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Representing data

Representing data. TWSSP Monday. Data Collection. Decide in a group on a question for which you would like to collect data from the class. Write all of your group’s responses to each question on a separate index card

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Representing data

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  1. Representing data TWSSP Monday

  2. Data Collection • Decide in a group on a question for which you would like to collect data from the class. • Write all of your group’s responses to each question on a separate index card • Introduce the person to your left, and include an interesting piece of information you learned about them during data collection

  3. Week Overview • Focus on variability in statistics and probability • What is variability? • The extent to which data points diverge or differ • Why variability? • Variability is…the essence of statistics as a discipline and it is not best understood by lecture. It must be experienced (Cobb, 1992) • Understanding Variability is • Key component of understanding distribution • Core component of statistical thinking • Essential for making statistical inferences (Garfield & Ben-Zvi, 2008)

  4. Week Overview • Content focused, but transparent in pedagogy • Time to discuss pedagogy as needed • Purple cups

  5. Monday Agenda • Before lunch: • Community Agreements • Preassessment • After lunch: • Analyze data collected this morning • Unknown variables activity • Characteristics of distributions • Goal for today: • Understand how to represent different types of data • Understand how variability appears in a graph and what it might reveal about the corresponding data • Identify the features of a distribution

  6. Community Agreements • What do you need from each other in order to be able to feel safe to explore mathematical ideas, share thinking, and build on and connect with others’ ideas? • What do you need to feel respected and valued as part of the mathematical community?

  7. Data Analysis • Organize the data for your group’s question into a meaningful graphic display to share with the group • What is “normal” for our class? • How much do we vary? • Is there another representation which would also be appropriate? • What do you predict the data would look like if we collected it for all the teachers in the institute?

  8. Unknown Variables • You will have a card with a question for which responses are numerical taped to your back. • Collect responses to your question from all of your classmates • NO UNITS when you respond!! • Create a visual representation of the responses to your question. • What do you think your question is? Why?

  9. Which Graph When? • Your group will be assigned the names of two types of graphs. • Your task is to prepare a brief presentation on each of the graph types for the rest of the class explaining: • What your graph looks like • For what type of data your graph is appropriate and inappropriate • What your graph represents well and not so well about data • How you see center and spread in your graph type

  10. Distinguishing Distributions • Imagine you are describing a person’s face to a friend who has never seen that person. • What features would be essential in your description? • Now think about describing a graphical representation. • What would be the essential features of a graphical representation of data which you would want to include in your description?

  11. Distinguishing Distributions • All of the graphs you see represent the exam scores of different classes. • For classes A, B, and C, what main feature(s) distinguish the graphs from one another? • What might be the source of this difference? • Do the same for D, E, & F, and G, H, & I

  12. Distinguishing Distributions • What strikes you as the most distinguishing characteristic of the distribution of exam scores in graph J? What might be an explanation for this characteristic? • Do the same for K and L • Go back to graph D. If you wanted to tell someone how the class did on the exam, what would you say? How would you describe the “bulk” of the data for class D? • Do the same for class E.

  13. Distinguishing Distributions • Suppose you are told that most exam scores for a class were between 65 and 85, and that the lowest score was 30 and the highest was 100 • What might a possible distribution look like? • Wrap up – Distinguishing Distributions: • What features of a graph are important in describing a distribution? • Are there any characteristics that some graphs may have but others won’t?

  14. Exit Ticket (sort of…) • Joel collected data about the weights of 100 dogs at a doggy day care. What type of graph should Joel use to tell the story of his data? Why? • What would you expect that graph to look like? Be sure you are addressing the important features of a graph.

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