Publication date: 03/23/2021

When you select Use Medians instead of Means, sigma is estimated using a scaled median range or median standard deviation. The table below gives the scaling factors, which were obtained using Monte Carlo simulation.

For subgroups of size n drawn from a normal distribution, the following are true:

• The theoretical median of the ranges is approximately d2_Median*σ, where d2_Median is the value corresponding to n.

• The theoretical median of the standard deviations is approximately c4_Median*σ, where c4_Median is the value corresponding to n.

n |
d2_Median |
c4_Median |
---|---|---|

2 |
0.953 |
0.675 |

3 |
1.588 |
0.833 |

4 |
1.978 |
0.888 |

5 |
2.257 |
0.917 |

6 |
2.471 |
0.933 |

7 |
2.646 |
0.944 |

8 |
2.792 |
0.952 |

9 |
2.915 |
0.959 |

10 |
3.024 |
0.963 |

11 |
3.118 |
0.967 |

12 |
3.208 |
0.969 |

13 |
3.286 |
0.972 |

14 |
3.357 |
0.975 |

15 |
3.422 |
0.976 |

16 |
3.483 |
0.978 |

17 |
3.539 |
0.979 |

18 |
3.590 |
0.980 |

19 |
3.640 |
0.981 |

20 |
3.685 |
0.982 |

21 |
3.731 |
0.983 |

22 |
3.770 |
0.984 |

23 |
3.811 |
0.984 |

24 |
3.846 |
0.985 |

25 |
3.883 |
0.986 |

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