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Range Estimator Table

Ratio of σ to range for random samples of n observations from a normal distribution.

n
2
3
4
5
6
7
8
9
10
12
σ/Range
0.886
0.591
0.486
0.430
0.395
0.370
0.351
0.337
0.325
0.307
  n
14
16
18
20
30
40
50
100
500
1000
σ/Range
0.294
0.283
0.275
0.268
0.245
0.231
0.222
0.200
0.167
0.154

Conversely, for a standard normal distribution, the mean range of (n = ) 2 observations is therefore (1/0.886 = ) 1.13. The ranges of other sample sizes, or other statistical distributions can readily be obtained by simulation - in other words, by repeatedly drawing samples of n observations, and calculating their mean range.

For example using R, for a sample of (n=) 13 observations from a standard normal distribution, you could enter this set of commands:

Which gave us a ratio of σ to range of 0.300