Data Analysis

1. Data Analysis Ana Floyd afloyd@randolph.k12.nc.us Wendy Rich wendyrich44@gmail.com

2. Development of Data Sense • Children are interested in themselves and their immediate surroundings. Use physical objects to display the answers to their questions. • Later, children learn other methods of representation using pictures, sticky notes, or tallies. What are our favorite colors? How many children ride the bus to school?

3. Development of Data Sense • Children’s interests expand outward to their surroundings, and their questions become more sophisticated. The amount of collectible data grows, and the task of keeping track of the data becomes more challenging. • Students learn the importance of framing good questions and planning carefully how to gather and display their data. • Students learn and create more complex data displays and do more analysis and interpretation of the data. Van de Walle, 2002

4. Development of Data Sense • Data sense can only develop through repeated experiences, frequent discussions, and skillful guidance from teachers. • Students must conduct their own investigations by posing questions and struggling with the best ways to collect and organize the data.

5. Development of Data Sense Results of students collecting their own data: • Creates ownership and self-confidence • Improves motivation and interest • Constructs fundamental understandings about data • Learn to pose more precise questions • Learn new ways to collect and organize data • Gains experience making decisions and communicating mathematically

6. Attributes in the Data Strand • A collection of objects with various attributes can be sorted in different ways. • A single object can belong to more than one class. • Classification is the first step in the organization of data.

7. Guess My Rule • Person fits one mystery rule • Person fits second mystery rule Where should people go that fit both rules? What if someone does not fit either rule? • Observe each person • Think: What attribute might each one represent? • Test conjectures by placing participants

8. Exploration of Attributes Questions to ask students after the game: • Were there other attributes or observable characteristics that could be a rule? • How do non-examples provide information about the rule? • Why are there so many possibilities before you know the exact rule? • What would be some attributes that are not observable?

9. Attributes • Characteristics or ways that materials can be sorted Unstructured attribute materials – Each attribute has a number of different values – For example: sea shells, leaves, people, children’s shoes

10. Attributes • Characteristics or ways that materials can be sorted Structured attribute materials -Have exactly one solution for every combination of values for each attribute -For example: commercial attribute blocks

11. Attributes (Structured Material Example) •large •red •thin •rectangle

12. Sink or Float??? Make a representation for your collection of things!

13. Categorical & Numerical Data Students need to distinguish between questions that give categorical and numerical data before they pose a question and try to interpret the data

14. Categorical Data • Values (most often words) that represent possible responses with respect to a given category • Represent individuals or objects by one or more characteristics or traits that they share Examples: • Months in which people have birthdays • Favorite color T-shirt • Favorite fruits • Kinds of pets

15. Numerical Data • Values that are numbers such as counts and measurements. • Represent objects or individuals by numbers assigned to certain measurable properties - Examples: • Number of children in families • Time in minutes that students spend watching television each day • Number of pets

16. Process of Statistical Investigation • Pose the question • Collect the data • Analyze the data • Interpret the data

17. PCAI Model

18. Pose the Question • Step 1: Identify a specific question to explore, and decide what data to collect to address the question

19. Pose the Question • All data investigations begin with a problem or question • Questions should be focused & precise • Questions may need to be refined • Students need multiple experiences with posing questions and carrying-out investigations • Each question should have a purpose

20. Pose the Question Four Purposes for Investigations: • To describe or summarize what was learned from a set of data • To determine preference and opinions from a set of data • To compare and contrast two or more sets of data • To generalize or make predictions from a set of data

21. Collect the Data • Step 2: Decide how to collect the data, and collect the data

22. Collect the Data • Students should collect their own data • Students need to have a plan for collecting data and understand where data come from • Data collection methods include: observations, surveys, experiments, measurements, interviews, polls, simulations, examinations of past records, and searches of the internet, library, or other sources

23. Animals in the Neighborhood • What animals have you seen that live in your neighborhood? • We’re going to make up categories for how the animals move. • Make a representation to show how these animals move.

24. Analyze the Data • Step 3: Organize, summarize, describe, and display the data; and look for patterns in the data.

25. Analysis • Analysis is the process of reflecting on assigned values in a collection of data to obtain new information and gain understanding of the population from which the data were collected.

26. Analyze the Data • Representing the data in order to identify patterns of variation in the data • Manner of representation depends on why the data have been collected and what type of data have been collected • Displays provide visual descriptions of variability in data (where the data is clumped or unusual data points) and ways to analyze the data (how it is spread and what is typical).

27. Types of Graphs • Graphs provide a means for: • Communicating and classifying data • Comparing data and displaying mathematical relationships that often cannot be easily seen in numeric form

28. Picture Graphs • Use pictures to depict quantities of objects or people • Used with discrete data • Symbols must be the same size and shape • May represent real objects or be more abstract representations (such as shapes) • Legends or keys are used when the object ratio is not one-to-one

29. Picture Graphs

30. Picture Graphs :

31. Bar Graph • Horizontal or vertical bars of uniform width • Compares frequencies of GROUPED, discrete quantities • Axes are labeled to indicate value or frequency

32. Bar Graph Bar Graph showing ungrouped data

33. Bar Graph

34. Bar Graph

35. Dominant Hand • How many X’s can you make with your right hand? With your left hand? • How is this numerical data different from the categorical data of “Animals in the Neighborhood”?

36. Line Plots • Quick, simple way to organize data • Uses X’s (or other same sized symbols) on a single horizontal axis • Includes all numbers within the range of the data set on the axis to show holes and the shape of the data

37. Line Plots

38. Interpret the Results • Step 4: Use the results from the analyses to make decisions about the original question

39. Interpret the Results • Requires making sense from the analysis in order to address the question being asked “How do results from the data analysis relate to the original question?” • Reviews each stage of the process • May lead to more questions and investigations

40. Interpret the Results Examples of “interpreting” questions: • How would we describe people in this group based on the data we collected? • If someone walked into this room, what might we predict would be…? • What can we say about the ways people chose to represent the data? • What might we want to ask next to refine our understanding of…..?

41. Raisins! • How many raisins are in a half-ounce box? • Describe the shape of the data for your brand of raisins. • If we open 5 more boxes, what is your best guess of numbers of raisins in the boxes? • Compare both data sets to see which brand has the most raisins.