The best data comes from measuring skeletons. To start with the medieval period, for which I have data readily to hand, here’s the measurements of skeletons from medieval England:
St. Peter’s Church, Barton-upon-Humber, England
950-1149:
Mean height for males: 1.69 (5’5)
Mean height for females: 1.61 (5’2)
1150-1299:
Mean height for males: 1.70 (5’5)
Mean height for females: 1.59 (5’2)
Modern-day British:
Mean height for males: 1.76 (5’7)
Mean height for females: 1.62 (5’3)
From The Cemetery of St Nicholas Shambles (1988), by W.J. White:
Average height for a male (11-12th centuries): 1.72 (5’8)
Average height for a female (11-12th centuries): 1.58 (5’2)
From Death and Burial in Medieval England, 1066-1550 (1998) by Christopher Daniel:
Taunton, England
Male: (average height) 1.71cm (5’6)
Female: (average height) 1.56 (5’1)
Male: (shortest) 1.65 (5’4)
Female: (shortest) 1.46 (4’7)
Male: (tallest) 1.80 (5’9)
Female: (tallest) 1.71 (5’6)
From Medieval Towns (2003) by John Schofield and A. G. Vince:
St. Helen, York, England (10-16th centuries)
Male: (average height) 1.69 (5’6)
Female: (average height) 1.57 (5’2)
St. Mary’s Priory, Thetford, England (12-13th centuries)
Male: (average height) 1.77 (5’9)
Female: (average height) no data
St. Leonard’s, Kent, England (14-15th centuries)
Male: (average height) 1.70 (5’7)
Female: (average height) 1.57 (5’2)