Random-Sampling

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• 11th GRADE Random Sampling STATISTICS AND PROBABILITY

Page 2: Basic Terms

• Population: A collection of people, objects, places, or things sharing a common characteristic to be studied.

• Sample: A subset or subgroup of the population.

Page 3: Illustration

• Sample vs Population Illustration

Page 4: Sampling

• Sampling: The process of selecting a sample.

• Two types of samples: Non-Probability Samples and Probability Samples.

Page 5: Probability Samples

• Probability Samples: Involve random sampling methods.

Page 6: Random Sampling

• Random Sampling: A type of sampling in which data is collected using randomization, also known as probability sampling.

Page 7: Sampling Frame

• Sampling Frame: A researcher's list specifying the population of interest.

Page 8: Types of Sampling

• Simple Random Sample

• Systematic Sample

• Stratified Sample

• Cluster Sample

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Page 10: Simple Random Sampling (SRS)

• Simple Random Sampling (SRS): The simplest type of random sampling where each element has an equal chance of being selected from the population.

• Two types: SRS with replacement and SRS without replacement.

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Page 12: SRS with Replacement

• SRS with Replacement: Once an element is selected randomly, it is replaced back into the population before drawing the next sample.

• Probability of selection remains unchanged for each draw.

Page 13: Example

• Example: Jane selects 7 flavors from a box of lollipops, replacing each flavor she draws.

Page 14: Example Continuation

• The situation is SRS with replacement as she can repeatedly select and replace flavors until 7 are identified.

Page 15: SRS without Replacement

• SRS without Replacement: Once an element is selected, it is not replaced in the population, making the selected units distinct; probabilities change for each draw.

Page 16: Example

• Example: Teacher draws names from a bowl to select 3 students during recitation.

Page 17: Example Continuation

• This is SRS without replacement, as students can be called only once.

Page 18: Stratified Sample

Page 19: Stratified Random Sampling

• Stratified Random Sampling: Divides a population into strata differing in key characteristics and selects a random sample from each stratum.

Page 20: Illustration

• Population is divided into strata for stratified sampling.

Page 21: Example

• Example: Survey to determine student preference for e-books, dividing respondents into classes (grade 1-2, 3-4, 5-6).

Page 22: Example Continuation

• This exemplifies stratified random sampling as students are grouped into strata (Class A, B, C).

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Page 24: Systematic Random Sampling

• Systematic Random Sampling: The first unit is randomly selected, with subsequent selections made following a predetermined pattern.

Page 25: Explanation

• Use sampling interval k; select every k-th member of the population starting from a random point:

  • Formula: k = N/n where N is the population size and n is the sample size.

Page 26: Example

• Example: Selecting every 7th member from N=100, starting randomly provides positions 3, 10, 17, 24, 94.

Page 27: Cluster Sample

Page 28: Cluster Sampling

• Cluster Sampling: A form of random sampling where the population is divided into clusters. A simple random sample is taken from each selected cluster.

Page 29: Illustration

• Division of population into clusters for sampling.

Page 30: Example

• Example: Determining average student expenses by randomly selecting 5 undergraduate courses and including all students within those courses.

Page 31: Example Continuation

• This situation describes random cluster sampling, as all students in sampled courses are chosen.

Page 32: Stratification vs. Clustering

• Stratification: Divides into different groups, samples from each group (more expensive).

• Clustering: Divides into comparable groups, samples some groups, reducing cost.

Page 33: Let's Try This

Page 34: Multiple Choice Example 1

• Select the type of sampling from the Lotto draw:

  • A. without replacement

  • B. with replacement

  • C. stratifying

  • D. clustering

Page 35: Multiple Choice Example 2

• Repeat of previous question.

Page 36: Multiple Choice Example 3

• Marketing company offers products to every 75th respondent. Identify the sampling type:

• A. Simple Random Sampling

• B. Systematic Random Sampling

• C. Stratified Random Sampling

• D. Random Cluster Sampling

Page 37: Multiple Choice Example 4

• Repeat of previous question.

Page 38: Multiple Choice Example 5

• DEPED survey on K12 curriculum; identify the claim about sampling:

• A. Cluster sampling

• B. Equal chance sampling

• C. Interest population selection

Page 39: Multiple Choice Example 6

• Repeat of previous question.

Page 40: Multiple Choice Example 7

• Identify the non-characteristic of cluster sampling from options.

Page 41: Multiple Choice Example 8

• Repeat of previous question.

Page 42: Multiple Choice Example 9

• Describe the probability of selection in systematic sampling:

• A. known, equal

• B. unknown, not equal

• C. changing, equal

• D. unchanging, not equal

Page 43: Multiple Choice Example 10

• Repeat of previous question.

Page 44: Non-probability Samples

• Non-Probability Samples: Obtained conveniently or purposively; not suitable for statistical inference. Includes judgment, accidental, and purposive sampling.

Page 45: Types of Non-Probability Samples

• Convenience sample, Purposive sample, Snowball sample, Quota sample.

Page 46: Convenience Sampling

• Convenience Sampling: Non-probability method where easiest accessible units are selected.

Page 47: Purposive Sampling

• Purposive Sampling: Researchers use judgment to choose members of the population for surveys.

Page 48: Snowball Sampling

• Snowball Sampling: Participants help identify other potential subjects for research.

Page 49: Quota Sampling

• Quota Sampling: Non-probability method relying on the non-random selection of a predetermined number of units.

Page 50: Example

• Example: A quick street interview represents judgment sampling.

Page 51: Summary

• Sampling is the selection process for a sample. Two types: non-probability and probability samples. Random sampling is conducted through randomization. Major types of probability sampling include simple random sampling, stratified random sampling, systematic random sampling, and random cluster sampling.