Gertrude,
The NOTAM Q) line does contain the position, radius and vertical extent of the area in a well defined format which is amenable to automatic transcription - this is what gives you the big red circles you see on third party plotting tools.
This is also the circular extent of the NOTAM which is used by route briefing reports (including the AIS).
Some third party tools (such as mine) also parse co-ordinate data within the free form E) line text and interpret it as route or extent data. Whilst for complex NOTAMs containing multiple routes or extents this may not be entirely sufficient, it does immediately flag up gross errors in the NOTAM preparation, particularly where the free-form co-ordinate data clearly doesn't correspond to the stated centre and radius data in the Q) line.
Take for example, this initial attempt at a NOTAM for a Red Arrows' transit for today, 19th June:
H2186/10
Q) EGTT/QWVLW/IV/M/W/000/030/5115N00120W020
B) FROM: 10/06/19 10:57C) TO: 10/06/19 11:52
E) FORMATION TRANSIT BY RED ARROWS ACFT ROUTING:
5121N 00121E (MANSTON AD, KENT) 1107 HR
5114N 00118E (BETTESHANGER, KENT) 1109 HR
5114N 00108E (BISHOPSBOURNE, KENT) 1110 HR
5107N 00114E (WEST HOUGHAM, KENT) 1112 HR
5112N 00123E (KINGSDOWN, KENT) 1113 HR
5124N 00125E (MARGATE, KENT) DISPLAY 1115-1139 HR
5121N 00121E (MANSTON AD, KENT) 1142 HR
FORMATION PLANS TO TRANSIT AT 2000FT AGL. TIMINGS, HGT AND ROUTE ARE
APRX AND MAY CHANGE DUE TO WX OR OTHER REQUIREMENTS.
SEE SEPARATE NOTAM FOR THE RESTRICTED AREA (TEMPORARY) FOR MARGATE
AIRSHOW. AUS 10-06-0452/AS1
LOWER: SFC
UPPER: 3000FT AMSL
A simple plot of the Q) line and E) line data show a gross error:
http://metutil-test.appspot.com/NotamData?type=KML&ids=H2186/10 - Google Maps
...which was corrected after a few hours, but it does raise a couple of points (which arguably have been done to death, but since the problem is clearly recurring, aren't quite dead yet)
1) Why wasn't the data verified before publication? - there is a recurring problem with NOTAM source from this particular origin. The NOTAM for the reciprocal transit had the same problem
2) The Narrow Route Brief for a route passing through the actual track of the Red's transit would not have returned any details of the NOTAM, since the extent of the NOTAM used by the NRB was on the other side of the country.
The XML-encoded NOTAM format which will be with us in a few years - probably - might catch this sort of problem earlier, but until then we're stuck with the system we've got. Make the best of it.