Chapter 6 · Lesson 8 of 12 · Grade 6 · Statistics & Probability · MAT-06-SP-008
Choose Measures of Center and Spread
Represent and solve choose measures of center and spread problems using precise mathematical notation, models, and reasoning.
Math V4 · Course chapter
Chapter 6: Statistics, Variability, and Mathematical Modeling
Using data and reasoning to support claims
Essential question: How can data, models, and mathematical arguments be used responsibly to describe variation and evaluate conclusions?
Where this lesson fits
Lesson 8 of 12. Each lesson builds on earlier chapter representations and ideas rather than resetting the topic.
Chapter destination
Collect a small data set, choose appropriate displays and summary measures, critique a misleading claim, and present a defensible conclusion.
Learning objectives
What you should be able to do
- Represent and solve choose measures of center and spread problems using precise mathematical notation, models, and reasoning.
- Explain why a method for choose measures of center and spread works, interpret the result in context, and verify it independently.
Prerequisite check
Make sure the foundation is ready.
The new lesson depends on this prerequisite as active knowledge.
The new lesson depends on this prerequisite as active knowledge.
Learn
Build the idea from meaning, not memorization.
Chapter 6: Statistics, Variability, and Mathematical Modeling
Using data and reasoning to support claims. This is Lesson 8 of 12 in Chapter 6. It builds on earlier chapter ideas instead of restarting the topic from scratch.
Connection to the course
Cumulative knowledge used here includes all previous chapters. As you work, connect today's idea to earlier lessons in the chapter and keep those earlier representations available for comparison.
Mathematical meaning
Choose Measures of Center and Spread describes data or chance while accounting for variability. Calculations must be interpreted in the context of data collection or a probability model.
Represent the relationship
The Math Box uses statistics plot to expose the structure. Change one input, predict the result, then connect the visual change to an equation, table, graph, number line, or geometric model.
Calculate, interpret, and verify
Verify calculations from the raw values, then decide whether the sample, display, center, spread, or probability model actually supports the claim.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Statistics Lab
Change the data and watch center and spread respond.
- Model one example of choose measures of center and spread in the Math Box.
- Change one input, predict the effect, and test the prediction.
- Connect the model to another representation used earlier in this chapter.
- State the relationship or invariant that explains what stayed mathematically consistent.
Worked examples
Twenty different ways to see the concept work.
A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 1.
medianThe median depends on order, not the magnitude of an extreme value.
Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 2.
medianThe representation should show the same mathematical relationship as the calculation. The median depends on order, not the magnitude of an extreme value.
Explain why a valid method works, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 3.
medianA complete explanation names the relationship or property being preserved. The median depends on order, not the magnitude of an extreme value.
Estimate or predict first, then calculate and decide whether the result is reasonable: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 4.
medianThe estimate is a reasonableness check, not a replacement for the exact result. The median depends on order, not the magnitude of an extreme value.
Solve and verify the result with a second method, inverse operation, or equivalent representation: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 5.
medianVerification should independently support the result. The median depends on order, not the magnitude of an extreme value.
Interpret the answer in context after solving. What does the result mean here? A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 6.
medianState the result with its meaning, units, direction, or comparison—not only a number. The median depends on order, not the magnitude of an extreme value.
Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 7.
Interpret center with spread, shape, and sampling method. Correct solution: medianError analysis requires identifying the broken idea, not merely replacing the final answer. The median depends on order, not the magnitude of an extreme value.
Compare two related cases and explain what changes and what stays mathematically consistent. Case A: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 8. Case B: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 17.
Case A: median Case B: medianCompare the structure, representation, units, and result rather than only the numbers. The median depends on order, not the magnitude of an extreme value.
A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 9.
medianThe median depends on order, not the magnitude of an extreme value.
Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 10.
medianThe representation should show the same mathematical relationship as the calculation. The median depends on order, not the magnitude of an extreme value.
Explain why a valid method works, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 11.
medianA complete explanation names the relationship or property being preserved. The median depends on order, not the magnitude of an extreme value.
Estimate or predict first, then calculate and decide whether the result is reasonable: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 12.
medianThe estimate is a reasonableness check, not a replacement for the exact result. The median depends on order, not the magnitude of an extreme value.
Solve and verify the result with a second method, inverse operation, or equivalent representation: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 13.
medianVerification should independently support the result. The median depends on order, not the magnitude of an extreme value.
Interpret the answer in context after solving. What does the result mean here? A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 14.
medianState the result with its meaning, units, direction, or comparison—not only a number. The median depends on order, not the magnitude of an extreme value.
Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 15.
Interpret center with spread, shape, and sampling method. Correct solution: medianError analysis requires identifying the broken idea, not merely replacing the final answer. The median depends on order, not the magnitude of an extreme value.
