Symmetry and Skew for Histograms and Stem and Leaf Plots in Statistics

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

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