As alluded to in earlier sections, the big idea in this unit is that the way we collect data influences what we can and cannot say about a population.
To avoid the effects of bias on your data, the best method of implementing a study is by using random sampling in which a chance process is used to determine which members of a population are included in the sample.
Types of Non-Biased Sampling Methods
Simple Random Sample (SRS)
A simple random sample (SRS) is a sample in which every group of a given size has an equal chance of being chosen. This means that every individual in the population has an equal chance of being selected for the sample, and that the sample is representative of the overall population.
There are several mechanisms that can be used to obtain a simple random sample, including numbering individuals and using a random number generator, using a table of random numbers, or drawing cards from a deck without replacement. These mechanisms ensure that the sample is selected randomly and that every group of a given size has an equal chance of being chosen.
Simple random sampling is a widely used sampling method because it is relatively easy to implement and provides a representative sample of the population. It is often used as a baseline comparison for other sampling methods and is the basis for many types of sampling mechanisms.
In a calculator, SRS chooses a sample size “n” in a way that a group of individuals in the population has an equal chance to be selected as the sample.
Choosing an SRS using a TI-84 Calculator:
- Label each individual in the population with a different label from 1 to “N,” where N is the total number of individuals in the population.
- Randomize the way you choose the individuals for the sample. Use a random number generator to get “n” different integers from 1 to N, where n is the sample size.
- Select the individuals that were chosen by the calculator. NOTE: When an item from a population can be selected only once, this is called sampling without replacement. When an item from the population can be selected more than once, this is called sampling with replacement.
Stratified Random Sample
Strata are groups of individuals in a population who share characteristics thought to be associated with the variables being measured in a study.
A stratified random sample involves dividing the population into separate strata, based on shared characteristics or attributes. This ensures that the sample is representative of the overall population in terms of these characteristics.
Within each stratum, a simple random sample is then selected using one of the mechanisms described above, such as numbering individuals and using a random number generator or using a table of random numbers. The selected units from each stratum are then combined to form the final sample.
Stratified random sampling is often used when the population is heterogeneous, or diverse, in terms of the characteristics being studied. By dividing the population into strata based on these characteristics, researchers can ensure that the sample is representative of the overall population in terms of these characteristics.
Stratified random samples also reduce variability in the data and give more precise results.
Example
Remember the practice question in the previous section about confounding variables? We could use those as strata!
An example of stratified random sampling might involve conducting a study to investigate the relationship between diet and heart disease. To ensure that the sample is representative of the overall population, the population might be stratified based on age, gender, and income.
We can, then, number individuals using a random number generator or using a table of random numbers. The selected units from each stratum would then be combined to form the final sample.
This approach would ensure that the sample is representative of the overall population in terms of age, gender, and income, allowing researchers to more accurately interpret the results of the study. It would also allow researchers to investigate any potential interactions between these variables and the relationship between diet and heart disease.
Cluster Sample
A cluster sample involves the division of a population into smaller groups, called clusters. Ideally, there is heterogeneity within each cluster, and clusters are similar to one another in their composition. A simple random sample of clusters is selected from the population to form the sample of clusters. Data are collected from all observations in the selected clusters.
How is this different from stratified sampling? In a cluster sampling design, the population is first divided into smaller groups, or clusters, and a sample of these clusters is selected. Data is then collected from all observations within the selected clusters.
One of the main advantages of cluster sampling is that it can be more cost-effective and efficient than simple random sampling, especially when the population is spread out over a large geographic area. It is also useful when it is difficult to obtain a complete list of the individuals in the population, as is often the case in developing countries or in studying hard-to-reach populations.
However, cluster sampling can also introduce bias if the clusters are not representative of the overall population. It is important to carefully consider the sampling frame and the sampling method to ensure that the sample is representative of the population.
Example
Imagine that you're a researcher who wants to study the attitudes of high school students towards school lunches. You want to study a sample of high schools in a large city to get a sense of the attitudes of students across the city. Instead of sampling students from all the high schools in the city individually (which would be time-consuming and expensive), you decide to use cluster sampling.
