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Unit 1, Section 3: Wrapping Up the Case

Section 3: Wrapping Up the Case

Overarching Themes

This section advances students from graphical inspection to formal numerical summarization within the Analyze Data and Interpret Data phases of the Data Cycle. Students investigate how numerical measures describe a distribution’s center and spread, beginning with the mean as a “fair share” value and the Mean Absolute Deviation (MAD) as average distance from the center. By examining datasets with extreme values, students discover the need for alternative measures of center and spread: the median and the Interquartile Range (IQR). Students build a foundational statistical decision framework for pairing the mean and MAD with symmetric distributions and the median and IQR with skewed distributions.

Daily Overview

Lesson Title Vocabulary Lesson Activities GAISE Level B Guidelines
Lesson 13:
The Average Suspect		 center
fair share
mean
average
  • Fair Share: Redistributing tokens across plates to model equal sharing
  • Algorithm Practice: Applying mean formula
  • CODAP Analysis: Adding mean lines to plots
  • B.III.2: Learn to use key features of distributions (center: mean as a balance point)
  • B.IV.1: Use statistical evidence from analyses to answer questions
Lesson 14:
Getting MAD About It		 spread
deviation
absolute value
MAD (mean absolute deviation)
  • Human Number Line: Using yarn to physically measure distances from the mean
  • Three-Step MAD: Calculating absolute deviations and finding their average
  • CODAP Analysis: Graphing mean and MAD
  • B.III.1: Represent variability of quantitative variables
  • B.III.2: Learn to use key features of distributions (variability: MAD)
  • B.IV.1: Use statistical evidence from analyses to answer questions
Lesson 15:
When the Mean is Unfair - Introducing the Median		 median
extreme value
  • Carnival Line-Up: Demonstrating how an extreme low ride count pulls down the mean
  • Finding the Median: Ordering values and crossing off ends to determine the median
  • Parallel Tasks: Calculating and comparing MAD with and without extreme values
  • B.III.2: Learn to use key features of distributions (center: median as middle-ordered value)
  • B.IV.5: State limitations of sample information and sensitivity of measures
Lesson 16:
Boxing Up the Evidence		 quartile
Q1
Q3
IQR (interquartile range)
minimum
maximum
  • Quartering Data: Physically identifying the five-number summary on a floor number line
  • Building Boxplots: Manually sketching boxplots from the five-number summary values and calculating the IQR
  • B.III.1: Represent variability of quantitative variables using appropriate displays (boxplots)
  • B.III.2: Key features of distributions (variability: IQR)
Lesson 17:
Connecting Shape, Center, and Spread		 n/a
  • Plot Match: Pairing matching histograms, dotplots, and boxplots based on shape
  • Decision Framework: Mapping symmetric data to Mean/MAD and skewed data to Median/IQR
  • CODAP Analysis: Generating boxplots
  • B.III.2: Coordinate key features of distributions (shape, center, and variability)
  • B.III.3: Use reasoning about distributions to compare summary statistics
Lesson 18:
Wrapping Up the Case of the Candy Culprit		 n/a
  • Culprit Unmasking: Cross-referencing remaining suspects against all case evidence
  • Data Cycle Synthesis: Connecting Pose Questions through Interpret Data
  • B.IV.1: Communicate results with comprehensive answers and reports
  • B.IV.3: Generalize and make final evidence-backed conclusions
Progress Check 3:
Can You Interpret Evidence?		 n/a
  • Investigative Task 1: Gamer Profiles Revisited
  • Investigative Task 2: The Impact of Extreme Players
  • Investigative Task 3: Creating & Interpreting Boxplots
  • Investigative Task 4: Choosing the Right Tool
  • B.III.1: Represent variability via boxplots
  • B.III.2: Apply center (mean/median), spread (MAD/IQR), and shape rules
  • B.IV.1: Support conclusions using statistical evidence