HSS.IC.A.1Common CoreMathStatistics and ProbabilityGrades 9-12
HSS.IC.A.1: Statistics as Inference from a Random Sample
In plain English: HSS.IC.A.1 is the Common Core statistics standard that asks students to see statistics as a process: take a random sample from a population, compute a statistic from it, and use that statistic to draw a conclusion about an unknown population parameter. Because samples vary, the conclusion is an estimate with uncertainty. It is usually taught in Algebra II or an introductory Statistics course.
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Common Core State Standards for Mathematics · Domain: Making Inferences and Justifying Conclusions (IC) · Cluster: Understand and evaluate random processes underlying statistical experiments Also written as HSS-IC.A.1 or S-IC.1 · Official standard
Students learn that statistics is a process for answering questions about a whole population when only part of it can be measured. A population parameter, such as the proportion of all students at a school who have a part-time job, is a fixed number that is usually unknown. A statistic, such as the proportion in a random sample of 150 of those students, is computed from data and changes from sample to sample. Inference is the step from the statistic back to the parameter.
The lesson stresses why the sample must be random: chance selection gives every member a fair chance to be included, so the sample tends to resemble the population and the size of chance error can be judged. Students compute sample proportions and sample means, watch statistics vary in a physical simulation, see that larger random samples vary less, and learn to spot convenience and voluntary response samples that do not support inference.
Learning Objectives
By the end of this lesson, students will be able to:
Identify the population, parameter, sample and statistic in a statistical study
Compute a sample proportion or sample mean and use it to estimate the matching population parameter
Explain why a statistic varies from one random sample to another while the parameter stays fixed, and why larger random samples vary less
Explain why random selection is needed for a sample to support an inference, and recognize convenience and voluntary response samples
Write an inference statement that names the population and admits uncertainty
Prior Knowledge Required
Students should already be comfortable with:
Recognizing statistical questions that anticipate variability 6.SP.A.1
Using a sample to learn about a population, and why random samples tend to be representative 7.SP.A.1
Drawing informal inferences from random samples and gauging variation across samples 7.SP.A.2
Computing a mean and writing a fraction as a decimal or percent
Display the scenario and give students two minutes to write an answer before discussing it with a partner:
Warm-Up Prompt
"A cafeteria manager wants to know what fraction of the school's 1,200 students would buy a salad-bar lunch. On pizza day she asks the first 40 students in line, and 6 say yes. She reports that 15% of the school would buy it. Would you trust her number? What would you change about how she collected the data?"
Collect ideas. Students usually notice that students in the pizza line on pizza day are not like the whole school, and that the first 40 in line may share a schedule or a friend group. Record the words students use (fair, representative, random, biased). Tell them the lesson gives names to each part of this situation: the 1,200 students are the population, the 40 are the sample, 6/40 = 0.15 is a statistic, and the true fraction for the whole school is the parameter she wanted.
Direct Instruction20 minutes
Vocabulary. Define four terms and keep them posted: a population is the entire group the question is about; a parameter is a number that describes the population (written p for a proportion, μ for a mean); a sample is the part of the population actually measured; a statistic is a number computed from the sample (written p̂ or x̄). A memory aid: parameter goes with population, statistic with sample. Use Diagram 1 to show the whole process:
Ask a question about a population and name the parameter that answers it.
Select a random sample, so chance, not the researcher or the respondents, decides who is included.
Measure the sample and compute a statistic such as p̂ or x̄.
Infer: use the statistic as an estimate of the parameter, and state that the estimate could be off because of sampling variability.
Limit the conclusion to the population the sample was drawn from.
Parameter and statistic (proportion)
A district wants the proportion of its 4,800 high school students who have a part-time job. It randomly selects 150 students from its enrollment list, and 63 of them have a job.
Equation: Statistic p̂ = 63/150 = 0.42. Parameter p is unknown; estimate: about 42% of the district's high school students.
Parameter and statistic (mean)
A random sample of 8 of a town's 3,500 bus riders reports one-way commute times of 12, 25, 18, 30, 9, 22, 15 and 21 minutes.
Equation: x̄ = 152/8 = 19 minutes, an estimate of μ, the mean commute of all 3,500 riders.
Sampling variability
Four different random samples of 50 from the same population give p̂ = 0.46, 0.40, 0.52 and 0.44.
Equation: The statistic changes from sample to sample (mean of the four: 1.82/4 = 0.455); the parameter p is one fixed number.
