Grade 7 · Statistics & Probability · MAT-07-SP-008
Evaluate Statistical Claims from Samples
Represent and solve evaluate statistical claims from samples problems using precise mathematical notation, models, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve evaluate statistical claims from samples problems using precise mathematical notation, models, and reasoning.
- Explain why a method for evaluate statistical claims from samples 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.
Mathematical meaning
Evaluate Statistical Claims from Samples 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 sampling simulator 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.
Sampling & Inference Lab
- Model one example of evaluate statistical claims from samples 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.
Survey 1 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 2 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 3 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 4 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 5 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 6 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 7 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 8 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 9 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 10 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 11 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 12 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 13 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 14 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 15 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 16 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 17 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 18 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 19 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Survey 20 about school lunch is given only to students in the pizza line. Is it representative of all students?
noThe selection method creates selection bias.
Practice
Guided practice with hints
01Survey 21 about school lunch is given only to students in the pizza line. Is it representative of all students?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: no
02Survey 22 about school lunch is given only to students in the pizza line. Is it representative of all students?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: no
03Survey 23 about school lunch is given only to students in the pizza line. Is it representative of all students?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: no
04Survey 24 about school lunch is given only to students in the pizza line. Is it representative of all students?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: no
05Survey 25 about school lunch is given only to students in the pizza line. Is it representative of all students?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: no
06Survey 26 about school lunch is given only to students in the pizza line. Is it representative of all students?
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: no
Practice
Independent practice
01Survey 27 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
02Survey 28 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
03Survey 29 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
04Survey 30 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
05Survey 31 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
06Survey 32 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
07Survey 33 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
08Survey 34 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
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
Survey 35 about school lunch is given only to students in the pizza line. Is it representative of all students?
no
Survey 36 about school lunch is given only to students in the pizza line. Is it representative of all students?
no
Survey 37 about school lunch is given only to students in the pizza line. Is it representative of all students?
no
Survey 38 about school lunch is given only to students in the pizza line. Is it representative of all students?
no
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 7 Reasoning Sprint
Solve evaluate statistical claims from samples problems accurately and justify each result with a valid check.
Practice
Mastery check
01Survey 39 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
02Survey 40 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
03Survey 41 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
04Survey 42 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
05Survey 43 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
06Survey 44 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
07Survey 45 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
08Survey 46 about school lunch is given only to students in the pizza line. Is it representative of all students?
Answer: no
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.