Analyzing Statistical Descriptions for Falsehood

The question asks to identify the incorrect statement among the given descriptions of statistical measures.

Examining Each Statistical Description

• Option 1: Karl Pearson's Empirical Relationship

  For moderately asymmetrical distributions, Karl Pearson proposed the relationship: $ \text{Mean} - \text{Mode} = 3 (\text{Mean} - \text{Median}) $. This statement accurately describes the empirical relationship.

• Option 2: Coefficient of Variation (CV) as Absolute Measure

  The Coefficient of Variation measures relative dispersion, calculated as $ \text{CV} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100\% $. It compares variability irrespective of the mean's magnitude. Absolute measures of dispersion include variance ($ \sigma^2 $) and standard deviation ($ \sigma $). Therefore, stating CV is an absolute measure is incorrect.

• Option 3: Measure of Skewness Purpose

  Skewness quantifies the asymmetry of a distribution, indicating both the direction (positive or negative) and the extent of the deviation from symmetry. This description is accurate.

• Option 4: Kurtosis Definition

  Kurtosis describes the peakedness or flatness of a distribution's central region (around the mode) relative to a normal distribution. This description correctly defines kurtosis.

Identifying the False Statement

Based on the analysis, the statement that the Coefficient of Variation is an absolute measure of dispersion is false. It is a relative measure used for comparing variability across different datasets.

Therefore, the false description is found in Option 2.