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

Random Sampling

Understand that statistics can be used to gain information about a population by examining a representative sample of it.

How to explain it

At this standard, students identify populations and samples, classify samples as random or biased, and evaluate whether inferences about a population are valid based on the sampling method used.

The anchor students hold onto: A random sample gives every member of a population an equal chance of being selected; random samples tend to be representative, making inferences about the population valid.

A valid random sample makes your inferences reliable — in 7.SP.A.2, you will use random sample data to draw inferences and make predictions about an entire population.

Worked examples

Example 1 Identify Population and Sample
Lottery draw — 50 of 300 names.
Step 1Population: all 300 students in the school.
Step 250 names drawn at random from a hat = the sample.
Step 3Every student had an equal chance of selection.
AnswerPopulation: all 300 students; Sample: 50 drawn
Example 2 Random or Biased?
First 20 at school dance.
Step 1Early arrivers volunteered — not random selection.
Step 2This is a convenience sample (biased).
Step 3Inference about all students: NOT valid.
AnswerBiased — not a valid inference

Common mistakes

What students write A larger sample is always more reliable.
The fix Reliability depends on random selection, not just size. A large biased sample is still biased.
Try this A reporter surveys the first 20 students to arrive at a school dance and concludes that most students enjoy school events. Rivera says the inference is valid because "20 students were asked, and 20 is a reasonable number to survey." Identify and correct Rivera's error.
What students write Any sample taken from a population supports valid inferences.
The fix Only a random sample — where every member had an equal chance of selection — supports valid inferences.
Try this A school places all 600 student names in a hat and randomly draws 30 names to survey about lunch preferences. Tran says the inference about all 600 students is not valid because "30 is only 5% of 600 students — too small a sample." Identify and correct Tran's error.

Teacher tip

Head off the two predictable errors before they happen. First: Reliability depends on random selection, not just size. A large biased sample is still biased. Second: Only a random sample — where every member had an equal chance of selection — supports valid inferences.