Compare two related cases and explain what changes and what stays mathematically consistent. Case A: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 16. Case B: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 25.
Case A: median Case B: medianCompare the structure, representation, units, and result rather than only the numbers. The median depends on order, not the magnitude of an extreme value.
A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 17.
medianThe median depends on order, not the magnitude of an extreme value.
Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 18.
medianThe representation should show the same mathematical relationship as the calculation. The median depends on order, not the magnitude of an extreme value.
Explain why a valid method works, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 19.
medianA complete explanation names the relationship or property being preserved. The median depends on order, not the magnitude of an extreme value.
Estimate or predict first, then calculate and decide whether the result is reasonable: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 20.
medianThe estimate is a reasonableness check, not a replacement for the exact result. The median depends on order, not the magnitude of an extreme value.
Practice
Guided practice with hints
01Solve and verify the result with a second method, inverse operation, or equivalent representation: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 21.
Hint: Choose a representation before computing.
Answer: median
02Interpret the answer in context after solving. What does the result mean here? A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 22.
Hint: Explain what relationship or property makes your method valid.
Answer: median
03Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 23.
Hint: Choose a representation before computing.
Answer: Interpret center with spread, shape, and sampling method. Correct solution: median
04Compare two related cases and explain what changes and what stays mathematically consistent. Case A: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 24. Case B: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 33.
Hint: Explain what relationship or property makes your method valid.
Answer: Case A: median Case B: median
05A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 25.
Hint: Choose a representation before computing.
Answer: median
06Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 26.
Hint: Explain what relationship or property makes your method valid.
Answer: median
Practice
Independent practice
01Explain why a valid method works, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 27.
Answer: median
02Estimate or predict first, then calculate and decide whether the result is reasonable: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 28.
Answer: median
03Solve and verify the result with a second method, inverse operation, or equivalent representation: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 29.
Answer: median
04Interpret the answer in context after solving. What does the result mean here? A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 30.
Answer: median
05Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 31.
Answer: Interpret center with spread, shape, and sampling method. Correct solution: median
06Compare two related cases and explain what changes and what stays mathematically consistent. Case A: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 32. Case B: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 41.
Answer: Case A: median Case B: median
07A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 33.
Answer: median
08Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 34.
Answer: median
Common mistakes
Learn to catch the error, not just the answer.
Interpret center with spread, shape, and sampling method.
Finite experimental frequencies vary even when a model is correct.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Summarize data, compare groups, evaluate survey claims, and describe uncertainty.
- Build probability models and simulations for repeated random processes.
Challenge problems
Explain why a valid method works, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 35.
median
Estimate or predict first, then calculate and decide whether the result is reasonable: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 36.
median
Solve and verify the result with a second method, inverse operation, or equivalent representation: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 37.
median
Interpret the answer in context after solving. What does the result mean here? A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 38.
median
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 6 Chapter 6 Reasoning Lab
Solve choose measures of center and spread problems accurately, choose an appropriate representation, and justify each result with a check.
Practice
Mastery check
01Error analysis: a student says, "Reporting one statistic without considering variability." Explain the mistake, then solve this related task correctly: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 39.
Answer: Interpret center with spread, shape, and sampling method. Correct solution: median
02Compare two related cases and explain what changes and what stays mathematically consistent. Case A: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 40. Case B: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 49.
Answer: Case A: median Case B: median
03A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 41.
Answer: median
04Represent before calculating. Use a data display, ordered data set, summary measure, or written statistical claim for this task, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 42.
Answer: median
05Explain why a valid method works, then solve: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 43.
Answer: median
06Estimate or predict first, then calculate and decide whether the result is reasonable: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 44.
Answer: median
07Solve and verify the result with a second method, inverse operation, or equivalent representation: A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 45.
Answer: median
08Interpret the answer in context after solving. What does the result mean here? A data set has one extreme high outlier. Which center is more resistant: mean or median? Case 46.
Answer: median
Terminology
Words to know
- distribution
- The pattern of values including center, spread, shape, and unusual features.
- variability
- The degree to which observations differ.
- sample
- A subset of a population used to collect information.
- probability
- A number from 0 to 1 describing likelihood.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
Grade 6 scope, sequence, standards, and public task structure
Reference for coherent sequencing, representations, dependency-aware progression, and reasoning-rich task types.Eureka Math² Grade 6 program structure
Reference for module/topic coherence, recap, mixed-practice, and cumulative-learning patterns.enVision Mathematics Grade 6 instructional model
Reference for problem-based entry points, visual learning, modeling, and application patterns.Common Core State Standards for Mathematics — Grade 6
Grade-level content and mathematical-practice expectations.