Symmetry and Skew
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The document discusses different types of distributions in graphs of test score data: - Positive skew occurs when a small number of high scores stretch the graph out to the right, with the mean higher than the median and mode. - Negative skew is the opposite, with a small number of low scores stretching the graph left and the mean lower than the median and mode. - A symmetrical distribution has scores evenly distributed on both sides of the median, with the mean, median and mode close together.
Symmetry and Skew
- 1. 0–29 8 6 4 2 0 Test Result in % The Shape of Graphed Results involves Symmetry and Skew
- 2. 0–29 8 6 4 2 0 Test Result in % There are a small number of students who have done well, which makes this Graph stretch out horizontally to the right. Going to the Right is Positive, so it has “Positive Skew”
- 3. 0–29 8 6 4 2 0 Test Result in % The Kangaroo fits onto our graph with its tail going to the RIGHT. Going to the Right is Positive, so it has “Positive Skew”
- 4. 0–29 8 6 4 2 0 Test Result in % This particular group has lots of Low scores and has not performed well. The Mode will be to the left of the Median, and the Mean to the right. Mode < Median < Mean
- 5. 0–29 8 6 4 2 0 Test Result in % There are a small number of students who have done poorly, which makes this Graph stretch out horizontally to the left. Going to the Left is Negative, so it has “Negative Skew”
- 6. 0–29 8 6 4 2 0 Test Result in % The Kangaroo fits onto our graph with its tail going to the LEFT. Going to the Left is Negative, so it has “Negative Skew”
- 7. 0–29 8 6 4 2 0 Test Result in % This particular class has lots of High scores and has performed very well. The Mode will be to the right of the Median, and the Mean to the left. Mean < Median < Mode
- 8. 0–29 8 6 4 2 0 Test Result in % This particular class is fairly normal and has both low and high scores. This graph stretches out evenly on both sides of the Mode at 60-69. The Graph is “Symmetrical”
- 9. 0–29 8 6 4 2 0 Test Result in % Two identical Kangaroos show this graph is a mirror image type shape. The Graph is “Symmetrical”
- 10. 0–29 8 6 4 2 0 Test Result in % This particular class is fairly normal and has both low and high scores. The Mean, Median, and Mode will all be close together in the middle. Mean ~ Median ~ Mode
- 11. The Kangaroo fits onto our graph with its tail going to the RIGHT. Going to the Right is Positive, so it has “Positive Skew” Stem Leaf 0 1 1 2 4 7 8 1 2 2 3 5 6 6 8 9 2 1 5 6 7 7 8 8 9 9 9 3 2 4 4 5 7 7 8 4 1 3 5 8 5 2 3 7 6 2 3 4 7 2 6 8 3 9 2 Look at the S&L Plot sideways, and form a rotated 90 degrees view StemLeaf 0112478 122356689 21567788999 32445778 41358 5237 6234 726 83 92
- 12. The Kangaroo fits onto our graph with its tail going to the LEFT. Going to the Left is Negative, so it has “Negative Skew” Stem Leaf 0 1 1 2 2 1 5 3 2 4 8 4 1 3 5 5 2 3 7 6 2 3 4 5 6 6 7 7 7 2 2 5 5 6 7 7 7 8 8 9 8 1 3 4 4 5 6 6 7 7 7 9 2 3 4 5 6 6 7 8 StemLeaf 01 12 215 3248 4135 5237 623456677 722556777889 81344566777 923456678 Look at the S&L Plot sideways to form a rotated 90 degrees view
- 13. Stem Leaf 0 1 2 1 2 4 6 2 1 5 6 6 3 2 4 8 8 9 4 1 3 5 6 7 7 8 5 2 3 4 5 6 6 9 9 9 6 2 3 4 5 6 6 7 7 2 2 5 5 6 8 1 3 4 7 9 2 3 5 Look from the side of the S&L Plot and form a rotated 90 degrees view StemLeaf 012 1246 21566 324889 41356778 5234566999 62345667 722556 81347 9235 Two identical Kangaroos show this graph is a mirror image type shape. The S&L Plot is “Symmetrical”
- 14. SYMMETRIC RIGHT LEFT DATA SKEWED SKEWED 3 7 3 58 3 0 4 36 4 013345569 4 5 5 017 5 2446 5 6 1120 6 17 6 2 7 356789 7 7 17 8 0158 8 2 8 2445 9 43 9 5 9 012235569 10 0 10 0 10 000