Random Sample
In short: Random sample means a smaller set pulled from a bigger group by chance alone, so each member had the same likelihood of selection and the results stay fair.
7th GradeStatistics7.SP.A.1
What is Random Sample?
Drawing 35 numbered cards from a shuffled stack of every student’s number gives a random sample, because chance alone decides who is included. Asking only the first 35 kids in the cafeteria line would favor early eaters instead.
Randomness keeps the group representative: its percentages tend to mirror those of everybody, so an estimate can be scaled up to the whole population. Larger random draws vary less than small ones.
How to spot it
- A survey has to describe a big crowd, like a school, a town or a factory batch, with no way to ask everyone.
- The problem asks whether a method of choosing people is fair or biased.
- Names are drawn from a hat, numbers come from a random generator, or dice pick the members.
- Percentages from a small group are used to estimate a count for the whole population.
The method
- List or number every member of the population.
- Pick members with a chance device, such as a number generator, shuffled cards or names from a hat.
- Record the answers from the chosen members only.
- Compute the share in the sample, then scale it by the head count of everybody to estimate the total.
Random Sample: solved example
Problem
A Boise middle school enrolls 600 students. A teacher lets a computer pick 40 ID numbers and asks those students whether they pedal to school. Fourteen say yes. Estimate how many of the 600 students bike.
Solution
Sample percentage: \(\frac{14}{40} = 0.35\), or 35%.
Scale to the school: \(0.35 \times 600 = 210\). The estimate is about 210 students who bike.
Try it
Question 1
A coach asks only the players who linger after drills about the team schedule. Does that give a random sample of the whole team?
Show the answer
No. Players who linger may feel differently from the rest, and the quick leavers never get a turn at all.
Question 2
Among 50 shoppers chosen by chance, 18 favor self-checkout. Estimate how many of 2,400 shoppers favor it.
Show the answer
\(\frac{18}{50} = 0.36\) and \(0.36 \times 2{,}400 = 864\) shoppers.
Random Sample vs. Population
The population is everyone the question covers; the random sample is the smaller part you actually measure. The sample exists to describe the population. A sample can be taken in many ways, and only the chance-based way gives each member an equal shot at being picked.
Keep going
Lessons
Worksheets and quizzes
- Random Sampling and Inference – Worksheet
- Random Sampling and Inference – Quiz
- Comparing Two Populations – Worksheet
- Comparing Two Populations – Quiz
Related words
Whole dictionary: A–Z · 7th Grade · Statistics