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SigmaCalc
How likely are extreme outliers, compared to a normal distribution?
Kurtosis measures how concentrated a distribution is in its tails versus its center — a normal distribution has a raw kurtosis of exactly 3, so this calculator reports 'excess kurtosis' (kurtosis − 3), where 0 means normal-like tail behavior.
Positive excess kurtosis (leptokurtic) means more extreme outliers than a normal distribution would predict — this is a big deal in finance and risk modeling, where underestimating tail risk (a 'fat tail') has historically preceded major market blowups.
Excess kurtosis
-0.141
mesokurtic (similar to a normal distribution)
What you entered
Mean
Σx ÷ 10= 12.7Second moment: average of (x−mean)²
Σ(x−mean)² ÷ n= 17.81Fourth moment: average of (x−mean)⁴
Σ(x−mean)⁴ ÷ n= 907.0217Kurtosis: fourth moment ÷ (second moment)²
907.0217 ÷ 17.81²= 2.8595Excess kurtosis: subtract 3 (normal distribution baseline)
2.8595 − 3= -0.1405Interpretation
excess kurtosis = -0.1405= mesokurtic (similar to a normal distribution)Result
Excess kurtosis: -0.141
Excess kurtosis of -0.141 — this dataset is mesokurtic (similar to a normal distribution).