**Question:** Pearson’s Skewness Coefficient is given by

A. (x̄ - μ)² / σ²
B. (x̄ - μ)² / (n * σ²)
C. (x̄ - μ)² / (n * σ²) * (n + 1)
D. (x̄ - μ)³ / (n * σ³)

**Correct Answer:** C. (x̄ - μ)² / (n * σ²) * (n + 1)

**Core Concept:** Pearson's Skewness Coefficient is a measure of the asymmetry of a probability distribution around its mean. It indicates the degree to which the distribution deviates from a normal distribution (Gaussian distribution). Skewness is calculated as the ratio of the squared difference between the sample mean (x̄) and the population mean (μ), divided by the product of the standard deviation (σ) and the square root of (n + 1), where n is the sample size.

**Why the Correct Answer is Right:**

The correct answer (C) is derived from the formula for skewness in a population using a sample. This formula is derived by considering the sample mean (x̄) and the population mean (μ) and dividing the squared difference between them by the product of the standard deviation (σ) and the square root of (n + 1). This calculation accounts for the fact that a larger sample size (n) reduces the impact of the squared difference between the sample mean and population mean on the skewness coefficient.

**Why Each Wrong Option is Invalid:**

A. The formula provided (A) is incorrect, as it involves the population standard deviation (σ) instead of the sample standard deviation (s), which is typically used in calculating skewness using a sample.

B. The formula provided (B) is incorrect, as it includes the term n², which is not present in the correct formula. Including n² would lead to an incorrect skewness value in most cases.

D. The formula provided (D) is incorrect, as it includes the term (n - 1) instead of (n + 1) in the denominator. Using n - 1 would lead to an inaccurate calculation of skewness using a sample.

**Clinical Pearl:**

Understanding Pearson's skewness formula is crucial for interpreting the results of statistical analyses, particularly when dealing with sample data, as it helps to account for the impact of sample size on the calculated skewness value. This is particularly important in medical research, where sample data is commonly used to estimate population parameters, including skewness.

By correctly understanding and applying Pearson's skewness formula, medical researchers can ensure that their findings accurately reflect the distributional properties of the population being studied, leading to more reliable conclusions and informed decision-making in clinical practice and public health interventions.