Math calculators
Descriptive statistics
Mean, median, mode, range, sample or population standard deviation and variance, quartiles, IQR, skewness and kurtosis.
Inputs
Results
Methodology
Conventions
- Sample statistics divide by n − 1 (Bessel's correction); population statistics divide by n.
- Quartiles interpolate between ordered values (Hyndman and Fan type 7, as in Excel and NumPy).
- Sample skewness and excess kurtosis use the adjusted estimators of Excel's SKEW and KURT.
References
- Hyndman and Fan, Sample quantiles in statistical packages, The American Statistician (1996)
- Joanes and Gill, Comparing measures of sample skewness and kurtosis (1998)
Formulas
- Mean
- \bar x = \frac{1}{n}\sum x_i
- Sample variance
- s^2 = \frac{1}{n - 1}\sum (x_i - \bar x)^2
- Standard error
- SE = s / \sqrt{n}
- Skewness
- G_1 = \frac{\sqrt{n(n - 1)}}{n - 2} \cdot \frac{m_3}{m_2^{3/2}}