Accurately calculate kurtosis and skewness for your statistical data. Our user-friendly online tool helps you understand the shape and asymmetry of your dataset distribution, providing crucial insights for various analytical tasks. Simply input your data values to get instant results.
Formula:
The calculator computes Sample Skewness (g1) and Excess Sample Kurtosis (g2) based on your input data. These measures help describe the shape of your data's distribution.
Variables explained:
- xi: Each individual data point
- μ̄ (x̄): The mean (average) of the data set
- s: The sample standard deviation of the data set
- n: The number of data points in the set
1. Sample Skewness (g1) Formula:
g1 = ∑i=1n (xi - μ̄)3 / ( (n-1)(n-2)s3 / n )
(A more common computational form for g1 is: g1 = [ n / ((n-1)(n-2)) ] ∑ ( (xi - μ̄) / s )3)
2. Excess Sample Kurtosis (g2) Formula:
g2 = [ ( n(n+1) / ((n-1)(n-2)(n-3)) ) ∑ ( (xi - μ̄) / s )4 ] - [ 3(n-1)2 / ((n-2)(n-3)) ]
(Note: Skewness requires at least 3 data points, and Kurtosis requires at least 4 data points for calculation.)