A sample that does not support inference
A gaming website asks visitors to report how many hours a week they play video games and posts the average as the value for "all teens".
Equation: Voluntary response from gaming-site visitors: the sample is not random and not drawn from all teens, so no inference about all teens is justified.
Close with Diagram 2. Each dot is the p̂ from one computer-simulated random sample drawn from a population where p = 0.30. Ask: "Where do the dots pile up? Which sample size gives estimates you would trust more?" Students should see that both sets center near 0.30 and that samples of 100 stay much closer to it than samples of 25. Stress that a random sample does not give the exact parameter; it gives an estimate whose typical error can be judged, and larger random samples make that error smaller. Randomness also has to survive the whole process: if many of the people selected never respond, the ones who do answer chose themselves, and the sample can be biased again (nonresponse).
Guided Practice15 minutes
Pairs work through four short scenarios. For each one, they name the population, parameter, sample and statistic, then decide whether an inference to the population is justified. Discuss each before moving on.
A park ranger randomly selects 60 of the 2,000 campsites reserved this summer and finds that 45 had a campfire permit. (Population: the 2,000 reserved campsites; parameter: proportion of them with a permit; statistic: 45/60 = 0.75; inference justified.)
A phone maker tests the battery life of 25 phones chosen at random from one day's production of 10,000. (Population: that day's 10,000 phones; parameter: their mean battery life; statistic: the mean of the 25; inference justified for that day's production only.)
A radio host asks listeners to call in about a new traffic law; 88% of callers oppose it. (Voluntary response: callers chose themselves, so no inference about the listening area.)
A teacher surveys her own first-period class about homework time and reports it as the school average. (Convenience sample: one class is not a random sample of the school.)
Listen for students who call the population "the people surveyed" and for students who think a large number of respondents fixes a biased method.
Independent Practice15 minutes
Students work alone on the data below. It is invented data for a random sample of 10 of the 640 juniors at a high school, who reported how many hours they slept on a school night.
Invented sleep data for a random sample of 10 juniors
Student
1
2
3
4
5
6
7
8
9
10
Hours of sleep
7
6.5
8
5.5
7
9
6
7.5
6
7.5
Tasks: (1) Name the population, the parameter and the statistic. (2) Compute the sample mean. (Answer: 70/10 = 7.0 hours.) (3) Compute the sample proportion who slept at least 8 hours. (Answer: 2/10 = 0.2.) (4) Write one sentence that estimates each parameter for all 640 juniors, including a word such as "about" or "estimate". (5) Explain why a second random sample of 10 juniors would probably give different answers to (2) and (3).
Closure5-10 minutes
Exit ticket: (1) In your own words, explain the difference between a parameter and a statistic, and say which one changes from sample to sample. (2) A club wants to know the proportion of the school's students who would attend a spring concert. Describe how it could get a random sample of 50 students. (3) Give one reason why asking the students in the band room would not support an inference about the whole school.
Differentiation Strategies
For Struggling Students
Give a four-row organizer (population, parameter, sample, statistic) with a sentence frame for each row, and fill in the first scenario together
Use the memory aid p for population and parameter, s for sample and statistic, and have students circle the number that was computed from data
In the bag simulation, let students compute p̂ as a fraction first and convert to a decimal only after the class dot plot is built
For Advanced Students
Ask students to explain why a random sample of 1,000 adults can estimate a proportion for a country of millions about as well as for a city of 100,000, as long as the population is much larger than the sample
Have students compare simple random sampling with stratified sampling by grade level and argue when stratifying would give more consistent estimates
Ask students to find a news report that states a percentage from a poll and identify its population, sample size and how the sample was chosen
Assessment Guidance
What to Look For
Listen for the four terms used correctly: students should call the computed value a statistic and the unknown population value a parameter, not the reverse. Strong inference statements name the population the sample came from, use "about" or "estimate" rather than "exactly", and do not stretch the conclusion to a larger group. When a sampling method is not random, students should name the specific way it could over- or under-represent part of the population, not just say "it's biased".
02
Classroom Activities
3 Activities
1
The Population in a Bag
25 minGroups of 3-4
Each group gets a paper bag holding 200 slips, of which 60 say Yes and 140 say No. Students do not know the mix. They take random samples, compute p̂ and pool their results into a class dot plot, then estimate the parameter before the teacher reveals it.
