The only way to know for sure when your gun was made/shipped is to get a letter on it from the Savage historian --
Fox serial numbers are in blocks by gauge and whether Sterlingworth or graded gun --
12-gauge Graded Guns -- 1 to 35280
12-gauge Sterlingworths -- 50000 to 161556
16-gauge Graded Guns -- 300000 to 303875
16-gauge Sterlingworths -- 350000 to 378481
20-gauge Graded Guns -- 200000 to 203974
20-gauge Sterlingworths -- 250000 to 271304
Single Barrel Trap Guns -- 400000 to 400568
I have some real problems with the published Fox serial number list, which was originally put out in 1976 by Lightner Library.
For 16-gauge Fox-Sterlingworths they are showing 500 (1931), 600 (1932), 600 (1933), 700 (1934), 1100 (1935), 1500 (1936), 700 (1937) and then 1600 for 1938. Then the serial numbers from 374800 to 378481 are given for 1939 up to the last gun made 8/9/1939. I don't believe there is anyway they all of a sudden pumped out 3681 16-gauge Fox-Sterlingworths in eight or nine months!!! From my 18 or so years of recording serial numbers of observed Sterlingworths, guns in the 375,xxx, 376,xxx, 377,xxx and 378,xxx range certainly exist.
On the 12-gauge Fox-Sterlingworths they estimate the highest serial number for for 1937 as 145000, for 1938 as 150000 and for 1939 as 155000. Again from my years of observing and recording serial numbers, I haven't recorded a gun between 143802 and 160195, leading me to believe there were about 16000 serial numbers skipped. Perhaps the high 143xxx range was the end of regular production and the guns in the 160xxx and 161xxx range were cleanup of parts and barrels on hand?!? All of the guns I've recorded in that range are 26-inch barrels except one two-barrel set that also has a pair of 28-inch barrels.