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.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Nobody can ask every voter in a state or test every light bulb a factory makes, so statisticians study a sample, a smaller group taken from the whole population, and use it to learn about the population. Seventh graders meet the big idea that makes this work: conclusions drawn from a sample are trustworthy only when the sample represents the population fairly.
Random sampling, where every member of the population has an equal chance of being picked, is the best everyday tool for getting a representative sample. Asking only friends, only people at a skate shop, or only the first students through the door builds in bias, because those groups differ in predictable ways from everyone else. Students learn to name the population and the sample in a study, spot sampling methods likely to mislead, and explain why a random sample of a modest size can support valid conclusions about a much larger group, while a large biased sample still cannot.
A survey of 2,000 readers of one sports website is large but still biased toward sports fans. Size helps only when the selection method is fair.
In everyday speech 'random' can mean haphazard, so students think grabbing whoever is nearby is random. In statistics it means every member has an equal chance, which takes deliberate planning.
Students may reject a sample because its results differ slightly from the true value. Random samples vary, and a small difference is expected, not a sign of a bad sample.
A school of 900 students wants to know how many favor a later start time. The council compares surveying 60 students from the basketball team with surveying 60 students chosen at random from the roster. In the random sample, 21 favor a later start. Which survey is better, and what estimate does it give?
Answer: Use the random sample; it suggests about 315 students favor a later start.
Run a quick demonstration with a bag of mixed colored counters as the 'population'. Some students sample by choosing counters they can see on top, others draw blindly, and the class compares results with the true mix. The difference between convenient and random sampling becomes obvious.
Assessment items usually describe a study and ask which sampling method is most representative or what is wrong with a given method. Practicing short written critiques of real headlines and polls builds the reasoning these items require.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: A) 50 students chosen at random from the full school roster
Only the random sample from the whole roster gives every student an equal chance of being picked. The other groups share features that may affect their answers.
Answer: D) The sample is likely biased toward people who support a skate park
People at a skate shop are more likely to skate, so they are more likely to want a skate park than the town as a whole.
Answer: 1/4 (also accepted: 0.25, 25%, 10/40)
10 out of 40 is 10/40, which simplifies to 1/4 or 25%.
Answer: B) Every member of the population has an equal chance of being chosen
A random sample is chosen so that every member of the population is equally likely to be selected, which helps it represent the population.
Answer: 300
20 out of 80 is 1/4 of the sample. One quarter of 1,200 is 300 students.
Answer: D) All workers in the city
The population is the whole group the city wants to learn about: all of its workers. The 400 surveyed workers are the sample.
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
A full lesson with slides, activities and an exit ticket on samples, populations and random sampling, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 7.SP.A.1 with an answer key, ready in about a minute.
Make a worksheet βTurn samples, populations and random sampling into a quiz students answer online that marks itself, with a class summary for you.
Build a test βBecause every member has an equal chance of selection, no group is systematically favored, so the sample tends to mirror the population. Results still vary a little from sample to sample.
No. It is about understanding samples, populations and bias informally. Margins of error and formal inference belong to high school statistics.