IB MYP 4-5 Maths- Sampling techniques- Study Notes - New Syllabus
IB MYP 4-5 Maths- Sampling techniques – Study Notes
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IB MYP 4-5 Maths- Sampling techniques – Study Notes – All topics
Sampling Techniques
Sampling Techniques
Sampling is the process of selecting a smaller group (sample) from a larger group (population) to collect data and make conclusions about the entire population.
Key Terms:
- Population: The entire group you are studying. Example: All students in a school.
- Sample: A smaller group selected from the population for analysis. Example: 50 students chosen from the school.
- Census: Collecting data from the entire population (very time-consuming and costly).
- Bias: A sample that does not fairly represent the population. Example: Asking only basketball players about favorite sports.
Why Use Sampling?
- It is quicker and cheaper than a census.
- Provides useful estimates if the sample is representative.
Main Sampling Methods:
| Method | Description |
|---|---|
| Random Sampling | Each member of the population has an equal chance of selection. Example: Drawing names from a hat. |
| Systematic Sampling | Choose every nth item from a list after a random start. |
| Stratified Sampling | Divide population into groups (strata) and select random samples from each proportionally. |
| Convenience Sampling | Select individuals easiest to reach (may cause bias). |
Example:
A school has 600 students: 360 boys and 240 girls. A sample of 50 students is needed using stratified sampling. How many boys and girls should be in the sample?
▶️Answer/Explanation
Step 1: Find proportion of boys and girls:
Boys: \( \dfrac{360}{600} = 0.6 \), Girls: \( \dfrac{240}{600} = 0.4 \).
Step 2: Allocate sample:
Boys: \( 50 \times 0.6 = 30 \), Girls: \( 50 \times 0.4 = 20 \).
Answer: 30 boys and 20 girls should be selected.
Example:
A researcher selects every 10th household from a list of 1,000 after choosing a random starting point. What sampling method is used?
▶️Answer/Explanation
Answer: This is systematic sampling because items are chosen at regular intervals (every 10th) after a random start.
Advantages of Random Sampling:
- Unbiased if selection is truly random.
- Easy to understand and apply.
Disadvantages:
- Requires a full list of the population.
- Can be time-consuming for large populations.