First, you divide the high schools in the city into clusters based on geographic location (e.g., north, south, east, west). Then, you randomly select a sample of these clusters (e.g., you might randomly select the north and west clusters). Finally, you collect data from all the students in the selected clusters to get a sample of students from across the city.
In this example, the population is all high school students in the city, the clusters are the geographic regions of the high schools, and the sample is the students in the geographic region selected.
Systematic Random Sample
A systematic random sample is unique in that sample members are selected from a population by starting at a randomly chosen point and then selecting every kth element from the sampling frame, where k is the periodic interval.
For example, if you have a list of 1000 people and you want to select a sample of 100 people using a systematic random sample, you might choose a random starting point between 1 and 10, and then select every 10th person on the list (e.g., the 1st person, the 11th person, the 21st person, and so on). This ensures that every member of the population has an equal probability of being selected.
Systematic random sampling is a popular sampling method because it is relatively easy to implement and it can be more efficient than simple random sampling. However, it is important to ensure that the periodic interval (k) is chosen correctly to avoid introducing bias into the sample. For example, if the periodic interval is not chosen randomly, it may result in oversampling or undersampling of certain subgroups within the population.
Example
Imagine that you are a researcher who wants to study the attitudes of grocery store customers towards the store's loyalty program. You want to study a sample of customers from a large grocery store chain to get a sense of the attitudes of customers across the chain. Instead of sampling customers from all the stores in the chain individually (which would be time-consuming and expensive), you decide to use systematic random sampling.
First, you create a list of all the customers who have shopped at the store in the past month. This list will be your sampling frame. Next, you choose a random starting point on the list (e.g., you might choose the 15th person on the list). Finally, you select every 10th person on the list after the starting point (e.g., the 15th person, the 25th person, the 35th person, and so on). This will give you a sample of customers from across the chain.
In this example, the population is all customers who have shopped at the store in the past month, the sampling frame is the list of customers, and the sample is the customers selected according to the periodic interval.
Altogether, being able to identify which method to use depends on what the question is asking. Identify the population and variables to figure out how large of a difference there is between the sample. Make your decision based on that information.
Practice Problem
You are a researcher who wants to study the attitudes of college students towards climate change. Your goal is to get a sense of the attitudes of college students across the United States. You have a budget of $$10,000 and six months to complete the study.
There are three potential sampling methods that you could use:
- Simple random sampling: You could create a list of all the college students in the United States and use a random number generator to select a sample of students from the list. This method would ensure that every student in the population has an equal chance of being selected, but it would be time-consuming and expensive to create a complete list of all the college students in the United States.
- Cluster sampling: You could divide the college students in the United States into clusters based on geographic location (e.g., east coast, west coast, midwest) and randomly select a sample of these clusters. You could then collect data from all the students in the selected clusters. This method would be more efficient and cost-effective than simple random sampling, but it could introduce bias if the clusters are not representative of the overall population.
- Systematic random sampling: You could create a list of all the college students in the United States and choose a random starting point on the list. You could then select every 100th student on the list after the starting point to get a sample of students from across the United States. This method would be relatively easy to implement and could be more efficient than simple random sampling, but it could introduce bias if the periodic interval (100 students) is not chosen randomly.
Which sampling method do you think would be the best to use in this situation, and why?
Answer
In this situation, cluster sampling might be the best method to use because it would be more efficient and cost-effective than simple random sampling, and it would not require creating a complete list of all the college students in the United States. However, it is important to ensure that the clusters are representative of the overall population to avoid introducing bias into the sample.
Here's the fun part: AP Stats graders are actually open-minded if you picked either simple random sampling or systematic random sampling (instead of cluster sampling). Your job is to create a very persuasive argument that'll convince them that either sampling method might work, too (in comparison to the other two)!