Procedure
Shake the bag, draw 10 slips without looking, record the number of Yes slips, and return the slips. Repeat until the group has 5 samples of size 10
Compute p̂ for each sample and place a sticky dot for each one on a class number line from 0 to 1
Each group then draws 3 samples of size 40 and adds those p̂ values to a second number line
Before the reveal, each group writes an estimate of the proportion of Yes slips in the bag and a sentence explaining how confident it is
Reveal the parameter: 60 of 200, so p = 0.30. Compare it with the center and spread of each dot plot
Discussion Questions
Why did different groups get different values of p̂ from identical bags?
Which dot plot is more tightly clustered around 0.30, and why?
What would happen to the estimate if one group peeked and picked slips it could see?
Modification for Distance Learning
Replace the bag with a random number generator: integers 1-200, where 1-60 count as Yes. Students enter their p̂ values in a shared spreadsheet that builds the dot plot.
2
Can We Infer? Sampling-Plan Sort
20 minPairs
Pairs sort 8 cards into two piles: plans that support an inference to the stated population and plans that do not. For each card in the second pile, they name the problem and rewrite the plan so it would work.
The 8 Cards
To estimate the mean age of cars in a city, record the cars in one new-car dealership's lot (does not support: those cars are not typical)
To estimate the proportion of a school's 900 students who own a bike, draw 60 ID numbers with a random number generator (supports)
To estimate support for a later school start, post an optional online form in the school newsletter (does not support: voluntary response)
To estimate the mean weight of apples in a 500-crate orchard shipment, choose 20 crates at random and weigh every apple in them (supports, with care that apples in a crate are alike)
To estimate the proportion of adults in a county who have a library card, call 300 numbers chosen at random from a list of all county phone numbers (supports, if nearly all adults have a listed number)
To estimate the mean time teens spend on homework, ask the 25 students in the library after school (does not support: convenience sample)
To estimate the proportion of defective chargers in a batch of 5,000, test every 100th charger starting from a randomly chosen one among the first 100 (supports if defects do not repeat in a pattern)
To estimate the proportion of U.S. teens who play a school sport, survey a random sample of students at one high school (does not support: the sample comes from one school, not all U.S. teens)
Procedure
Each pair sorts the cards, then writes the population and the parameter on each card
For every card in the "does not support" pile, the pair writes a better plan on the back
Two pairs compare piles and resolve any disagreements
Challenge Variation
Pairs write a ninth card whose plan looks random but still does not support the stated inference, then trade with another pair.
3
Judgment Versus Chance: Mean Word Length
20 minIndividual, then whole class
Students estimate the mean word length of a 100-word passage two ways: with a sample of 5 words they choose because they seem typical, and with a sample of 5 words picked by random numbers. Comparing the two class dot plots shows how a human choice can pull an estimate away from the parameter.
Procedure
Give each student the printed passage with its 100 words numbered 00-99
Round 1: in 30 seconds, circle 5 words that look typical, count their letters and compute the mean. Add it to the "judgment" dot plot
Round 2: use a random number generator to pick 5 two-digit numbers from 00-99, find those words, and compute the mean. Add it to the "random" dot plot
The teacher, who counted every word ahead of time, reveals the population mean
Discussion Questions
Which dot plot is centered closer to the population mean? Why might people choose longer words by eye?
Both plots vary. What is different about the kind of error in each one?
Would choosing 20 words by judgment instead of 5 fix the problem?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: From a Random Sample Back to the Population
A population of 60 members, 18 of whom have the trait (filled), so the parameter is p = 0.30. A random sample of 10 happened to include 4 with the trait, so p̂ = 4/10 = 0.4. Inference runs from the statistic back to the parameter, and a different random sample would give a different p̂.
Diagram 2: Sample Proportions Vary, Less for Larger Samples
Sample proportions from 30 computer-simulated random samples of size 25 and 30 of size 100, all drawn from a population with p = 0.30, plotted to scale. The samples of 25 range from 0.16 to 0.44; the samples of 100 range from 0.21 to 0.38. Both center near the parameter, and larger samples cluster more tightly.
04
Homework Assignment
~30 min
HSS.IC.A.1 Homework: Inference from Random Samples
Directions: Answer in complete sentences. When you compute a statistic, show the fraction or sum you used. Every inference statement must name the population and use a word such as "about" or "estimate". All data are invented for practice.
