Skewness Calculator
Skewness Calculator computes the sample skewness of a dataset, measuring its distribution’s asymmetry. Positive skewness indicates a right-skewed distribution, while negative indicates left-skewed.
Enter comma-separated values (e.g., 1,2,3,4):
Methodology Used in Skewness Calculator
The calculator computes sample skewness using:
1. Skewness: \\( S = \frac{n}{(n-1)(n-2)} \cdot \frac{\sum (x_i – \bar{x})^3}{s^3} \\)
Where:
- \\( S \\): Sample skewness
- \\( n \\): Sample size
- \\( x_i \\): Data points
- \\( \bar{x} \\): Sample mean
- \\( s \\): Sample standard deviation
Measures asymmetry relative to a normal distribution.
Example Calculation
Sample Input
Dataset = 1, 2, 3, 4, 5
Step 1: Mean: \\( \bar{x} = \frac{1+2+3+4+5}{5} = 3 \\)
Step 2: Standard deviation: \\( s = \sqrt{\frac{\sum (x_i – 3)^2}{4}} = \sqrt{\frac{10}{4}} \approx 1.58 \\)
Step 3: Third moment: \\( \sum (x_i – 3)^3 = 0 \\)
Step 4: Skewness: \\( S = \frac{5}{4 \cdot 3} \cdot \frac{0}{1.58^3} = 0 \\)
Result: Skewness = 0 (symmetric).