Random-Sampling

Page 1

  • 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

Page 9

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).

Page 23

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.

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