Grade 7 · Statistics & Probability · MAT-07-SP-003
Compare Two Populations with Measures of Center and Spread
Represent and solve compare two populations with measures of center and spread problems using precise mathematical notation, models, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve compare two populations with measures of center and spread problems using precise mathematical notation, models, and reasoning.
- Explain why a method for compare two populations with 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.
Learn
Build the idea from meaning, not memorization.
Mathematical meaning
Compare Two Populations with 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 compare two populations with measures of center and spread in the Math Box.
- Change one input, predict the effect, and test the prediction.
- State the relationship or invariant that explains what stayed mathematically consistent.
Worked examples
Twenty different ways to see the concept work.
Population A has median 10; B has median 14. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 11; B has median 15. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 12; B has median 16. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 13; B has median 17. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 14; B has median 18. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 15; B has median 19. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 16; B has median 20. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 17; B has median 21. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 18; B has median 22. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 19; B has median 23. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 20; B has median 24. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 21; B has median 25. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 22; B has median 26. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 23; B has median 27. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 24; B has median 28. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 25; B has median 29. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 26; B has median 30. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 27; B has median 31. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 28; B has median 32. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Population A has median 29; B has median 33. Which has the larger median?
Population BCompare center, then also consider spread for a complete comparison.
Practice
Guided practice with hints
01Population A has median 30; B has median 34. Which has the larger median?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: Population B
02Population A has median 31; B has median 35. Which has the larger median?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: Population B
03Population A has median 32; B has median 36. Which has the larger median?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: Population B
04Population A has median 33; B has median 37. Which has the larger median?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: Population B
05Population A has median 34; B has median 38. Which has the larger median?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: Population B
06Population A has median 35; B has median 39. Which has the larger median?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: Population B
Practice
Independent practice
01Population A has median 36; B has median 40. Which has the larger median?
Answer: Population B
02Population A has median 37; B has median 41. Which has the larger median?
Answer: Population B
03Population A has median 38; B has median 42. Which has the larger median?
Answer: Population B
04Population A has median 39; B has median 43. Which has the larger median?
Answer: Population B
05Population A has median 40; B has median 44. Which has the larger median?
Answer: Population B
06Population A has median 41; B has median 45. Which has the larger median?
Answer: Population B
07Population A has median 42; B has median 46. Which has the larger median?
Answer: Population B
08Population A has median 43; B has median 47. Which has the larger median?
Answer: Population B
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
Population A has median 44; B has median 48. Which has the larger median?
Population B
Population A has median 45; B has median 49. Which has the larger median?
Population B
Population A has median 46; B has median 50. Which has the larger median?
Population B
Population A has median 47; B has median 51. Which has the larger median?
Population B
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 7 Reasoning Sprint
Solve compare two populations with measures of center and spread problems accurately and justify each result with a valid check.
Practice
Mastery check
01Population A has median 48; B has median 52. Which has the larger median?
Answer: Population B
02Population A has median 49; B has median 53. Which has the larger median?
Answer: Population B
03Population A has median 50; B has median 54. Which has the larger median?
Answer: Population B
04Population A has median 51; B has median 55. Which has the larger median?
Answer: Population B
05Population A has median 52; B has median 56. Which has the larger median?
Answer: Population B
06Population A has median 53; B has median 57. Which has the larger median?
Answer: Population B
07Population A has median 54; B has median 58. Which has the larger median?
Answer: Population B
08Population A has median 55; B has median 59. Which has the larger median?
Answer: Population B
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
California Mathematics Framework (2023)
Middle-school instructional guidance, mathematical practices, modeling, and coherent progression.Common Core State Standards for Mathematics — Grade 7
Grade-level expectations for ratios, number systems, algebra, geometry, statistics, and probability.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.