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.