**Question:** Pearson's Skewness Coefficient is given BY

A. Kurtosis
B. Standard Deviation
C. Mean
D. Median

**Core Concept:** Pearson's Skewness Coefficient is a measure of the asymmetry of a distribution around its mean. A positive skewness indicates a long right tail, while a negative skewness indicates a long left tail. A value of zero indicates a symmetrical distribution.

**Why the Correct Answer is Right:** Pearson's Skewness Coefficient is defined as the third central moment divided by the square of the standard deviation (μ3/σ^2). This formula demonstrates that it is connected to the standard deviation, which is a measure of the spread of the data.

**Why Each Wrong Option is Incorrect:**

A. Kurtosis: Kurtosis measures the "heaviness" of the tails of a distribution, not its symmetry.
B. Standard Deviation: Standard Deviation is a measure of the dispersion of a dataset, not the symmetry of a distribution.
C. Mean: The Mean (average) is the average value of a dataset, and does not represent the asymmetry of the distribution.

**Clinical Pearl:** Understanding Pearson's Skewness Coefficient is crucial for interpreting the distribution of numerical data, particularly when assessing the impact of interventions or comparing different datasets. A positive skewness indicates a leftward skew, while a negative skewness indicates a rightward skew.

**Correct Answer:** D. Median

**Why the Correct Answer is Right:** The Median is the value that divides the dataset into two equal parts. In a symmetrical distribution, the Median is the same as the Mean. However, for skewed distributions, the Mean and Median can differ, making the Median a more robust measure of the central tendency in skewed datasets.

**Why Each Wrong Option is Incorrect:**

A. Kurtosis: Kurtosis is a measure of the "heaviness" of the tails of the distribution and is not related to the central tendency.
B. Mean: The Mean is the average value of a dataset, which is not relevant for assessing the symmetry of a distribution.
C. Mode: The Mode is the value that appears most frequently in a dataset, which does not represent the central tendency of the distribution as a whole.

**Why the Correct Answer is Right:** In a skewed distribution, the Mean and Median can differ, making the Median a more robust measure of the central tendency when dealing with skewed distributions. In such cases, the Mean is influenced by the extreme values, while the Median remains unaffected.