# The Shape of Distributions of Data 1

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The Shape of Distributions of Data 1

Warm Up OBJECTIVE: Learn to describe the shape of a distribution of data using appropriate vocabulary. James kept track of how much he spent on lunch each day for a week, and got the following results: 5, 7, 4, 5, 10, 6, 5 1.What is the median of this data? 2.What is the mean of this data? 3.What is the range of this data? Alexis asked 10 people what their favorite color is, and got the following answers: Blue, green, orange, yellow, blue, blue, red, black, red, green 4. Why doesn’t it make sense to find the mean, median, or range of this data? Agenda 2

Launch – Next Step Lets take a look at the middle names of two classes, and compare their center and spread. Mr. Cheever's Class 5 5 4 4 Frequency Frequency Mrs. Smith's Class 3 2 3 2 1 1 0 0 0 1 2 3 4 5 6 7 Number of Letters Center: 4 Spread: 7 - 1 6 8 0 1 2 3 4 5 6 7 8 Number of Letters Center: 4 Spread: 7-1 6 Agenda 3

Launch B “These bar graphs have the same center and spread, but they are completely different!” Mr. Cheever's Class 5 5 4 4 Frequency Frequency Mrs. Smith's Class 3 2 3 2 1 1 0 0 0 1 2 3 4 5 6 Number of Letters 7 8 0 1 2 3 4 5 6 7 8 Number of Letters Agenda 4

Summary – Vocabulary To accurately describe the shape of a distribution, there is a standard group of vocabulary words that can help us. Copy the following vocabulary words and definitions onto your worksheet. Agenda 5

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 6

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 7

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 8

Summary – Vocabulary 4. Uniform: A graph that is evenly spread out, with no peaks. Examples: Uniform Agenda 9

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 10

Summary – Looking Back Let’s go back to the two graphs we looked at earlier. How can we describe them using the vocabulary that we just learned? Mr. Cheever's Class Mrs. Smith's Class 5 4 4 Frequency Frequency 5 3 2 3 2 1 1 0 0 0 1 2 3 4 5 6 7 8 Number of Letters 0 1 2 3 4 5 6 7 8 Number of Letters Hint: Go right down the vocabulary list and identify each one. Remember – Symmetry, Peaks, Skew, uniform, unusual features. scaffolding 11 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 12

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! No Outliers 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! 13 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 Not Skewed Skewness: Uniformity: Uniform Gaps: Gap at 7 Outliers: Outlier at 8 Agenda 14

Practice Describe the SHAPE of this graph: Symmetry: Not Symmetric Peaks: Two Peaks at 2 and 6 Not Skewed Skewness: Uniformity: Not Uniform Gaps: One Gap at 4 Outliers: No Outliers Agenda 15

Practice Describe the SHAPE of this graph: Symmetry: Not Symmetric Peaks: One peak at 1 Skewed right Skewness: 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 16