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Is there any skewness in the data?  Which direction? What is the cause of the skewness? Which wines are possible outliers and why?

Is there any skewness in the data?  Which direction? What is the cause of the skewness? Which wines are possible outliers and why?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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  1. Is there any skewness in the data?  Which direction?
  2. What is the cause of the skewness?
  3. Which wines are possible outliers and why?
1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 0.5 0.5 CO ថា @ 1.5 01 O N N 16 pH Sulphates Alcohol Quality 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 O N 0.2 0.6 0.8 1 1.2 18 Citric Acid Residual Sugar Chlorides Free Sulfur Dioxide 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 53 105 157 209 261 313 365 417 469 521 573 625 677 729 781 833 885 937 989 1041 1093 1145 1197 1249 1301 1353 1405 1457 1509 1561 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 0.2 0.8 0.6 0.8 1.2 250 300 350 co Density Total Sulfur Dioxide Fixed Acidity Volatile Acidity
Transcribed Image Text:1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 0.5 0.5 CO ថា @ 1.5 01 O N N 16 pH Sulphates Alcohol Quality 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 O N 0.2 0.6 0.8 1 1.2 18 Citric Acid Residual Sugar Chlorides Free Sulfur Dioxide 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 53 105 157 209 261 313 365 417 469 521 573 625 677 729 781 833 885 937 989 1041 1093 1145 1197 1249 1301 1353 1405 1457 1509 1561 1 55 109 163 217 271 325 379 433 487 541 595 649 703 757 811 865 919 973 1027 1081 1135 1189 1243 1297 1351 1405 1459 1513 1567 0.2 0.8 0.6 0.8 1.2 250 300 350 co Density Total Sulfur Dioxide Fixed Acidity Volatile Acidity
23 A Mean Standard 4 Error 5 Median 6 Mode Standard 7 Deviation Sample 8 Variance 9 Kurtosis 10 Skewness 11 Range 12 Minimum 13 Maximum 14 Sum 15 Count 16 17 18 19 20 Mean Standard 21 Error 22 Median 23 Mode Standard 24 Deviation Sample 25 Variance 26 Kurtosis 27 Skewness 28 Range 29 Minimum B 30 Maximum 31 Sum 32 Count 33 8.31963727 0.04354102 total sulfur dioxide 7.9 7.2 1.74109632 3.03141639 1.1321434 0.98275144 11.3 4.6 15.9 13303.1 1599 46.4677924 0.82264023 38 28 32.8953245 1082.10237 3.80982449 1.51553126 283 6 289 74302 1599 C D Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count E 0.52782051 0.00447789 0.52 0.6 0.1790597 density 0.03206238 1.22554225 0.67159257 1.46 0.12 1.58 843.985 1599 0.99674668 4.7198E-05 0.99675 0.9972 0.00188733 3.562E-06 0.93407907 0.07128766 0.01362 0.99007 1.00369 1593.79794 1599 F G Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count H 0.27097561 0.00487155 0.26 0 0.19480114 pH 0.03794748 -0.7889975 0.3183373 1 0 1 433.29 1599 3.3111132 0.00386087 3.31 3.3 0.15438646 0.02383518 0.80694251 0.1936835 1.27 2.74 4.01 5294.47 1599 I J Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count K 2.5388055 0.03525922 2.2 2 1.40992806 sulphates 1.98789713 28.6175954 4.54065543 14.6 0.9 15.5 4059.55 1599 0.65814884 0.004239 0.62 0.6 0.16950698 0.02873262 11.7202507 2.42867235 1.67 0.33 2 1052.38 1599 L M Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count N 0.08746654 0.001177 0.079 0.08 0.0470653 0.00221514 alcohol 41.7157872 5.68034657 0.599 0.012 0.611 139.859 1599 10.4229831 0.02665002 10.2 9.5 1.06566758 1.1356474 0.20002931 0.86082881 6.5 8.4 14.9 16666.35 1599 O P Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Q 15.8749218 0.26158568 14 6 10.460157 109.414884 quality 2.02356205 1.25056729 71 1 72 25384 1599 5.63602251 0.02019555 6 5 0.80756944 0.6521684 0.29670812 0.21780158 5 3 8 9012 1599
Transcribed Image Text:23 A Mean Standard 4 Error 5 Median 6 Mode Standard 7 Deviation Sample 8 Variance 9 Kurtosis 10 Skewness 11 Range 12 Minimum 13 Maximum 14 Sum 15 Count 16 17 18 19 20 Mean Standard 21 Error 22 Median 23 Mode Standard 24 Deviation Sample 25 Variance 26 Kurtosis 27 Skewness 28 Range 29 Minimum B 30 Maximum 31 Sum 32 Count 33 8.31963727 0.04354102 total sulfur dioxide 7.9 7.2 1.74109632 3.03141639 1.1321434 0.98275144 11.3 4.6 15.9 13303.1 1599 46.4677924 0.82264023 38 28 32.8953245 1082.10237 3.80982449 1.51553126 283 6 289 74302 1599 C D Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count E 0.52782051 0.00447789 0.52 0.6 0.1790597 density 0.03206238 1.22554225 0.67159257 1.46 0.12 1.58 843.985 1599 0.99674668 4.7198E-05 0.99675 0.9972 0.00188733 3.562E-06 0.93407907 0.07128766 0.01362 0.99007 1.00369 1593.79794 1599 F G Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count H 0.27097561 0.00487155 0.26 0 0.19480114 pH 0.03794748 -0.7889975 0.3183373 1 0 1 433.29 1599 3.3111132 0.00386087 3.31 3.3 0.15438646 0.02383518 0.80694251 0.1936835 1.27 2.74 4.01 5294.47 1599 I J Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count K 2.5388055 0.03525922 2.2 2 1.40992806 sulphates 1.98789713 28.6175954 4.54065543 14.6 0.9 15.5 4059.55 1599 0.65814884 0.004239 0.62 0.6 0.16950698 0.02873262 11.7202507 2.42867235 1.67 0.33 2 1052.38 1599 L M Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count N 0.08746654 0.001177 0.079 0.08 0.0470653 0.00221514 alcohol 41.7157872 5.68034657 0.599 0.012 0.611 139.859 1599 10.4229831 0.02665002 10.2 9.5 1.06566758 1.1356474 0.20002931 0.86082881 6.5 8.4 14.9 16666.35 1599 O P Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Q 15.8749218 0.26158568 14 6 10.460157 109.414884 quality 2.02356205 1.25056729 71 1 72 25384 1599 5.63602251 0.02019555 6 5 0.80756944 0.6521684 0.29670812 0.21780158 5 3 8 9012 1599
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