Hi Mike,
I just found this family group sheet on Ancestry.com. I can't attest to the accuracy of it, but there is a Frances Baum listed as being born in 1785.
This list is also interesting, because there is a sister to Frances named Diana, and Frances had a daughter who was known as Diana or Dinah. (There are often name patterns in families) :
Joseph Baum
B: 15 JUL 1750, Humberstone, Leicestershire, England
D: 3 AUG 1814
Wife: Ann
B: BEF 1754
D: ?
CHILDREN:
Elizabeth Baum
Daughter
23 JAN 1774
Humberstone, Leicestershire,England
William Baum
Son
28 JAN 1776
Humberstone, Leicestershire,England
13 SEP 1860
Humberstone, Leicestershire,England
Christian Baum
Daughter
3 JAN 1778
Humberstone, Leicestershire,England
Joseph Baum
Son
26 MAR 1780
Humberstone, Leicestershire,England
Ann Baum
Daughter
28 OCT 1782
Humberstone, Leicestershire,England
Frances Baum
Daughter
6 FEB 1785
Humberstone, Leicestershire,England
John Baum
Son
6 JAN 1788
Humberstone, Leicestershire,England
JAN 1790
Humberstone, Leicestershire,England
Diana Baum
Daughter
27 MAY 1791
Humberstone, Leicestershire,England
8 JUL 1846
Humberstone, Leicestershire,England