Suppose that heart rates $X$ in BPM are distributed $Norm(\mu_X = 75, \sigma_X = 4).$ The upper histogram below shows $n = 500$ heart rates simulated according to that distribution The curve is the density curve of $Norm(75, 4).$
The solid vertical blue lines are at $\mu - \sigma, \mu,$ and $\mu + \sigma.$
The dotted vertical red lines are at $\bar X - S_X, \bar X,$ and $\bar X + S_X,$
computed from my fake data. The sample values match the corresponding population values fairly well.
The lower histogram shows transformed values $Y = 60/X$ (seconds between beats).
Notice that this histogram is markedly skewed to the right. This means that the
standard deviation may not be a good measure of dispersion for my $Y$s.
The solid vertical brown lines are derived from the transformed values
$\bar Y - S_Y, \bar Y,$ and $\bar Y + S_Y.$ The dotted red lines are transforms
of the dotted red lines in the top histogram: $60/(\bar X + S_X), 60/\bar X,$
and $60/(\bar X - S_X).$
In theory, there is no reason that the red and brown lines should match.
In particular, $\bar Y$ is not the same thing as $60/\bar X,$ nor is
$S_Y$ the same thing as $60/S_X.$ That is because the transformation from $X$
to $Y$ is not a linear transformation. In spite of that, at the scale of my fake
data, these values match pretty well. I believe that explains your (ill-advised) workaround.
I see that another answer has appeared as I was messing around with graphs.
It includes comments similar to ones that I was about to make: I totally
agree (+1) with @SteveKass that you need to decide for which type of data (BPM
or intervals between) the standard deviation is "important ... for judging
heart rate variability." Whichever it is, you could compute your SDs directly
for that type of data. And you should check what standard medical usage
is in making your choice. I think it is very unlikely that SDs are appropriate for both the original and the reciprocal scale, but I wouldn't care to
speculate for which scale SDs would be appropriate. (My modeling of BPMs
as normal was a convenient choice for an illustration, not necessarily
There is no guarantee that either 'BPM' or 'Time between beats' is normally
distributed, or that getting 'approximately right' SDs by a fundamentally
flawed method won't turn to disaster at some point.