Part 1: Parameters, Statistics and Estimates (Problems 1-3)
A county library wants to know the mean number of books borrowed last year by its 36,000 card holders. It randomly selects 250 card holders from its database and finds that they borrowed a mean of 14.6 books. Identify the population, the parameter, the sample and the statistic, and write an inference statement.
A random sample of 80 of the 2,400 students at a high school found that 52 eat breakfast on school days. Compute the sample proportion. Then estimate how many of the 2,400 students eat breakfast on school days, and explain why your answer is an estimate and not an exact count.
A random sample of 6 seniors reported the hours they spent on their phones yesterday: 3.5, 5, 2, 4.5, 6 and 3. (a) Compute the sample mean. (b) A classmate takes a second random sample of 6 seniors and gets a mean of 4.6 hours. Does this mean one of you made an error? Explain, using the words parameter and statistic.
Part 2: Judging Samples and Sample Size (Problems 4-6)
A town council wants to estimate the proportion of its registered voters who support building a new skate park. Three plans are proposed: (a) survey people at the town's current skate park on a Saturday; (b) choose 300 names at random from the list of registered voters and contact each one; (c) post a poll on the local newspaper's website. For each plan, decide whether it supports an inference about the town's registered voters and explain why.
Maya and Jonah draw random samples from the same large population. Maya takes 5 samples of size 20 and gets p̂ = 0.35, 0.55, 0.40, 0.60 and 0.45. Jonah takes 5 samples of size 100 and gets p̂ = 0.47, 0.51, 0.44, 0.49 and 0.52. (a) Find the range and the mean of each student's five values. (b) Whose samples give more consistent estimates, and why? (c) Give a reasonable estimate of the population proportion.
Design a study about a question you care about at your school. State the population and the parameter, describe exactly how you would select a random sample of 40 students, name the statistic you would compute, and write the inference statement you would make if the statistic came out to 0.30.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Vocabulary
Population, parameter, sample and statistic identified correctly every time
One or two terms mixed up
Terms missing or mostly incorrect
Computation
Sample proportions, means, ranges and estimates correct with work shown
Method correct with one arithmetic error
Incorrect or no work shown
Inference Statements
Names the population, estimates the parameter and admits uncertainty
Estimate given but population or uncertainty missing
Claims an exact value or no statement
Judging Samples
Explains why each plan does or does not support inference, naming the specific problem
Correct decisions with vague reasons
Decisions incorrect or unexplained
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Answer each question, then read the explanation. Your score updates as you go, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which of these is a parameter?
Answer: B
A parameter describes an entire population, here all seniors in the state, and is usually unknown. Choices A, C and D are each computed from a sample, so they are statistics. Choice A is a common trap: a mean is not a parameter unless it is the mean of the whole population.
Question 2 of 20 · Multiple Choice
A city randomly selects 200 of its registered voters, and 118 say they support a new library bond. What is the sample proportion p̂?
Answer: C
p̂ = 118/200 = 0.59. Choice A is the proportion who did not say they support the bond (82/200). Choices B and D misplace the decimal point: 118/100 and 118/1000.
Question 3 of 20 · Multiple Choice
A random sample of 150 of a county's households finds that 36% have a vegetable garden. Which conclusion is best supported?
Answer: D
The sample was random and drawn from the county's households, so it supports an estimate for that population; the true percent may differ somewhat because of sampling variability. Choice A ignores sampling variability. Choice B is too cautious: a random sample of 150 does support an estimate. Choice C extends the conclusion to the state, a population that was not sampled.
Question 4 of 20 · Multiple Choice
Why is a random sample needed to make an inference about a population?
Answer: A
Random selection keeps the researcher's choices and the respondents' choices out of the sample, so no part of the population is favored, and statistics from random samples vary in a predictable way that lets us judge the size of chance error. Choice B is false: a random sample gives an estimate, not the exact parameter. Choice D contradicts sampling variability.
Question 5 of 20 · Multiple Choice
A fitness magazine invites readers to answer an online survey about how many days a week they exercise. Which is the main problem with using the results to estimate the exercise habits of all adults?
Answer: B
This is a voluntary response sample drawn from magazine readers: people interested in fitness are more likely both to read the magazine and to answer, so the estimate is likely too high. Choice D is a common misconception: a large number of responses does not fix a biased method.
Question 6 of 20 · Multiple Choice
Two random samples of 60 students are drawn from the same school. One gives p̂ = 0.35 for students who take the bus, the other gives p̂ = 0.43. What is the best explanation?
