I don't think I've ever checked my 38 for an exact number. Others will have to chime in but I believe most of the posts I've read about mileage indicate an all around mileage of 16-18. It's not good by today's standards but the cost of gas and pollution weren't a big issue back then.

On my 32 with the original carb my mileage was about 10-12 MPG. I think it was a 212s carb. I now have a 569S #421 and best Ican tell average is from 16-20 MPG depending on the type of driving-flatland or hilly. The 569S #421 is a replacement carb that came out in 1946 for the earlier downdraft carbs. It has a straight throttle arm whereas the later carbs have a bent throttle arm.

My experience is overall mileage on early six cylinders and late 20s is 15-18 for moderate speeds (up to 40-50 mph on the road). The early 1932 is closer to 10-15 depending on speed. The later properly set up gets the 15-18 as above. That is based on 30+ years driving several thousand miles on VCCA tours. As an example I calculate 18 mpg for my '28 Coupe on tours and that has proven to be accurate enough to have 1-2 gallons in the gas tank when the tour ends.

I drive my 37s to shows and to put it politely, "Mileage may vary". Example: The Ton & half ambulance gets 20 MPG and travels around 70 MPH on my 5000 mile trip to Bowling Green. When pulling the car trailer, it still gets 20 MPG cuz I only travel at 55 MPH. It can be seen on web page . . home.znet.com/t1937/ambl.htm . .
The 1938 Ton&half Canopy Express that went to Tahoe has same chassis as the Ambulance also gets 20 MPG at 65 mph. .
Also on the 131" WB chassis in the brown Superior bus that has 57 engine and 1950s GMC rear end gets only 10 MPG and top speed is 65 MPH. It can be seen on web page . . home.znet.com/p1937/Bus.htm . The Green Crown bus on that page is for sale. .
The yellow 37 half ton Canopy Express that I drove to the second Colorado national meet only gets 19 MPG at 65 MPH.
I had the Superior bus, the yellow canopy and the 37 tourer at the Santa Rosa national meet. The tourer is pictured on web page . . home.znet.com/p1937/Tour.htm . . It only gets 18 MPG at 60 MPH. The 37 Sedan Delivery only drove as far as the airport to attend the first national meet in Indianapolis. It can be seen on web page . . home.znet.com/p1937/Sddl.htm . . It got around 18 MPG at 70 MPH. You have to weigh "Driving Pleasure" with fuel cost. If you buy a new pickup that gets 14 MPG and tow a trailer with a car on it, you can understand why I just drive to car shows. .
. Many years ago, the Shell Economy run reported 157 MPG in their 1925 Chevy. An absolutely smooth, level track with speeds less than 15 MPH and other tweaks that could not be accomplished in normal driving assisted this mileage.