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Skewness Formula:
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Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. It describes the extent to which a distribution differs from a normal distribution in terms of symmetry.
The calculator uses the skewness formula:
Where:
Explanation: The third moment measures the asymmetry of the distribution, while dividing by the cube of standard deviation makes the measure dimensionless and scale-invariant.
Details: Skewness is crucial in statistics for understanding the shape of data distribution. It helps identify whether data is symmetric, positively skewed (right-tailed), or negatively skewed (left-tailed), which affects statistical analyses and modeling decisions.
Tips: Enter the third moment (μ₃) and standard deviation (σ) values. Both values must be numerical, and standard deviation must be non-zero. The result is dimensionless and indicates the direction and degree of skewness.
Q1: What do different skewness values indicate?
A: Skewness = 0 indicates symmetric distribution; >0 indicates positive skew (right-tailed); <0 indicates negative skew (left-tailed).
Q2: What is the range of skewness values?
A: There's no fixed range, but typically values between -2 and +2 are common. Extreme values indicate highly skewed distributions.
Q3: When is skewness calculation important?
A: Essential in finance for risk assessment, in quality control for process monitoring, and in research for data normality testing before parametric tests.
Q4: Are there limitations to this measure?
A: Sensitive to outliers and may not fully capture distribution shape in multimodal distributions. Sample skewness may differ from population skewness.
Q5: What are alternative skewness measures?
A: Pearson's first and second skewness coefficients, Bowley's measure, and sample skewness with bias correction are common alternatives.