I am calculating RPD (ratio of prediction to deviation = standard deviation/ RMSE) to evaluate the prediction ability of a regression model. An alternative of RPD is RPIQ which is calculated as (Interquartile range/ RMSE).
The RPD for my data is 1.85 while RPIQ is 3.22 which means that the interquartile range (IQR) is larger than the standard deviation (std) for the same distribution.
Skewness of distribution = (- 0.45),
Mean = (- 0.25),
Std = (0.94),
Q1 = (-1.37),
Q3 = (0.33),
IQR = (1.70),
Min = (-2.76),
Max = (1.49).
I would appreciate it if someone let me know when IQR and Std are equal and when are not.
I restrict my answer to symmetric distributions. From Raid's answer, IQR may be equal to sigma, the Population Standard Deviation for a symmetric distribution but with a narrower and therefore more leptokurtic distribution than the normal distribution, for example, one of the t-distributions.
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