AP Statistics Practice Quiz: Random Sampling and Data Collection

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

A high school administrator assigns a unique number to each of the 1,500 students in the school. A computer program is then used to randomly select 150 unique numbers. The students corresponding to these numbers are chosen for a survey. Which sampling method is being used?

A)Simple Random SampleB)Stratified Random SampleC)Cluster SampleD)Systematic Random Sample

All Questions (16)

A) Simple Random Sample

B) Stratified Random Sample

C) Cluster Sample

D) Systematic Random Sample

Correct Answer: A

This is a simple random sample (SRS) because every possible group of 150 students has an equal chance of being selected from the population of all 1,500 students.

A researcher wants to study the academic performance of college students in a state. They first categorize all colleges into 'public' and 'private'. Then, they take a simple random sample of students from each of these two groups. This is an example of which sampling method?

A) Simple Random Sample

B) Stratified Random Sample

C) Cluster Sample

D) Systematic Random Sample

Correct Answer: B

This is a stratified random sample because the population (college students) was divided into homogeneous groups, or strata (public and private), and an SRS was taken from each stratum.

A city is divided into 200 neighborhoods. A polling organization randomly selects 10 of these neighborhoods and attempts to interview every household within those 10 selected neighborhoods. Which sampling method does this describe?

A) Simple Random Sample

B) Stratified Random Sample

C) Cluster Sample

D) Systematic Random Sample

Correct Answer: C

This is a cluster sample because the population was divided into clusters (neighborhoods), a random sample of clusters was selected, and data was collected from all individuals within the chosen clusters.

A quality control inspector at a factory needs to check a batch of 5,000 light bulbs. She randomly selects the 7th bulb to come off the assembly line and then selects every 50th bulb thereafter for testing. This is an example of which sampling method?

A) Simple Random Sample

B) Stratified Random Sample

C) Cluster Sample

D) Systematic Random Sample

Correct Answer: D

This is a systematic random sample because it involves selecting members from the population at a fixed interval (every 50th bulb) after a random starting point (the 7th bulb).

A political pollster wants to gauge voter opinion in a state with diverse demographics across urban, suburban, and rural areas. To ensure all three types of areas are represented proportionally, which sampling method would be most appropriate?

A) Stratified random sample, with the area types as strata.

B) Simple random sample, as it gives every voter an equal chance.

C) Cluster sample, with counties as clusters.

D) A census, as it is the only way to get true proportions.

Correct Answer: A

A stratified random sample is most appropriate because the goal is to ensure representation from specific homogeneous groups (strata). By stratifying by area type, the pollster can guarantee that the sample reflects the urban, suburban, and rural makeup of the population.

A researcher draws a sample from a list of names. After a name is selected, it is put back into the pool of names and can be selected again. This process is known as:

A) Sampling without replacement

B) Sampling with replacement

C) A simple random sample

D) A census

Correct Answer: B

Sampling with replacement is the method where an item can be selected more than once because it is returned to the population after each selection.

What is the key characteristic that defines a simple random sample (SRS) of size n?

A) Every individual in the population has an equal chance of being selected.

B) Every group of size n in the population has an equal chance of being chosen.

C) The population is first divided into homogeneous groups before sampling.

D) A random starting point is chosen, and then every k-th individual is selected.

Correct Answer: B

While it is true that in an SRS every individual has an equal chance of being selected, the defining characteristic is that every possible group of the desired size (n) also has an equal chance of being the selected sample. This is a more precise definition.

The administration of a small company with 45 employees decides to survey every single employee about a new healthcare plan. This method of data collection is called a:

A) Simple Random Sample

B) Cluster Sample

C) Systematic Sample

D) Census

Correct Answer: D

A census is a data collection method that includes every item or subject in the entire population. Since all 45 employees are being surveyed, it is a census.

What is the primary distinction between stratified random sampling and cluster sampling?

A) Stratified sampling uses homogeneous groups, while cluster sampling uses heterogeneous groups.

B) A sample is taken from every group in stratified sampling, whereas only a sample of groups is chosen in cluster sampling.

C) Cluster sampling is a type of simple random sample, while stratified sampling is not.

D) Stratified sampling is only used for small populations, while cluster sampling is for large populations.

Correct Answer: B

In stratified sampling, the population is divided into strata, and a random sample is drawn from ALL strata. In cluster sampling, the population is divided into clusters, a random sample of the CLUSTERS is chosen, and then all individuals within the chosen clusters are surveyed.

