I was studying about probable error and I couldn't understand the reason behind using 0.6745 of standard error. Could someone please explain it? P.E=0.6745(S.E)
Probable Error = 0.6745 × 1−r2/√N

For a symetric distribution the probable error is equal to the median absolute deviation, which is related to the standard deviation as
$$MAD=0.67449\sigma.$$
From Wikipedia:

In statistics, probable error defines the half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside. Thus for a symmetric distribution it is equivalent to half the interquartile range, or the median absolute deviation.

