Karl Pearson’s coefficient of skewness lies between ..............

The correct answer is - (–)3 and (+)3

Key Points

• Karl Pearson’s coefficient of skewness measures the asymmetry of a distribution.
• The formula for Karl Pearson’s coefficient of skewness is: (Mean – Mode) / Standard Deviation.
• The value of Karl Pearson’s coefficient lies between (–)3 and (+)3. This range ensures the skewness is quantified effectively for most practical datasets.
• Interpretation of skewness values:
  • Positive skewness: Indicates the tail on the right side of the distribution is longer or fatter.
  • Negative skewness: Indicates the tail on the left side of the distribution is longer or fatter.
  • Zero skewness: Implies a symmetrical distribution.

Additional Information

• Skewness in Statistics:
  • Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable.
  • Positive skew: The mean is greater than the mode, and the distribution is skewed to the right.
  • Negative skew: The mean is smaller than the mode, and the distribution is skewed to the left.
• Other measures of skewness:
  • Bowley’s Coefficient of Skewness: Based on quartiles, defined as (Q3 + Q1 - 2Q2) / (Q3 - Q1).
  • Moment Coefficient of Skewness: Uses higher moments of the distribution.
• Why the range is (–)3 to (+)3:
  • This range is mathematically derived and widely applicable for most natural datasets.
  • Values outside this range may indicate extreme skewness or issues with data validity.