🎥 Watch: AP Stats - Sampling Methods and Sources of Bias
Vocabulary
The following words are mentioned explicitly in the College Board Course and Exam Description for this topic.
| Term | Definition |
|---|---|
| census | A data collection method that selects all items or subjects in a population. |
| cluster | Concentrations of data usually separated by gaps in a distribution. |
| cluster sample | A sampling method in which a population is divided into smaller groups called clusters, and a simple random sample of clusters is selected, with data collected from all observations in the selected clusters. |
| population | The entire group of individuals or items from which a sample is drawn and about which conclusions are to be made. |
| random number generator | A tool or method used to randomly select items from a population for inclusion in a simple random sample. |
| sample | A subset of individuals or items selected from a population for the purpose of data collection and analysis. |
| sampling method | A specific procedure or technique used to select a subset of individuals from a population for data collection and analysis. |
| sampling with replacement | A sampling method in which an item selected from a population can be selected again in subsequent draws. |
| sampling without replacement | A sampling method in which an item selected from a population cannot be selected again in subsequent draws. |
| strata | Separate groups within a population created by dividing it based on shared attributes or characteristics for stratified sampling. |
| stratified random sample | A sampling method in which a population is divided into separate groups called strata based on shared characteristics, and a simple random sample is selected from each stratum. |
| systematic random sample | A sampling method in which sample members are selected from a population according to a random starting point and a fixed, periodic interval. |
Frequently Asked Questions
What's the difference between sampling with replacement and without replacement?
Sampling with replacement vs. without replacement is simple but important (CED DAT-2.C.1). - With replacement: once you pick an item (or person), you put it back so it can be picked again. Each draw is independent and has the same probabilities every time. This is often used in probability models and some simulations. - Without replacement: once an item is picked, it can’t be picked again. Draws are dependent because the composition of the population changes after each pick. Many real-world surveys (like drawing names from a hat or selecting people for an SRS) use without replacement. Why it matters for AP Stats: an SRS requires every group of a given size to have equal chance (DAT-2.C.2)—you can get an SRS either by ignoring repeats from a random-number list (effectively without replacement) or by using replacement when the problem specifies it. For calculations, with replacement → independent trials (use binomial models); without replacement → dependent trials (use hypergeometric unless n is ≤10% of the population, then dependence is negligible). Practice problems and more on sampling are in the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew), the Unit 3 overview (https://library.fiveable.me/ap-statistics/unit-3), and lots of AP-style practice (https://library.fiveable.me/practice/ap-statistics).
How do I know if a study is using simple random sampling or not?
Simple random sampling (SRS) means every possible group of the chosen size has an equal chance of being selected (CED DAT-2.C.2). To tell if a study used an SRS, ask these quick checks: - Did they number every individual in the population and use a random number generator or table to pick numbers? (Yes → likely SRS.) - Did they pick individuals one at a time ignoring repeats (sampling without replacement)? That’s consistent with SRS. - If they picked entire groups (regions, classrooms) at random and surveyed everyone in those groups, that’s cluster sampling, not SRS (CED DAT-2.C.4). - If they split the population into homogeneous strata and then sampled randomly within each stratum, that’s stratified sampling (CED DAT-2.C.3). - If they used a fixed interval (every 10th name after a random start), that’s systematic sampling (CED DAT-2.C.5). - If they surveyed everyone, it’s a census (CED DAT-2.C.6). So look for language about “every individual numbered and chosen by random number/table” or explicit statements of cluster/strata/systematic methods. For more examples and practice, check the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew), the Unit 3 overview (https://library.fiveable.me/ap-statistics/unit-3), and practice problems (https://library.fiveable.me/practice/ap-statistics).
When do I use stratified sampling vs cluster sampling?
Use stratified sampling when you want guaranteed, precise representation of known subgroups (strata). Strata are formed so members are similar (homogeneous) on a key characteristic (e.g., grade level, gender). Then take an SRS from each stratum and combine. Stratified reduces variability and improves estimates for those subgroups—use it when you care about subgroup estimates or when a subgroup is rare. Use cluster sampling for practicality and cost when the population is naturally grouped into clusters that each look like the population (heterogeneous within, similar across clusters)—for example, schools or city blocks. Randomly select a few clusters, then collect data from all units in those clusters. Cluster is efficient for widespread populations but usually has larger sampling error than stratified. On the AP exam you should identify which method fits a description (CED DAT-2.C: stratified = homogeneous strata + SRS within strata; cluster = SRS of clusters + all units). For a quick review see the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and try practice problems (https://library.fiveable.me/practice/ap-statistics).
