7.SP.1: Random Samples and Populations
Also written as 7.SP.A.1 and CCSS.MATH.CONTENT.7.SP.A.1 · Cluster: Use random sampling to draw inferences about a population.
The Official Wording
Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
Common Core State Standards, Grade 7, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 7.SP.1 Means in Plain English
Seventh graders learn that a sample can speak for a population only when it looks like that population. To learn about reading time at a 600-student school, 25 names drawn at random from the roster beat 25 students found in the library at lunch.
Random selection is the safeguard: every student has the same 1 in 24 chance, so no group is favored. 7.SP.2 uses random samples to make estimates, and high school treats sampling as the basis of statistical inference (HSS-IC.1).
7.SP.1 I Can Statements
- I can name the population and the sample in a survey.
- I can explain why a sample is or is not representative.
- I can describe a fair way to choose a random sample.
7.SP.1 Worked Example
Three plans for one survey question, and why only one of them can speak for the whole school.
A school of 600 students, 200 in each of grades 6, 7 and 8, wants to know how many minutes students typically read each week. Plan A surveys the 25 students in the library at lunch. Plan B surveys one 7th-grade homeroom of 25. Plan C numbers the roster 1 to 600 and uses a random number generator to pick 25. Which plan gives a representative sample?
- Name the population first: everyone the question is about. Every plan has to be judged against it.Population: all 600 students
- Plan A picks students who chose to spend lunch with books. They likely read more than most, so the sample leans one way.Plan A: biased toward readers
- Plan B is one grade with one teacher’s reading assignments. It cannot speak for 6th or 8th graders.Plan B: only 7th graders, not representative
- Plan C gives every student on the roster the same chance of being picked, so no group is favored.Plan C: each student’s chance is 25/600 = 1/24
Check it: Compare the sample to the school on something already known: a third of the school is in 7th grade, so about a third of Plan C’s 25, roughly 8, should be 7th graders. Plan B has 25 of 25.
Common Mistakes with 7.SP.1
Trusting a large biased sample
We asked 200 shoppers at the bookstore, so the result must be reliable
Try this: Ask who could never have been chosen: 200 bookstore shoppers still leave out nonreaders, and a bigger sample repeats the same lean.
Calling a convenient group random
I picked the first 25 students through the door, so it was random
Try this: Define random as an equal chance for everyone, then use a name draw or a random number generator, not whoever arrives first.
Sampling the wrong population
We surveyed 7th graders to learn about the whole school
Try this: Write the population at the top of the plan and check that every member of it could be picked by the method.
Where 7.SP.1 Fits
Practice 7.SP.1
Quick Check
- A town asks every 10th person leaving a gym how much exercise they get each week. Will the sample represent the town?
- A class of 30 draws 6 names from a hat holding every student’s name once. What is each student’s chance of being chosen?
- Name the population and the sample: a cafeteria surveys 50 randomly chosen students out of 900 about lunch choices.