math class 678 4-in-1 skill sheets
7.SP.A.2 7th Grade Statistics & Probability

Inferences from Random Samples

Use data from a random sample to draw inferences about a population, and gauge the variation in estimates from multiple samples.

How to explain it

At this standard, students use sample data to calculate statistics, draw inferences about a population, and use multiple samples to evaluate the variability and reliability of those inferences.

The anchor students hold onto: Use sample data to estimate a population characteristic — but remember that different samples give different estimates, so inferences are predictions, not exact values.

Drawing inferences from one population sets the stage for 7.SP.B.3 and B.4, where students compare two populations using measures of center and variability to evaluate differences.

Worked examples

Example 1 Calculate Sample Mean
Scores: 80, 75, 90, 85, 70.
Step 1Sum = 80 + 75 + 90 + 85 + 70 = 400.
Step 2Mean = 400 / 5 = 80.
Step 3Inference: we estimate the class average is about 80.
AnswerSample mean = 80; we estimate the class average is about 80
Example 2 Inference from Proportion
6 of 20 sampled prefer biking.
Step 16/20 = 30% prefer biking in the sample.
Step 2Population = 500 students.
Step 330% of 500: 0.30 x 500 = 150 students.
AnswerEstimate about 150 of 500 students prefer biking
Example 3 Compare Two Samples
A mean = 42. B mean = 38.
Step 1Sample A range: 4. Sample B range: 18.
Step 2Both estimate the population mean near 40.
Step 3Sample A is more reliable — less variability.
AnswerBoth infer mean is near 40; Sample A more reliable (less spread)

Common mistakes

What students write The sample mean is the exact population mean.
The fix The sample mean estimates the population mean. Different samples give different means — the true population mean may vary slightly from any single sample.
Try this A student generates 3 random samples (n = 5 each) to estimate the average daily fruit servings at school. Sample means: 1.8, 2.4, and 1.6 servings. Rivera says: "My three samples gave very different results — the range is 0.8 servings. This proves random sampling does not work, and I cannot make an inference." Identify and correct Rivera's error.
What students write If two samples give different means, the sampling method failed.
The fix Variability across samples is normal and expected. Average multiple sample means for the best estimate of the population.
Try this A class randomly surveys 30 students and finds the sample mean for nightly study time is 22 minutes. Tran writes: "The data shows students study exactly 22 minutes per night." Identify and correct Tran's error.

Teacher tip

Head off the two predictable errors before they happen. First: The sample mean estimates the population mean. Different samples give different means — the true population mean may vary slightly from any single sample. Second: Variability across samples is normal and expected. Average multiple sample means for the best estimate of the population.