1) Skewness: meaning
Skewness measures the degree of asymmetry of a distribution.
- Symmetric distribution: mean = median = mode.
- Positive (right) skew: long tail to the right
Typically: Mean > Median > Mode - Negative (left) skew: long tail to the left
Typically: Mean < Median < Mode
2) Measures of skewness (CUET-level)
2.1 Karl Pearson’s coefficient of skewness
If mode is defined:
If mode is ill-defined (common case):
Interpretation:
- Sk > 0 : positively skewed
- Sk < 0 : negatively skewed
- Sk = 0 : symmetric
2.2 Bowley’s coefficient of skewness (quartile-based)
Merit: less affected by extreme values.
3) Correlation: meaning
Correlation measures the direction and strength of relationship between two variables.