7.SP.2: Draw Inferences from Random Samples
Also written as 7.SP.A.2 and CCSS.MATH.CONTENT.7.SP.A.2 · Cluster: Use random sampling to draw inferences about a population.
The Official Wording
Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
Common Core State Standards, Grade 7, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 7.SP.2 Means in Plain English
Seventh graders use a random sample to estimate something about a population they cannot fully measure. If 22 of 40 randomly chosen students back Candidate A, about 55% of all 800 students might, which predicts roughly 440 votes.
Then they draw more samples of the same size, see estimates like 62.5% and 47.5%, and say how far off a prediction might be. High school turns that spread into a margin of error found by simulation (HSS-IC.4).
7.SP.2 I Can Statements
- I can estimate a population value from a random sample.
- I can scale a sample percent up to the whole population.
- I can use several samples to judge how far off an estimate might be.
7.SP.2 Worked Example
Three random samples from one school election: a prediction, and an honest statement of how far off it might be.
A school has 800 students. Three random samples of 40 students each were asked whom they will vote for. Candidate A got 22, 25 and 19 votes in the three samples. Predict A’s share of the vote and say how far off the prediction might be.
- Turn each sample into a percent for Candidate A.22/40 = 55%, 25/40 = 62.5%, 19/40 = 47.5%
- Pool the three samples for one estimate: 66 votes from 120 students.66 ÷ 120 = 0.55 = 55%
- Scale the estimate up to the whole school.0.55 × 800 = 440 votes for A
- Gauge the error from the spread of the samples: they ran from 47.5% to 62.5%, which is 7.5 points either side of 55%.55% ± 7.5 points, and 7.5% of 800 = 60 votes
- Interpret: one sample of the three had A under half, so a win is likely but not certain.A probably wins, with about 440 of 800 votes, give or take 60
Check it: Scale the estimate back down: 55% of 40 is 22, exactly sample 1. And 440 − 60 = 380 is below 400, half the school, which is why the prediction is not a sure thing.
Common Mistakes with 7.SP.2
Treating one sample as the exact answer
22 of 40 said A, so exactly 440 students will vote for A
Try this: Draw two more samples of 40 and compare; when estimates range from 47.5% to 62.5%, report about 440 votes with a range.
Forgetting to scale up
Candidate A will get 22 votes
Try this: Convert the sample count to a percent first, then take that percent of the population: 55% of 800 students is 440.
Throwing out a sample that disagrees
Sample 3 gave 47.5%, so we did it wrong and should ignore it
Try this: Expect random samples to differ and keep every one; the spread between them is exactly how you gauge the error.
Where 7.SP.2 Fits
Practice 7.SP.2
Quick Check
- In a random sample of 50 students, 18 bring lunch from home. Estimate how many of the school’s 650 students do.
- Four random samples estimate the mean word length in a book as 4.2, 4.6, 4.4 and 4.8 letters. Give an estimate and a sense of the error.
- Why take several samples of the same size instead of one?