Pearsonian measure of skewness –
**Core Concept**
Pearsonian measure of skewness assesses the asymmetry of a distribution using the relationship between the mean, mode, and standard deviation. It is a statistical tool that quantifies the direction and magnitude of skewness in a dataset, particularly useful in descriptive statistics and epidemiological data analysis.
**Why the Correct Answer is Right**
The Pearsonian coefficient of skewness is defined as (Mean β Mode) / Standard Deviation. This formula captures the deviation of the mean from the mode relative to the spread of the data. When the mean is greater than the mode, the distribution is positively skewed; when less, it is negatively skewed. This formula is widely used in social and preventive medicine for analyzing health-related data distributions.
**Why Each Wrong Option is Incorrect**
Option A: Mode β Mean / SD is incorrect because it reverses the direction of the mean-mode difference, leading to a negative skewness value when the actual distribution is positively skewed.
Option C: SD / (Mode β Mean) is dimensionally and mathematically invalid as it introduces an inverse relationship that does not reflect the standard definition of skewness.
Option D: Mean β Mode / SD is structurally correct but appears as a distractor due to incorrect formatting (lack of parentheses); however, it is still mathematically equivalent to option B. Still, B is the standard and accepted form in textbooks.
**Clinical Pearl / High-Yield Fact**
In public health surveys, Pearsonian skewness helps identify whether a health outcome (like income or BMI) is skewed, which affects the choice of central tendency measures and statistical inference.
β Correct Answer: B. Mean - Mode/ SD