Let us assume that for a given galaxy we have n measurements 
(i=1,n) of a given parameter obtained from different references,
each reference having a weight 
,
where 
is the standard error of the i-th individual measurement.
The actual uncertainty is calculated as:
The first term 
denotes the inverse of the total weight
The total weight, 
, is simply the sum of individual weights.
(i.e. 
).
This first term accounts for the accuracy of the reference of each
individual measurement because the standard error of a given measurement
is assigned globaly from e.g., the reference or the resolution etc...
It is obvious that some individual measurements coming
from a good reference can be affected by a local problem (e.g., multiplicity
of the galaxy, star superimposed on the galaxy, bad seeing, misidentification
etc...). This fact will be taken into account by the second term.
The second term in the definition of the actual error is a measure of
the consistency of the different measurements
building the mean measurement. It is calculated as the weighted standard
deviation:
where:
, 
, 
.
The main advantage of the actual error is that it clearly shows any internal uncertainty and any external discrepancy.
Appendix B: LEDA's Astrophysical parameters
--------------------------------------------------------------------------------
Parameter FORTRAN FORTRAN columns definition
name name format
================================================================================
pgc pgcleda a11 1- 11 PGC or LEDA name (PGC = LEDA)
ident ident a16 12- 27 1st name (NGC,IC,UGC,ESO...)
ipad ipadc a1 28- 28 `*' for coordinates better than 10"
al1950 al1950 f10.5 29- 38 R.A. (B1950) (decimal hours)
de1950 de1950 f10.5 39- 48 DEC. (B1950) (decimal degrees)
al2000 al2000 f10.5 49- 58 R.A. (J2000) (decimal hours)
de2000 de2000 f10.5 59- 68 DEC. (J2000) (decimal degrees)
l2 al2 f10.3 69- 78 galactic longitude (degrees)
b2 ab2 f10.3 79- 88 galactic latitude (degrees)
sgl sgl f10.3 89- 98 supergalactic longitude (degrees)
sgb sgb f10.3 99-108 supergalactic latitude (degrees)
typ typc a5,1x 109-114 morph. type (e.g. `E', `Sab', `SBa', `SO')
morph morphc a4 115-118 `B' for Barred gal. (see note below)
`R' for Ring gal.
`M' for multiple gal.
`C' for compact, 'D' for diffuse
t t f10.3 119-128 morph. type code ($-$5 to 10)
st st f10.3 129-138 actual uncertainty on t
lc alc f10.3 139-148 luminosity class (1 to 11)
slc slc f10.3 149-158 actual uncertainty on lc
log$d25$ alog$d25$ f10.3 159-168 log10 of isophotal diameter ($d$25 in 0.1$'$)
slog$d25$ slog$d25$ f10.3 169-178 actual uncertainty on log$d25$
log$r25$ alog$r25$ f10.3 179-188 log10 of the axis ratio (major/minor axis)
slog$r25$ slog$r25$ f10.3 189-198 actual uncertainty on log$r25$
pa pa f10.3 199-208 position angle (N->E) in degrees
brief brief f10.3 209-218 effective surface brightness (mag arcsec-2)
sbrief sbrief f10.3 219-228 actual uncertainty on brief
bt bt f10.3 229-238 total $B$-magnitude
sbt sbt f10.3 239-248 actual uncertainty on bt
ubt ubt f10.3 249-258 ($U-B)_{\rm T}$
bvt bvt f10.3 259-268 ($B-V)_{\rm T}
ube ube f10.3 269-278 ($U-B)_{\rm e}
bve bve f10.3 279-288 ($B-V)_{\rm e}
w20 w20 f10.3 289-298 21-cm line width at 20% of peak (in km/s)
sw20 sw20 f10.3 299-308 actual uncertainty on w20
w50 w50 f10.3 309-318 21-cm line width at 50% of peak (in km/s)
sw50 sw50 f10.3 319-328 actual uncertainty on w50
logs alog$s$ f10.3 329-338 log of the central velocity disp.(s in km/s)
slogs slog$s$ f10.3 339-348 actual uncertainty on logs
m21 am21 f10.3 349-358 HI-magnitude
sm21 sm21 f10.3 359-368 actual uncertainty on $m_{21}$
mfir amfir f10.3 369-378 far-infrared magnitude
vrad vrad f10.3 379-388 radio heliocentric radial velocity in km/s
svrad svrad f10.3 389-398 actual uncertainty on $v$rad
vopt vopt f10.3 399-408 optical heliocentric radial velocity in km/s
svopt svopt f10.3 409-418 actual uncertainty on $v$opt
v v f10.3 419-428 actual heliocentric radial velocity in km/s
sv sv f10.3 429-438 actual uncertainty on $v$
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Parameter FORTRAN FORTRAN columns definition
name name format
================================================================================
lgg algg f10.3 439-448 Lyon's galaxy group number
ag ag f10.3 449-458 galactic extinction in $B$-mag
ai ai f10.3 459-468 internal absorption (in $B$-mag)
incl aincl f10.3 469-478 inclination
a21 a21 f10.3 479-488 HI self-absorption
lambda alambda f10.3 489-498 luminosity-index
logdc alogdc f10.3 499-508 log of the corrected diameter ($dc$ in 0.1$'$)
btc btc f10.3 509-518 corrected $B$-magnitude
ubtc ubtc f10.3 519-528 ($U-B)_0$
bvtc bvtc f10.3 529-538 ($B-V)_0$
bri25 bri25 f10.3 539-548 mean surf. brightness within 25 m/"
logvm alogvm f10.3 549-558 log of max.circ. rot. vel.
slogvm slogvm f10.3 559-568 actual uncertainty on logvm
m21c am21c f10.3 569-578 corrected HI-magnitude
hic hic f10.3 579-588 HI color index
vlg vlg f10.3 589-598 radial vel. relative to the LG
vgsr vgsr f10.3 599-608 radial vel. relative to the GSR
vvir vvir f10.3 609-618 radial vel. corrected for Virgo infall
v3k v3k f10.3 619-628 radial vel. relative to the CBR
mucin amucin f10.3 629-638 kinematical distance modulus ($H$ = 75 km/s/Mpc)
mabs amabs f10.3 639-648 absolute $B$ magnitude from mucin and mupar
identi identi 20a16 649-968 alternate names
--------------------------------------------------------------------------------
note: The parameter "morph" can be read as 4 parameters (4a1 format)
for Bar, Ring, Multiple and Compactness, respectively.