A process where an item from a population can be selected only one time for a given sample is known as:

A) Sampling with replacement

B) Sampling without replacement

C) A census

D) A systematic sample

Correct Answer: B

Sampling without replacement means that once an individual or item is selected for the sample, it is removed from the population and cannot be selected again.

A national park is home to a specific type of pine tree. The park is geographically diverse, with mountains and valleys. A biologist wants to estimate the average height of these trees. They divide the park into 50 equally-sized plots, randomly select 5 plots, and measure every pine tree in those 5 plots. Why might this cluster sampling method be inappropriate for this situation?

A) It is too much work to measure every tree in the selected plots.

B) The plots chosen might all be in the valleys, or all on the mountains, leading to an unrepresentative sample.

C) A simple random sample would require numbering every tree, which is impossible.

D) The sample size of 5 plots is too small to draw any conclusions.

Correct Answer: B

A disadvantage of cluster sampling is that the clusters themselves might not be representative of the population. If the selected plots (clusters) are not a good mix of the different terrains, the sample could be biased. For example, trees in valleys may be taller than trees on mountains.

In a stratified random sample, the population is divided into strata. The ideal characteristic of these strata is that each one is:

A) As heterogeneous as possible.

B) As homogeneous as possible.

C) A small-scale version of the overall population.

D) Geographically convenient.

Correct Answer: B

Stratified random sampling works best when the population is divided into strata that are homogeneous, meaning the individuals within each group share a similar characteristic relevant to the study.

A large corporation wants to survey its employees, who are spread across many office buildings throughout a city. To reduce travel time and costs, the research team randomly selects 5 of the 30 office buildings and surveys every employee within those 5 buildings. The primary advantage of this cluster sampling method in this context is:

A) It provides a more accurate estimate of the population parameter than an SRS.

B) It is more practical and less costly than other methods that require sampling from all locations.

C) It guarantees that every employee has an equal chance of being selected.

D) It ensures that every department within the corporation is represented in the sample.

Correct Answer: B

One of the main advantages of cluster sampling is logistical convenience. By sampling entire clusters (office buildings) that are geographically concentrated, researchers can save significant time and money compared to tracking down randomly selected individuals across all 30 buildings.

A factory assembly line produces 1,000 widgets per day. There is a known, periodic flaw that occurs in every 25th widget due to a machine cycle. If a quality control manager uses a systematic random sample by selecting every 25th widget for inspection, why is this method inappropriate?

A) The sample size will be too small to be meaningful.

B) A simple random sample is always a better choice than a systematic sample.

C) The sampling interval coincides with a periodic pattern in the population, which can lead to a very biased sample.

D) The starting point was not chosen randomly, which invalidates the sample.

Correct Answer: C

A major disadvantage of systematic sampling occurs when there is a hidden pattern or periodicity in the population that aligns with the sampling interval. In this case, the sample could consist entirely of flawed widgets or entirely of non-flawed widgets, making it completely unrepresentative.

The manager of a large apartment complex wants to survey residents about a new parking policy. There are 10 identical buildings in the complex, each with 30 apartments. The manager randomly selects two buildings and surveys all residents in those two buildings. Which sampling method was used?

A) Simple Random Sample

B) Stratified Random Sample

C) Systematic Random Sample

D) Cluster Sample

Correct Answer: D

This is a cluster sample. The population of residents is already divided into clusters (buildings). The manager randomly selects some of the clusters (2 buildings) and collects data from all individuals within the selected clusters.

A university has 30,000 students: 18,000 undergraduates and 12,000 graduate students. A researcher wants to sample 100 students to ask about library services, ensuring the proportion of undergraduates to graduates in the sample matches the university's proportion. Which method should be used?

A) Select an SRS of 100 students from the entire university.

B) Systematically select every 300th student from an alphabetical list.

C) Stratify by student type, then randomly sample 60 undergraduates and 40 graduates.

D) Cluster by major, randomly select 3 majors, and survey all students in those majors.

Correct Answer: C

Stratified random sampling is the most appropriate method. By creating strata based on student type (undergraduate/graduate) and sampling proportionally (18,000/30,000 = 60%; 12,000/30,000 = 40%), the researcher ensures the sample accurately reflects the composition of the population.