Answer: A
Statistics vary from one random sample to another even when nothing is wrong, while the parameter, the true proportion for the school, stays fixed. Choice B confuses the statistic with the parameter. Choices C and D assume an error that the difference alone does not show.
Question 7 of 20 · Multiple Choice
All of these random samples come from the same large population. Which sample size tends to give a sample proportion closest to the population proportion?
Answer: D
Larger random samples produce statistics that vary less from sample to sample, so they tend to land closer to the parameter. Diagram 2 shows this for samples of 25 and 100. Choice A, the smallest sample, gives the most variable estimates.
Question 8 of 20 · Multiple Choice
A random sample of 6 students reported minutes of homework last night: 35, 50, 20, 80, 45, 70. What is the sample mean?
Answer: C
The sum is 35 + 50 + 20 + 80 + 45 + 70 = 300, and 300/6 = 50 minutes. Choice A is the median (the mean of 45 and 50), not the mean. Choice B divides by 5 instead of 6. Choice D is the sum, not the mean.
Question 9 of 20 · Multiple Choice
A school has 1,600 students. In a random sample of 80 of them, 12 walk to school. What is the best estimate of the number of students in the school who walk?
Answer: D
p̂ = 12/80 = 0.15, and 0.15 × 1,600 = 240 students. Choice A treats the sample count as the population count. Choice B confuses the percent 15 with a count and multiplies by 10. Choice C subtracts the sample count from the school size.
Question 10 of 20 · Multiple Choice
An inspector randomly selects 30 light bulbs from a shipment of 5,000 and finds a mean lifetime of 1,180 hours. What is the population?
Answer: A
The sample was drawn from this shipment, so the population is the 5,000 bulbs in it. Choice B is the sample. Choice C is larger than the group that was sampled. Choice D is a statistic, not a group.
Question 11 of 20 · Multiple Choice
A report gives four symbols. Which one stands for a population parameter?
Answer: C
μ is the population mean, a parameter. Choices A and B, x̄ and p̂, are the sample mean and sample proportion, which are statistics computed from data. Choice D, n, is the sample size, which describes the sample, not the population.
Question 12 of 20 · Multiple Choice
To estimate how many hours a week the town's adults exercise, a student surveys 50 people leaving a gym. How is the estimate likely to compare with the true mean for all adults in the town?
Answer: B
This convenience sample over-represents people who exercise, so the sample mean is likely to overestimate the population mean. Choice A ignores how the sample was chosen: sample size does not fix bias. Choice D confuses being in the population with being chosen at random from it.
Question 13 of 20 · Multiple Choice
A random sample of 400 teens in California finds that 22% have a paid summer job. To which population does the estimate apply?
Answer: D
An inference applies to the population the random sample was drawn from: teens in California. Choice A extends it to teens who had no chance of being selected. Choice B gives up the inference altogether, and choice C changes the population from teens to all ages.
Question 14 of 20 · Multiple Choice
Which method gives a random sample of 30 of a school's 900 students?
Answer: A
Only choice A lets chance alone decide who is chosen, giving every student the same chance of selection. Choice B is voluntary response, choice C is a convenience sample, and choice D is a judgment sample; each lets people's choices shape the sample.
Question 15 of 20 · Short Answer
To estimate the mean number of hours per week that a company's 900 employees spend in meetings, the human resources office randomly selects 45 employees and finds a mean of 6.2 hours. Identify the population, the parameter, the sample and the statistic.
Population: the company's 900 employees. Parameter: the mean weekly meeting hours μ of all 900 employees (unknown). Sample: the 45 randomly selected employees. Statistic: their mean, x̄ = 6.2 hours. A common error is to call 6.2 the parameter.
Question 16 of 20 · Short Answer
Suppose the office in the previous question took a second random sample of 45 employees. Would its mean be likely to equal 6.2 hours? Would the value the office is trying to estimate change? Explain.
The statistic would probably change, because a new random sample contains different employees; this is sampling variability. The parameter would not change: it is the mean for all 900 employees, one fixed number. The new sample would give a second estimate of the same parameter.
Question 17 of 20 · Short Answer
A random sample of 8 portable speakers of one model from a warehouse of 4,000 had battery lives of 11, 13, 12, 10, 14, 12, 11 and 13 hours. Compute the sample mean and write an inference statement.
The sum is 96 hours, so x̄ = 96/8 = 12 hours. Inference: the mean battery life of the 4,000 speakers of this model in the warehouse is about 12 hours; with only 8 speakers, the true mean could be somewhat higher or lower.
