7.SP.4: Compare Two Populations from Samples
Also written as 7.SP.B.4 and CCSS.MATH.CONTENT.7.SP.B.4 · Cluster: Draw informal comparative inferences about two populations.
The Official Wording
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
Common Core State Standards, Grade 7, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 7.SP.4 Means in Plain English
Seventh graders compare two populations from random samples, using a center and a spread together. Ten random 7th graders read a mean of 30 minutes a night and ten random 8th graders read 25, but with MADs of 10 and 12 minutes, that gap is only half a MAD.
So the honest conclusion is no clear difference between the grades; a gap of two or three MADs would have been convincing. High school turns these informal comparisons into randomized experiments, judging differences by simulation (HSS-IC.5).
7.SP.4 I Can Statements
- I can compare two random samples using a center and a spread.
- I can tell whether a gap between samples is large or small.
- I can write a conclusion about two populations from sample data.
7.SP.4 Worked Example
Two random samples, one question about two whole grades, and a conclusion that the data cannot quite support.
A school drew a random sample of 10 students from each grade and recorded minutes of reading on a school night. 7th grade: 10, 15, 20, 25, 30, 30, 35, 40, 45, 50. 8th grade: 0, 10, 15, 20, 20, 30, 30, 35, 40, 50. Do 7th graders at the school generally read more?
- Find each center.7th: 300 ÷ 10 = 30 min; 8th: 250 ÷ 10 = 25 min
- Find each spread with the mean absolute deviation.7th MAD = 100 ÷ 10 = 10 min; 8th MAD = 120 ÷ 10 = 12 min
- Size the gap against the spread.30 − 25 = 5 min, about half of either MAD
- Picture the two dot plots. They cover the same stretch and pile up in the same place.9 of the 10 eighth graders fall inside the 7th graders’ 10 to 50 min range
- Infer about the grades, not just these 20 students. A 5-minute gap could easily come from which students happened to be drawn.No clear difference in reading time between the grades
Check it: Compare medians as a second center: 30 minutes for 7th grade and 25 for 8th, the same 5-minute gap. A difference worth claiming would need the centers about two MADs apart, 20 minutes or more here.
Common Mistakes with 7.SP.4
Declaring a winner from the means alone
30 is more than 25, so 7th graders read more
Try this: Divide the gap by the MAD first; 5 minutes against a 10-minute MAD is half a MAD, too small to call a difference.
Stopping at the samples
These ten 7th graders read more than these ten 8th graders
Try this: Write the conclusion about the whole grades, which random samples allow, and say how sure the data let you be.
Comparing samples that were not random
We compared our homeroom with the 8th-grade book club
Try this: Check how each sample was chosen before comparing; a book club overstates reading time, so the gap says nothing about the grade.
Where 7.SP.4 Fits
Practice 7.SP.4
Quick Check
- Random samples of two brands of batteries last a mean of 20 and 32 hours, each with a MAD of 3 hours. Is one brand generally longer lasting?
- Sample A has a median of 14 and an IQR of 8; sample B has a median of 15 and an IQR of 9. Is there a clear difference?
- Why must both samples be random before comparing two populations?