What's the formula for systematic random sampling and how do I calculate the interval?
Systematic random sampling: pick a random starting position r (1 ≤ r ≤ k) and then select every k-th item: r, r + k, r + 2k, … until you have n items. The interval k is k = N / n (rounded appropriately). If N/n isn’t an integer, use k = floor(N/n) or round and make sure your random start r is chosen from 1 to k so every unit has an (approximately) equal chance. This is sampling without replacement (you don’t pick the same item twice). Example: population N = 1,000, want n = 50 ⇒ k = 1000/50 = 20. Choose a random start r from 1–20 (say r = 7), then pick 7, 27, 47, …, 987. On the AP CED this is DAT-2.C.5: you must show a random start and fixed periodic interval. For more review and examples see the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and extra practice (https://library.fiveable.me/practice/ap-statistics).
I'm confused about strata vs clusters - can someone explain the difference?
Short version: strata are groups you form to make your sample more precise by sampling within each group (homogeneous within); clusters are groups you form to make sampling easier by randomly selecting whole groups and measuring everyone in them (heterogeneous within). Details tied to the CED: - Stratified random sample (DAT-2.C.3): divide the population into strata that share a key attribute (e.g., grade level). Then do an SRS inside each stratum and combine those results. Strata are chosen because units within a stratum are similar (low variability)—this reduces sampling error. - Cluster sample (DAT-2.C.4): split the population into clusters that each look like the population (e.g., city blocks). Randomly select some clusters, then measure every unit in those clusters. Clusters should be heterogeneous within and similar to each other. This saves cost/time. When to use which: use stratified sampling when you want more precise estimates for known subgroups; use cluster sampling when a full list of individuals is hard to get but clusters are easy to sample. For review, see the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and more unit resources (https://library.fiveable.me/ap-statistics/unit-3). For practice, try problems at (https://library.fiveable.me/practice/ap-statistics).
How do I identify which sampling method was used in a word problem?
Start by looking for keywords and how the population is broken up or chosen—that tells you the method. Quick checklist (use CED terms): - Simple random sample (SRS): every group of size n has equal chance; look for “randomly select individuals,” “random number generator,” or “numbered list” (DAT-2.C.2). - Stratified: population split into strata (homogeneous groups) and you SRS within each stratum (look for “by grade,” “by gender,” etc.) (DAT-2.C.3). - Cluster: population split into clusters that are mini-populations (heterogeneous within); you randomly pick whole clusters and sample everyone in them (look for “select 5 schools and survey all students”) (DAT-2.C.4). - Systematic: “random start” then every k-th item (e.g., every 10th name) (DAT-2.C.5). - Census: everyone is measured. - Convenience: volunteers or whoever’s easiest. Also note replacement vs without replacement: does an item/person get picked more than once? (DAT-2.C.1). On the exam, explicitly tie wording to these definitions (DAT-2.C). For a quick refresher and examples, check the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and more unit review (https://library.fiveable.me/ap-statistics/unit-3). For extra practice, try problems at (https://library.fiveable.me/practice/ap-statistics).
What are the advantages and disadvantages of each sampling method for the AP exam?
Short answer: each method trades bias, precision, and practicality—know those trade-offs and how the CED definitions apply so you can identify or justify methods on the exam. - Simple random sample (SRS): every group of size n equally likely. - Advantages: unbiased, easy to justify for inference (foundation for many procedures). - Disadvantages: can be costly or impractical for large/population-wide lists. - Stratified random sample (strata = homogeneous groups): SRS within strata. - Advantages: more precise estimates when strata differ (reduces variability), ensures representation of key subgroups. - Disadvantages: requires good strata info and correct allocation; mis-stratifying can hurt. - Cluster sample (clusters = mini-populations, heterogeneous within): - Advantages: efficient and cheaper for geographically spread populations (sample all units in selected clusters). - Disadvantages: larger sampling variability than SRS if clusters differ; risk of undercoverage. - Systematic sample (random start + fixed interval): - Advantages: easy to implement; roughly like SRS if no periodicity. - Disadvantages: can be biased if list has periodic patterns. - Census: - Advantages: measures whole population (no sampling error). - Disadvantages: costly, slow, nonresponse and measurement errors still matter. - With vs without replacement: - Without replacement is usual in surveys (no duplicate units); with replacement simpler theoretically but rarely used in practice. On the AP exam you’ll be asked to identify methods and explain appropriateness (CED DAT-2.C, DAT-2.D). For quick prep, review the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and practice many questions (https://library.fiveable.me/practice/ap-statistics).
