Enter a data set (or count, minimum, Q1, median, Q3 and maximum) to compute Q1, Q2, Q3 and the interquartile range, and mark outlier bounds by the 1.5 x IQR rule for box plots.
超出边界的数据点可视为异常值。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Interquartile range | IQR = Q3 - Q1, spanning the middle 50% of observations | Tukey JW, Exploratory Data Analysis (1977), Addison-Wesley |
| 1.5 IQR outlier rule | Flag as outliers: x < Q1 - 1.5·IQR or x > Q3 + 1.5·IQR | Tukey JW, Exploratory Data Analysis (1977) |
| Extreme value rule | Values beyond Q1 - 3·IQR or Q3 + 3·IQR are far-out extremes | Tukey JW, Exploratory Data Analysis (1977) |
| Normal-population relation | For a normal population IQR ≈ 1.349·sigma, hence sigma ≈ IQR / 1.349 | NIST/SEMATECH e-Handbook of Statistical Methods, normal quantiles |