Enter a data set to compute skewness and kurtosis and judge whether the distribution is left- or right-skewed and more peaked or flatter than normal, spotting tail features.
偏度>0 右偏，<0 左偏；峰度>0 比正态更尖。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Sample skewness | g1 = m3 / m2^(3/2), measuring asymmetry of the distribution | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.11 |
| Sample excess kurtosis | g2 = m4 / m2^2 - 3, benchmarked against the normal distribution | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.11 |
| Normal benchmark | The normal distribution has kurtosis 3, i.e. excess kurtosis 0 | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.11 |
| Shape interpretation | Excess kurtosis > 0 means heavier tails and a sharper peak; skewness > 0 means right skew | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.11 |