Simple random sampling is a way to choose a smaller group from a larger population so that every individual has an equal chance of being selected. It matters because statistics often uses a sample to make an estimate about a whole population. When the sample is chosen fairly, the results are more likely to represent the population accurately.
This method is a foundation for surveys, experiments, quality control, and many data studies.
Key Facts
- In a simple random sample, every individual has the same chance of selection.
- If the population size is N and the sample size is n, then P(one specific individual is selected) = n/N.
- A sample is unbiased when the selection method does not systematically favor some outcomes over others.
- Random selection can be done using random number tables, computer random number generators, or drawing labeled items fairly.
- Sampling without replacement means an individual can be selected only once.
- Larger random samples usually reduce sampling variability, but they do not fix bias from a poor sampling method.
Vocabulary
- Population
- The entire group of individuals or items that a study wants to learn about.
- Sample
- A smaller group selected from the population to collect data from.
- Simple random sample
- A sample chosen so that every possible group of the same size has an equal chance of being selected.
- Bias
- A systematic error caused by a method that tends to overrepresent or underrepresent certain parts of the population.
- Random number generator
- A tool that produces numbers unpredictably so they can be used to choose sample members fairly.
Common Mistakes to Avoid
- Choosing the easiest people to reach is wrong because convenience samples often leave out important parts of the population.
- Letting volunteers choose themselves is wrong because people with strong opinions may be more likely to respond.
- Using a random method without numbering the whole population is wrong because every individual must have a known chance to be selected.
- Assuming a random sample is automatically perfect is wrong because random samples still have sampling variability and can differ from the population by chance.
Practice Questions
- 1 A school has 800 students, and a researcher selects a simple random sample of 40 students. What is the probability that one specific student is selected?
- 2 A population has 250 numbered items from 001 to 250. A random number generator gives 017, 249, 301, 118, 017, 064, and 230. If sampling is without replacement and the desired sample size is 5, which items are selected?
- 3 A teacher wants to estimate average homework time for all students in a school and surveys only students in the library after school. Explain why this is not a simple random sample and describe one better method.