Standard percentile range

The SPR is a statistical technology developed by Perezgonzalez as a measure of dispersion which may be fitter and more informative than the IQR. It does so by mimicking the standard deviation in two accounts:

  • it measures dispersion on one side of the median (like the standard deviation, and unlike the IQR)
  • the lower and upper bounds of the SPR are the percentiles 16 and 84, respectively, thus covering 68% of the distribution (approximately similar to the standard deviation, and unlike the IQR, which only covers 50% of the distribution).

The SPR is, thus, half the IPR, approximates the standard deviation when the distribution is normal, and is a measure of dispersion that can be compared against the standard deviation much better than the IQR or the SQR.

But does the SPR stands to scrutiny? Does it work as expected?

IPR/SPR as a measure of dispersion & skewness

Potato chips
BNI N.P. Ranked P. US N.P. Ranked P.
CT Md=82.65 M,Md=82.65 CT Md=70.61 M,Md=70.61
[ SD --- 18.33 ] [ SD --- 18.33 ]
+SD --- 80.00 (P20) +SD --- 68.95 (P20)
-SD --- 94.29 (P79) -SD --- 96.03 (P79)
IQR P25 80.07 80.07 IQR P25 69.08 69.08
IQR P75 92.60 92.60 IQR P75 77.14 77.14
IPR P16 79.58 79.58 IPR P16 68.09 68.09
IPR P84 98.35 98.35 IPR P84 82.75 82.75
Skew (IQR) z=3.39 RS=3.69 Skew (IQR) z=2.62 RS=2.50
Skew (SQR) z=3.39 RS=6.39 Skew (SQR) z=2.62 RS=5.08
1. full reference in the following format AUTHOR (date work).Title. Reference location, date publication. ISBN/ISSN.
+++ Notes +++
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