When would you use a census instead of sampling?
Use a census when you need data from every unit in the population rather than an estimate from a sample. The CED defines a census as selecting all items/subjects in a population (DAT-2.C.6). A census is appropriate when the population is small and reachable (e.g., all 25 students in a classroom), when legal/administrative reasons require full counts (like a national census), or when you need complete accuracy and can’t tolerate sampling variability. Remember trade-offs: a census removes sampling variability but can be expensive, slow, and still vulnerable to measurement error or nonresponse. For large or hard-to-reach populations, a properly designed sample (SRS, stratified, cluster, or systematic) is usually more practical and aligns with AP objectives about choosing methods and justifying them (DAT-2.D.1, DAT-2.C.*). For a quick refresher, check the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and try practice problems (https://library.fiveable.me/practice/ap-statistics).
How do I solve problems about random number generators and simple random samples?
Think of random-number-generator (RNG) problems as a 3-step checklist: label, generate, decide. 1. Label the population (CED: SRS basis). Give each unit a unique number with the same number of digits. If you’re sampling without replacement, ignore repeats; with replacement, keep repeats. State which you’re doing—that matters for probabilities (DAT-2.C.1). 2. Use the RNG or table to pick numbers. Start at a random place and read blocks of digits equal to your labels. If a number is outside the label range or a repeat you’re ignoring, skip it and continue (DAT-2.C.2; systematic/random-start ideas are related in DAT-2.C.5). 3. Check SRS conditions: every group of the given size must be equally likely. If you stratify, cluster, or use systematic selection, explain why that’s not an SRS (DAT-2.C.3–5). For probabilities, treat selections as binomial when sampling with replacement or when n is small relative to population and sampling is effectively independent (use n p for expected counts). For practice, work through the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and try many problems on Fiveable’s practice page (https://library.fiveable.me/practice/ap-statistics). Those mirror AP exam wording and conditions you’ll be tested on.
What's the step-by-step process for stratified random sampling?
Step-by-step for stratified random sampling (AP Stats style): 1. Define the population and the variable(s) you care about. 2. Identify relevant strata—groups that are homogeneous with respect to the key characteristic(s) (e.g., grade level, gender, region). Explain why strata reduce variability. 3. Decide sample size n and whether you’ll sample with or without replacement (CED notes without replacement is common). 4. Determine how many from each stratum: proportional allocation (ni = n·(size of stratum / population)) or equal/other allocation if justified. 5. Within each stratum, create a sampling frame (list individuals) and use a simple random sample (SRS) to pick ni units (random number generator, table, etc.). 6. Combine the selected units from all strata to form the full sample. 7. Check for potential bias and document method (helps you justify appropriateness on the exam: identify sampling method, cite homogeneity within strata, and SRS within strata). For more practice and AP-aligned reminders, see the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and Unit 3 overview (https://library.fiveable.me/ap-statistics/unit-3). For lots of practice problems, use (https://library.fiveable.me/practice/ap-statistics).
I don't understand when cluster sampling is appropriate vs when it's not good to use
Use cluster sampling when it's practical and the population naturally falls into groups (clusters) that look like mini–populations—and each cluster is internally diverse (heterogeneous) while clusters are similar to each other. Example: dividing a city into neighborhoods, randomly selecting some neighborhoods, then surveying every household in those selected neighborhoods. That matches DAT-2.C.4: pick clusters at random and collect from all units in chosen clusters. Don't use cluster sampling when clusters are very different from one another or when clusters are internally homogeneous for the characteristic you care about—that can give biased, unrepresentative results and inflate sampling error. Also avoid it when you can easily do a simple random or stratified sample (those give better precision if you care about subgroups). Quick tip for the AP: identify cluster sampling by “randomly choose groups, then sample everyone in chosen groups.” See the Topic 3.3 study guide for examples (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and practice more problems at (https://library.fiveable.me/practice/ap-statistics).
