A researcher draws repeated random samples of size 100 from a population whose distribution of serum uric acid is markedly skewed. As sample size increases, the sampling distribution of the mean approaches normality even though the parent distribution remains skewed. This property is known as:
- A Law of large numbers
- B Regression to the mean
- C Central limit theorem ✓
- D Law of statistical regularity
Correct answer: C. Central limit theorem
Explanation
The central limit theorem states that for sufficiently large samples the distribution of sample means tends to be normal irrespective of the shape of the underlying population distribution. This is why parametric tests remain valid for large samples from skewed populations. Regression to the mean describes extreme values moving toward the average on repeat measurement, an entirely different concept.
Reference: Mahajan's Methods in Biostatistics for Medical Students and Research Workers, 10th ed.
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