11th GRADE Random Sampling STATISTICS AND PROBABILITY
Population: A collection of people, objects, places, or things sharing a common characteristic to be studied.
Sample: A subset or subgroup of the population.
Sample vs Population Illustration
Sampling: The process of selecting a sample.
Two types of samples: Non-Probability Samples and Probability Samples.
Probability Samples: Involve random sampling methods.
Random Sampling: A type of sampling in which data is collected using randomization, also known as probability sampling.
Sampling Frame: A researcher's list specifying the population of interest.
Simple Random Sample
Systematic Sample
Stratified Sample
Cluster Sample
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.
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.
Example: Jane selects 7 flavors from a box of lollipops, replacing each flavor she draws.
The situation is SRS with replacement as she can repeatedly select and replace flavors until 7 are identified.
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.
Example: Teacher draws names from a bowl to select 3 students during recitation.
This is SRS without replacement, as students can be called only once.
Stratified Random Sampling: Divides a population into strata differing in key characteristics and selects a random sample from each stratum.
Population is divided into strata for stratified sampling.
Example: Survey to determine student preference for e-books, dividing respondents into classes (grade 1-2, 3-4, 5-6).
This exemplifies stratified random sampling as students are grouped into strata (Class A, B, C).
Systematic Random Sampling: The first unit is randomly selected, with subsequent selections made following a predetermined pattern.
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.
Example: Selecting every 7th member from N=100, starting randomly provides positions 3, 10, 17, 24, 94.
Cluster Sampling: A form of random sampling where the population is divided into clusters. A simple random sample is taken from each selected cluster.
Division of population into clusters for sampling.
Example: Determining average student expenses by randomly selecting 5 undergraduate courses and including all students within those courses.
This situation describes random cluster sampling, as all students in sampled courses are chosen.
Stratification: Divides into different groups, samples from each group (more expensive).
Clustering: Divides into comparable groups, samples some groups, reducing cost.
Select the type of sampling from the Lotto draw:
A. without replacement
B. with replacement
C. stratifying
D. clustering
Repeat of previous question.
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
Repeat of previous question.
DEPED survey on K12 curriculum; identify the claim about sampling:
A. Cluster sampling
B. Equal chance sampling
C. Interest population selection
Repeat of previous question.
Identify the non-characteristic of cluster sampling from options.
Repeat of previous question.
Describe the probability of selection in systematic sampling:
A. known, equal
B. unknown, not equal
C. changing, equal
D. unchanging, not equal
Repeat of previous question.
Non-Probability Samples: Obtained conveniently or purposively; not suitable for statistical inference. Includes judgment, accidental, and purposive sampling.
Convenience sample, Purposive sample, Snowball sample, Quota sample.
Convenience Sampling: Non-probability method where easiest accessible units are selected.
Purposive Sampling: Researchers use judgment to choose members of the population for surveys.
Snowball Sampling: Participants help identify other potential subjects for research.
Quota Sampling: Non-probability method relying on the non-random selection of a predetermined number of units.
Example: A quick street interview represents judgment sampling.
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.