Topic 3.3: Random Sampling and Data Collection

Learning Objectives:

Identify a census and several common random sampling methods.
Describe how to select a simple random sample.
Distinguish between simple random, cluster, stratified, and systematic sampling.
Explain why a sampling method is or is not appropriate for a given situation.
Compare practical advantages and disadvantages of common random sampling methods.

Essential Knowledge:

A census selects all items or subjects in a population.
Sampling without replacement means an item can be selected only once.
A simple random sample (SRS) gives every group of a given size an equal chance to be chosen.
A stratified random sample divides a population into homogeneous strata and takes a simple random sample within each stratum.
A cluster sample divides a population into clusters, randomly selects clusters, and collects data from all individuals in the selected clusters.
A systematic random sample uses a random starting point and a fixed periodic interval.
Different sampling methods have different advantages and disadvantages depending on the population and the question being studied.

Key Vocabulary

Census	A data collection method that includes every individual or item in the population.
Sampling Without Replacement	Sampling in which the same individual or item cannot be selected more than once.
Simple Random Sample (SRS)	A sample in which every group of a given size has an equal chance of being chosen.
Stratified Random Sample	A sample created by dividing a population into strata and taking a simple random sample within each stratum.
Strata	Groups formed from a shared characteristic in stratified sampling.
Cluster Sample	A sample created by randomly selecting whole clusters and collecting data from all individuals in them.
Cluster	A group of nearby individuals or items used in cluster sampling.
Systematic Random Sample	A sample selected from a random start using a fixed periodic interval.
Random Start	The first randomly chosen position in a systematic sample.
Periodic Interval	The fixed step size used after the random start in systematic sampling.
Homogeneous	Similar within a group.
Heterogeneous	Different within a group.

Video 1: Random Sampling and Data Collection

[0:00 – 9:05]

1. [0:00] Topic 3.3 focuses on and .

2. [0:14] We will learn how to collect a simple random sample, or , and how to use , , and random samples.

San Antonio Income Segregation [0:31 – 1:14] The lesson studies median household income in San Antonio, where incomes tend to be similar within neighborhoods but can differ a lot across neighborhoods. Because income is right-skewed, the video uses the median instead of the mean.

3. [1:14] A collects data from all individuals in the .

4. [1:42] If done well, a random sample should be of the population.

How to Select an SRS [2:23 – 2:38]

Every group of a given size must have an equal chance of being selected.
One common method is to number the population and use a random number generator.
Sampling without replacement means the same individual cannot be selected twice.

5. [2:23] In an SRS, every group of a given has an equal chance of being chosen.

6. [2:38] One way to get an SRS is to number the homes and use a to choose households without .

7. [4:11] The citywide SRS might be representative because it includes a good mix of household .

8. [4:11] Even if the SRS is representative, collecting data across the whole city would be very .

9. [5:00] A cluster random sample divides the population into nearby .

10. [5:00] In a cluster sample, a simple random sample of entire clusters is taken, and individuals in selected clusters are included.

11. [6:13] A stratified random sample divides the population into based on a similar characteristic.

12. [6:13] In a stratified sample, a simple random sample is taken within stratum.

13. [7:21] In good cluster sampling, groups are ideally within each cluster, but in good stratified sampling, groups are within each stratum.

14. [8:12] A systematic random sample uses a random and a fixed periodic .

15. [8:12] Surveying every 20th student in a lunch line after a random start is an example of sampling.

16. Reflection: Explain the difference between cluster sampling and stratified sampling. Include what gets randomly selected and what happens after the selection.

Video 2: Sampling Advantages and Disadvantages

[0:01 – 7:42]

Comparing the San Antonio Estimates [0:27 – 2:38] The second video revisits the San Antonio example and compares the sample median estimates from the SRS, cluster sample, and stratified sample to the true city median. The point is not just whether a method is random, but whether it is practical and whether it gives stable estimates in this setting.

17. [3:51] A simple random sample is fairly easy to explain, but it can be difficult to when sampled homes are spread across a city.

18. [4:51] Cluster sampling can be easier to perform because the sampled homes are concentrated in selected .

19. [4:51] Cluster sampling works best when clusters are within and to one another.

20. [6:44] Stratified sampling works best when strata are .

21. [6:44] Because a stratified sample takes some homes from region, it tends to give a more consistent mix of incomes.

22. [6:44] One disadvantage of stratified sampling is that it can be difficult to .

When Methods Work Best [4:51 – 7:42]

SRS is straightforward and random, but it can be hard to collect when the population is spread out.
Cluster sampling is practical when data can be gathered in selected areas and clusters are heterogeneous within themselves.
Stratified sampling is especially useful when strata are homogeneous and a sample from each group improves representation.

23. Reflection: Why might a stratified random sample give a better estimate than a cluster sample in the San Antonio income example, even though it may be harder to collect?

Exit Ticket

A high school wants to estimate the average number of hours students spend on homework each week. Administrators divide students into 9th-, 10th-, 11th-, and 12th-grade groups. Then they randomly choose 25 students from each grade and survey those students.

(a) Identify the population and the sampling method.

(b) Explain why this method could be appropriate for this situation.

(c) Explain why this is not a cluster sample.

(d) Describe one disadvantage or challenge of using this method.

Topic 3.3: Random Sampling and Data Collection

Key Vocabulary

Video 1: Random Sampling and Data Collection

Video 2: Sampling Advantages and Disadvantages

Exit Ticket

Class Responses (Esc to close)