21 st Century Lessons The Shape of Distributions

21 st Century Lessons The Shape of Distributions of Data Primary Lesson Designer(s): Corey Cheever 1

Summary – Vocabulary 1. Symmetry: When it is graphed, a symmetric distribution can be divided at the center so that each half is a reflection of the other. Examples: Agenda 2

Summary – Vocabulary 2. Peak: A point on the graph that is higher than the points directly to the left and right. Examples: One Peak Two Peaks Agenda 3

Summary – Vocabulary 3. Skewed left/right: A graph is skewed left if it is highest to the right, then becomes lower as it goes left. A graph is skewed right if it is highest at the left and lowers as it goes right. Examples: Skewed Left Skewed Right Agenda 4

Summary – Vocabulary 4. Uniform: A graph that is evenly spread out, with no peaks. Examples: Uniform Agenda 5

Summary – Vocabulary Distributions may also have unusual features. The two most common ones are: 6. Gap: An area of the distribution where there are no entries in the data set. 7. Outlier: An element of the data set that is much higher or much lower than all the other elements. Examples: Gap Outlier Agenda 6

Summary – Looking Back Let’s go back to the two graphs we analyzed earlier. How can we describe them using the vocabulary that we just learned? Hint: Go right down the vocabulary list and identify each one. Remember – Symmetry, Peaks, Skew, uniform, unusual features. scaffolding 7 Agenda

Practice – Interactive Classwork We will now complete the back side of your class work. Describe the shape of each graph with as much detail as possible. Agenda 8

Practice Describe the SHAPE of this graph: Symmetry: Symmetric about 4 Peaks: One peak at 4 Skewness: Not Skewed Uniformity: Not Uniform Gaps: No Gaps Take it further! Outliers: No Outliers Can you calculate a center for this graph? Graphs that are symmetric with one peak are also called “normal distributions” since they are the most common. Fun Fact! 9 Can you calculate a spread for this graph? Agenda

Practice Describe the SHAPE of this graph: Symmetry: Symmetric about 3. 5 (Disregard the outlier) Peaks: No Peak Skewness: Not Skewed Uniformity: Uniform Gaps: Gap at 7 Outliers: Outlier at 8 Agenda 10

Practice Describe the SHAPE of this graph: Symmetry: Not Symmetric Peaks: Two Peaks at 2 and 6 Skewness: Not Skewed Uniformity: Not Uniform Gaps: One Gap at 4 Outliers: No Outliers Agenda 11

Practice Describe the SHAPE of this graph: Symmetry: Not Symmetric Peaks: One peak at 1 Skewness: Skewed right Uniformity: Not Uniform Gaps: No Gaps Outliers: No Outliers Take it further! Can you calculate a center for this graph? Can you calculate a spread for this graph? Agenda 12