1. CHAPTER 21 Developing Concepts of Data Analysis
Elementary and Middle School Mathematics Teaching Developmentally
Ninth Edition
Van de Walle, Karp and Bay-Williams
Developed by E. Todd Brown /Professor Emeritus University of Louisville

2. Big Ideas
Statistics is its own field distinct from mathematics; one key difference is focus on variability of data in statistical reasoning.
Doing statistics involves a four-step process: formulating questions, collecting data, analyzing data, and interpreting results.
Data are gathered and organized in order to answer questions about the populations from which the data come.
Different types of graphs and other data representations provide different information about the data and, hence, the population from which the data were taken.
Measures that describe data with numbers are called statistics.
Both graphs and statistics can provide a sense of the shape of the data.

3. What Does It Mean to Do Statistics?
Statistical literacy is needed by all students to interpret the world
Statistics and mathematics are two different fields
The shape of the data
How data is spread out
or grouped
Characteristics about
the data set as whole can be described

4. Process of doing statistics

5. Formulate Questions
Data collection should be for a purpose, to answer a question.
Students should have opportunities to generate their own questions.
Student-generated questions make the data collection more meaningful.
Student- or teacher-initiated questions should be well defined.
Questions that can be answered using statistics.

6. Data Collection
Two types of data- Categorical- data grouped by labels Favorite ice cream, color of car etc.
Numerical- data that counts things or measures on a continuous scale How many miles to school, temperature over time, weight of student backpacks.

7. Sampling
Statistics DOES NOT involve gathering from the “whole” population. Uses a representative sample. Sampling takes into consideration- variability Variability means gender, time of day when surveyed, culture
Students need to
Consider how they will gather data that will include a representative sample
Asking-
What is the population for your question?
Who or what is the subject of your question?

8. Using Existing Data Sources
Print resources Newspaper Almanacs Sports record book Maps Children’s literature
Web Resources USDA Economic Research Service Food Consumption Google Public Data Explorer Better World Flux U.S. Census Bureau

9. Data Analysis: Classifications
Making decisions about how to categorize things Attribute materials

10. Try this one Activity 21. 5 Guess My Rule
Materials- use students in the class Directions- Decide on an attribute i.e. wearing jeans, glasses, hat Tell the students “I have a rule.” Call a person to the front that meets your rule and one that does not meet the rule.
Call up more students and ask the students to predict whether the person meets or does not meet the rule. Before announcing the rule, give all students a chance to consider the possibilities.

11. Data Analysis: Graphical Representations
Students should be involved in deciding how they want to represent their data.
Creating graphs requires skill and precision. Choosing appropriate scale and labels

12. Data Analysis: Graphical Representations
Object graph- small step from sorting, actual articles are used as the graph i.e. types of shoes, favorite fruit Picture graph- moves up a level of abstraction and used drawing or pictures to represent data i.e. book drawing could mean 5 books Bar graph-something is used to represent the data i.e. sticky note, multi-cube

13. Data Analysis: Graphical Representations
Pie charts/ Circle graphs- generally used to show percentages Early pie chart Ratio table with percent and degrees

14. Continuous Data Graphs
Line and dot plots Stem and Leaf plots
Histogram
Box Plots

15. Bivariate Graphs
Line Graph- coordinate axis for plotting bivariate data Scatter plot - best fit is determined by the line you select that defines the observed relationship

16. Data Analysis: Measures of Center and Variability

17. Measures of Center
Try this one Activity You Be the Judge

18. Variability Focusing only on outliers or extremes.
Considering change over time.
Examining variability as the full range of data.
Considering variability as the likely range or expected value.
Looking at how far points are from the center.
Looking at how far off a set of data is from some fixed value.

19. Variability
Range- related to the median- difference between highest and lowest data points Mean absolute deviation-related to mean- tells how the spread of data- high MAD (lot of deviation between data points and mean)

20. Analysis and Interpretation of Statistics
Questioning and assessment should focus on how effectively the graphical representations communicate the findings. Difference between actual facts and inferences that go beyond the data.
Questions should focus on the mathematical ideas as well as the statistical ideas.
Context of the situation
What can be learned or inferred from the data

21. Ideas for Meaningful Discussion about Interpreting Data
What do the numbers (symbols) tell us about our class (or other population)? How do the numbers in this graph (population) compare to this graph (population)? Where are the data “clustering”? How much of the data are in the cluster? How much are not in the cluster? What does the graph not tell us? What might we infer? What new questions arise from these data? What is the maker of the graph trying to tell us?