Students have collected data about their favorite lunch foods and created a simple bar graph. What’s the most important question to ask them first?
Section Making Sense of Data: Basic Analysis and Patterns
Once students have organized their data, they need to learn how to summarize it and identify patterns. This isn’t about calculating complex statistics—it’s about developing the habit of looking at data systematically and noticing what it reveals.
Checkpoint 47.
Exploration 17. Try This Week: Pattern Hunting.
Time needed: 15 minutes with any organized dataset
How it works: Use this progression with any data your students have collected or are studying:
1. Notice: “What do you see in this data? What stands out?”
2. Compare: “What’s the same? What’s different? What’s surprising?”
3. Quantify: “Can we put numbers on what we’re noticing?”
4. Extend: “What questions does this raise? What would we want to investigate next?”
Elementary Example: Classroom pet survey → Students notice dogs are most popular (Notice), cats got half as many votes as dogs (Compare), dogs got 12 votes out of 24 students (Quantify), “Do kids with pets vote differently than kids without pets?” (Extend)
Secondary Example: Student homework time data → Students notice wide variation (Notice), some students report 4+ hours while others report under 1 hour (Compare), the average is 2.3 hours but the range is 0.5-5 hours (Quantify), “Does homework time vary by subject or grade level?” (Extend)
Checkpoint 48.
When is it most important for students to understand the difference between average (mean) and median?
Solution.
When data has outliers (like one student reporting 8 hours of homework while others report 1-2 hours), the mean gets pulled toward the outlier while the median stays more representative of the typical experience. Understanding this helps students choose appropriate summaries and interpret data more accurately.
Students need to develop the skill of summarizing data in ways that reveal its most important characteristics. This builds naturally from simple counting to more sophisticated measures.
Exploration 18. Data Summary Progression.
Elementary Approach (Measures of Center):
• Start with “What’s typical?” or “What’s most common?”
• Use concrete language: “Most students chose...” or “About half the class...”
• Compare groups: “Boys tend to..., while girls tend to...”
Secondary Approach (Measures of Center and Spread):
• Calculate and compare mean, median, and mode when appropriate
• Discuss range and what it tells us about variability
• Identify outliers and discuss their impact on summaries
• Use these measures to support claims about the data
This video shows a teacher demonstrating how you’d like to model describing data patterns.
Checkpoint 49.
Students are working with survey data about transportation to school. How can organizing it into a frequency table help with analysis?
Solution.
Frequency tables organize responses by category (bus, car, walk, bike) and show counts or percentages, making it easy to see which transportation methods are most common, compare between options, and calculate what fraction of students use each method. This organized format also makes it easier to create visualizations and ask follow-up questions.
