Assertion (A): A reasonably sized sample drawn randomly from large sized population contains almost all the characteristics which exist in the population.
Reasoning (R): The theory of sampling is based on the two important laws of statistics, viz., Law of statistical Regularity and law of inertia of large numbers.
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Correct option is A

The correct answer is (a) Both (A) and (R) are correct and (R) is the complete explanation of (A).
The Assertion describes the Law of Statistical Regularity, which suggests that a random sample from a large population will likely possess the same characteristics as the whole. This happens because individual biases tend to cancel out as the sample size increases. The Reasoning identifies the two pillars of sampling: the Law of Statistical Regularity (the "why") and the Law of Inertia of Large Numbers (the "consistency"), which states that larger aggregates are more stable than smaller ones. Since these laws provide the mathematical foundation for why a sample represents a population, (R) perfectly explains (A).
Information Booster
· Representativeness: Random selection ensures every unit has an equal chance, minimizing selection bias.
· Large Numbers: The "Inertia" law implies that while individual items fluctuate, the total average remains stable.
· Precision: As sample size increases, the standard error decreases, leading to higher accuracy.
· Cost-Efficiency: These laws allow researchers to draw valid conclusions about millions using only a few thousand observations.