btwn 50 th and 75 th percentiles 4 th quartile: obs btwn 75 th and 100 th percentiles Quintiles: Divide variable into fifths: e.g. top quintile includes obs btwn 80 th and 100 th percentiles Deciles: Divide variable into tenths: e.g. bottom
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