Question 18 of 20 · Short Answer
A school district emails a survey to a random sample of 200 parents chosen from the list of parents who subscribe to the district newsletter. It reports the result as the opinion of all parents in the district. What is the problem with this inference?
The sample is random, but only from newsletter subscribers. The population actually sampled is the subscribers, so the inference applies to them. Parents who do not subscribe had no chance of being chosen, and they may differ (for example, in how involved they are with the school), so the result may not represent all parents. The district should sample from a list of all parents.
Question 19 of 20 · Short Answer
A club randomly selects 50 students from the school's enrollment list and emails them a survey about school lunches, but only 18 reply. Why might the results still not support a good inference about all students, and what could the club do?
The 18 who replied chose to answer, so the final sample is no longer decided by chance alone. Students with strong opinions about lunch, or who check email often, may be more likely to reply, so the results may be biased (nonresponse). The club should follow up with the 32 who did not reply, for example in person, to raise the response rate.
Question 20 of 20 · Short Answer
Anna took 20 random samples of size 10 from a population and got sample proportions from 0.10 to 0.70. Ben took 20 random samples of size 100 from the same population and got sample proportions from 0.31 to 0.49. What does this show, and whose single sample would you rather use to estimate the parameter?
It shows that statistics vary from sample to sample, and that larger random samples vary less: Ben's values span 0.18 while Anna's span 0.60. A single sample of size 100 is more likely to be close to the parameter, so Ben's sample is the better choice. Both sets suggest a population proportion near 0.4.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSS.IC.A.1 mean in simple terms?
It means students should understand statistics as a way to learn about a whole group by studying a random part of it. They take a random sample, compute a statistic such as a sample mean or proportion, and use it to estimate the unknown population parameter, knowing the estimate carries some uncertainty.
What is the difference between a parameter and a statistic?
A parameter describes a population; a statistic describes a sample. The parameter is what we want to know about the whole group; the statistic is what we can actually calculate from the part we measured, and it is our evidence about the parameter.
Is HSS.IC.A.1 taught in Algebra 1, Algebra 2 or Statistics?
It is usually taught in Algebra II or an introductory Statistics course. In integrated pathways it usually appears in Math III. It builds on grade 7 work on random sampling (7.SP.A.1 and 7.SP.A.2).
Why does the sample have to be random?
Because random selection is what lets a sample stand in for the population. When chance decides who is included, no part of the population is systematically favored, and the amount that statistics vary from sample to sample can be described. Samples chosen by convenience or by volunteers can be off in a consistent direction that no amount of data fixes.
Doesn't a bigger sample always give a better estimate?
Only if the sample is random. A larger random sample gives statistics that vary less, so the estimate is usually closer to the parameter. A larger biased sample just repeats the same bias with more data: 10,000 volunteers in an online poll still speak only for people who chose to answer.
What mistakes do students make with populations and samples?
A common one is calling the people surveyed the population. Others include treating a sample statistic as the exact parameter, extending a conclusion to a group that was never sampled (for example from one school to all teens), and believing that a large number of responses makes up for a non-random method.
How is HSS.IC.A.1 connected to margin of error?
It is the foundation for it. HSS.IC.A.1 establishes that statistics vary from sample to sample, so any estimate is uncertain. A later standard, HSS.IC.B.4, asks students to measure that uncertainty with a margin of error found by simulation.
How can I simulate sampling without computers?
Use a bag of paper slips or beads with a known mix, as in Activity 1, or a table of random digits in which some digits stand for the trait. Students draw many samples, compute p̂ for each and build a class dot plot. The physical version makes the variability visible before students see it on a computer.
Does this standard appear on the SAT?
Its ideas can appear in the Problem-Solving and Data Analysis domain of the digital SAT. Students may be asked whether a sample supports a conclusion about a population, or to which population a survey's result can be generalized. They are not asked to run simulations.
What is a good inference statement for a survey result?
A good statement names the population, gives the statistic as an estimate and admits uncertainty. For example: "Based on a random sample of 150 district students, about 42% of the district's high school students have a part-time job; the true percent may be somewhat higher or lower." It should not say "exactly" or apply the result to a group that was not sampled.
07
Related Standards
6 standards
These standards connect to HSS.IC.A.1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
7.SP.A.1Prerequisite
Use a sample to learn about a population; random samples tend to be representative
