Are you preparing for the CAIIB ABM exam and finding Sampling Numericals a bit tricky?
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.Why Sampling is Important in CAIIB ABM
These topics often carry direct numerical questions and conceptual MCQs.
Understanding them ensures you can quickly solve questions related to:
- Standard Error of Mean
- Sampling Distribution and its Mean
- Central Limit Theorem (CLT)
- Sample Size determination
- Different Sampling Methods (Random, Stratified, Cluster, Systematic)
Mastering this topic gives you a strong edge in scoring high in Module A – Statistics.
Key Concepts to Master Before Attempting Numericals
1. Types of Sampling
There are several ways to select samples from a population. You should know:
- Simple Random Sampling – Every item has an equal chance of selection.
- Systematic Sampling – Selecting every nth item from the list.
- Stratified Sampling – Dividing the population into subgroups (strata) and taking samples from each.
- Cluster Sampling – Dividing the population into clusters and selecting entire clusters randomly.
2. Sampling Distribution and Standard Error
A sampling distribution is the probability distribution of a sample statistic.
The most common statistic is the sample mean (x̄). The Standard Error (SE) of the mean is given by:
SE = σ / √n
where σ = population standard deviation and n = sample size.
Example: If σ = 600 and n = 100, then SE = 600 / √100 = 60.
3. Central Limit Theorem (CLT)
The CLT states that when the sample size (n) is large (usually n ≥ 30), the sampling distribution of the mean approaches a normal distribution, regardless of the population shape.
4. Relationship Between Population and Sample
- Mean of sampling distribution = Population mean (µ)
- Variance of sampling distribution = σ² / n
Common Numerical Problems and How to Solve Them
| Problem Type | Given Data | What to Find | Formula / Approach |
|---|---|---|---|
| Standard Error of Mean | σ and n | SE | SE = σ / √n |
| Sample Size for Desired SE | σ and SE | n | n = (σ / SE)² |
| Probability for Sample Mean | µ, σ, n, Range (a-b) | P(a < x̄ < b) | Use z = (x̄−µ)/(σ/√n) and find probability from normal table |
| Sampling Proportion | p and n | SE of proportion | SE = √[p(1−p)/n] |
Example Problem 1
Population Mean (µ) = 24, Sample Size (n) = 25.
Find: Mean of sampling distribution.
Solution: Mean of sampling distribution = µ = 24.
Example Problem 2
σ = 600, n = 100.
Find: Standard Error.
Solution: SE = 600 / √100 = 60.
These types of questions are directly asked in the CAIIB ABM exam and can be solved within seconds if formulas are clear.
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Preparation Strategy: How to Use Video + PDF
- Watch my CAIIB ABM Sampling Numericals Video
- Download the Sampling Numericals PDF
- Practice at least 10 questions daily from the PDF to build speed and accuracy.
- Revise the formulas every weekend to keep them fresh in your memory.
Remember, the more you practice, the faster you’ll be in solving numerical questions in the real exam.
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Exam-Day Tips for Sampling Questions
- Write down all known values (µ, σ, n) before substituting in formula.
- Always check whether question is about mean, proportion, or sample size.
- Use the correct formula — small mistakes in denominator (√n) cause errors.
- Keep normal distribution table handy for probability-based questions.
- Skip time-consuming questions and return to them later.
Common Mistakes to Avoid
- Confusing population SD (σ) with sample SD (s).
- Forgetting to take the square root of n when finding SE.
- Using wrong sampling method — revise definitions carefully.
- Ignoring Central Limit Theorem when n ≥ 30.
- Not showing intermediate steps — always write formula first.
Summary Table: Sampling Formulas
| Concept | Formula |
|---|---|
| Standard Error of Mean | SE = σ / √n |
| Sample Size for Given SE | n = (σ / SE)² |
| Standard Error of Proportion | SE = √[p(1−p)/n] |
| Variance of Sampling Distribution | σ² / n |
| Mean of Sampling Distribution | µ |
Conclusion & Motivation
The topic of Sampling Numericals is scoring and easy once you practice it systematically.
Focus on understanding formulas, not memorizing them blindly.
Keep learning, keep practicing — success is just one numerical away!
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