Ideally, each histogram would have a bin size such that
its width 
is larger than the uncertainties in the computed
parameters. This procedure would, in some cases, make the analysis
more difficult due to the relatively large bin width that would have to be
used. To overcome this problem a different approach was
chosen: for a given bin of width 
in an histogram, one asks the
question: what is the probability for a measurement of the parameter to
fall inside it? This is easily
computed by assuming that a measurement results from a normal
probability distribution with mean equal to the measured value and with
standard deviation equal to the uncertainty in the measurement, that is,
where, 
is the measured value and 
its uncertainty.
The height of a given bin is now the sum of the probabilities of all the measurements, ie.
where, 
is the height of bin j in the histogram, N is the
number of measurements of the parameters, 
and 
are the
end points of the
bin, 
and 
, i=1...N, are the measurements of the
parameter under study for the various stars and their associated
uncertainties.
The histogram is simply the values 
for all bins considered. In
the limit where the uncertainties tend to zero (
) one recovers the usual histogram.
