Unit Plan 29 (Grade 6 Math): Center & Variability—Mean, Median, MAD, IQR
6th graders compute and interpret mean, median, MAD, and IQR to describe data center and spread. Students compare groups using these measures, justify when each is most appropriate, and explain results clearly with context and caution.
Focus: Compute/interpret measures of center and variation (mean, median, MAD, IQR); use them to compare groups cautiously.
Grade Level: 6
Subject Area: Mathematics (Statistics & Probability — Center & Variability)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Building on data displays, students learn how single numbers can summarize a data set’s typical value (mean and median) and variability (mean absolute deviation—MAD and interquartile range—IQR). They compute these measures, explain what each tells about the distribution, and make careful comparisons between groups—always noting context, units, and the possible influence of outliers or skew.
Essential Questions
- What do mean and median communicate about what is typical?
- How do MAD and IQR communicate how much data vary?
- When is it better to use median/IQR instead of mean/MAD (and why)?
- How can we compare groups with center and variability without overclaiming?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Compute and interpret mean (as “fair share/balance point”) and median (middle value after ordering).
- Explain differences between mean and median when data include skew or outliers.
- Compute MAD (average distance of data values from the mean) and interpret it as typical spread.
- Find the five-number summary (minimum, Q1, median, Q3, maximum) and compute IQR (Q3 − Q1) as a measure of spread.
- Use center and variability to compare two groups in context, with cautious language and attention to units and sample size.
Standards Alignment — CCSS Grade 6
- 6.SP.3: Recognize that a measure of center summarizes all values with a single number and a measure of variation describes how values vary.
- (Connections used in practice: 6.SP.5 for summarizing data with quantitative measures and relating findings to the context.)
Success Criteria — Student Language
- I can find the mean and median and tell what each means in the real situation.
- I can find MAD and IQR and explain what they say about spread.
- I can decide whether to use mean/MAD or median/IQR and justify my choice.
- I can compare groups using center and variability and write a careful data story with units.