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Unit 5: Distributional ShapeLesson 1:Symmetry : 

Unit 5: Distributional ShapeLesson 1:Symmetry EDER 5210 – Educational Statistics Dr. Robin K. Henson University of North Texas © 2002 University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Describing (Understanding) Distributions : 

Describing (Understanding) Distributions Central Tendency Variability Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Symmetry(Coefficient of Skewness) : 

Symmetry(Coefficient of Skewness) Can you fold a distribution in half at the mean and the two halves match? Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Slide 4: 

Dr. Robin K. Henson © 2002 University of North Texas Kind of like the Rorschach Ink Blots used in Psychoanalytic therapy. Used with permission. www.jasonlove.com Next Slide

Positively skewed – tail goes toward larger #s : 

Positively skewed – tail goes toward larger #s Negatively skewed – tail goes toward smaller #s Not skewed – symmetrical Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Coefficient of Skewness (or Symmetry) : 

Coefficient of Skewness (or Symmetry) Symmetrical Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Slide 7: 

Dr. Robin K. Henson © 2002 University of North Texas Go to next slide for answer. Q: What type of symmetry characterizes the following distribution (consider the asterisks as the top line of the distribution)?   ** * * * * * * _*____________*__*_ 16 15 14 13 12 11   a. positively skewed b. negatively skewed c. symmetrical d. not skewed e. None of the above Click mouse to continue

Answer : 

Answer a. No, the tail goes toward the lower numbers. Do not memorize that tails to the right are positively skewed and tails to the left are negatively skewed. Pay attention to the values of the numbers. This will help you understand what skewness is rather than just memorizing images. b. Yes, the tail goes toward the lower numbers. See (a) for explanation. c. No, the distribution is not symmetrical. d. No, the distribution is not symmetrical and therefore is skewed. e. No, (b) is correct. Click mouse to go to next slide.

Slide 9: 

Z -.58 -.58 1.16 -.20 -.20 1.56 Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Slide 10: 

Z -1.16 .57 .57 -1.56 .19 .19 Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Slide 12: 

Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Unit 5: Distributional ShapeLesson 1:Symmetry : 

Unit 5: Distributional ShapeLesson 1:Symmetry EDER 5210 – Educational Statistics Dr. Robin K. Henson University of North Texas © 2002 University of North Texas Dr. Robin K. Henson © 2002 Next Slide

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