How do I know if the groups in a problem are homogeneous or heterogeneous?
Homogeneous groups have members who share the same key characteristic(s); heterogeneous groups contain a mix of different types. In AP terms: stratified sampling splits the population into strata that are homogeneous (e.g., males vs. females, grade levels) and then you take an SRS from each stratum. Cluster sampling splits the population into clusters that should be heterogeneous within and similar to one another (each cluster is like a mini-population), and you sample whole clusters. Quick checklist to decide: - Were groups formed by a shared attribute that’s relevant to the question? → homogeneous → stratified. - Are groups natural, intact mini-populations (each contains a mix like the whole pop) and clusters look alike? → heterogeneous within clusters → cluster sampling. - If unsure, ask: “Does the grouping reduce within-group variability for the thing I care about?” If yes, it’s homogeneous. This matches DAT-2.C (strata = homogeneous, clusters = heterogeneous). For more examples and practice, see the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and extra practice (https://library.fiveable.me/practice/ap-statistics).
What's the difference between systematic sampling and simple random sampling?
Simple random sample (SRS): every possible group of the chosen size has an equal chance of being selected. Practically, you number the population and pick numbers with a random number generator or table (sampling usually without replacement). That guarantees no systematic pattern and is the basis for many inference procedures on the AP exam (CED DAT-2.C.2). Systematic random sample: pick a random starting point, then select every k-th unit (random start + fixed interval)—e.g., every 10th name after a random start (CED DAT-2.C.5). It’s easier to carry out but can introduce bias if the list has a periodic pattern that lines up with your interval. Key difference: SRS gives equal chance to every group; systematic uses a random start plus a regular interval. For more examples and AP-style practice, see the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and practice problems (https://library.fiveable.me/practice/ap-statistics).
Can someone explain why you would divide a population into strata vs clusters?
You divide into strata when you want to reduce variability and make estimates more precise: strata are homogeneous groups (same characteristic, e.g., grade level), you take a simple random sample from each stratum, then combine results (CED: stratified random sample, DAT-2.C.3). Use strata when a characteristic is strongly related to the outcome so sampling within each group gives better representation. You divide into clusters when you need practicality or lower cost: clusters are mini-populations that should be heterogeneous internally and similar to each other (CED: cluster sample, DAT-2.C.4). You randomly pick whole clusters and survey all units in them—good when the population is geographically spread out, but it usually gives less precision than stratified sampling. On the AP exam you’ll be asked to identify which method fits a description (DAT-2.C and DAT-2.D). For a quick review see the Topic 3.3 study guide (https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew) and practice lots of examples (https://library.fiveable.me/practice/ap-statistics).
How do I determine if a sampling method is appropriate for a given situation on the FRQ?
Ask three quick questions for the situation: Who is the population? What exactly are you trying to estimate/compare? What resources or constraints matter (time, cost, access)? Then match a sampling method to those answers using CED ideas. Steps to decide on the FRQ: - Check representativeness and bias: Will the method give every relevant unit a chance? If not, it’s likely biased (avoid convenience or voluntary samples unless justified). - Match method to goal/structure: If every small group should be represented, use stratified (homogeneous strata, DAT-2.C.3). If natural groups exist and you’ll survey whole groups, cluster is OK (heterogeneous within clusters, DAT-2.C.4). If every k-th name is chosen after a random start, that’s systematic (DAT-2.C.5). If every possible sample of size n must be equally likely, say SRS (DAT-2.C.2). - Consider practicality: census (DAT-2.C.6) is best but often infeasible; clusters can save cost but increase variability. - State replacement: note if sampling with or without replacement matters (DAT-2.C.1). - Justify: in your answer say why the method reduces bias or fits logistics, mention any trade-offs per DAT-2.D.1. Use AP wording (identify method, justify why appropriate/ not) and check practice FRQs on Fiveable (study guide: https://library.fiveable.me/ap-statistics/unit-3/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew; unit overview: https://library.fiveable.me/ap-statistics/unit-3).