1a.  LDS.  Family Search: Internet Genealogy Service: Pedigree Resource File (index to CDs, online at FamilySearch.org).

David Houseman Marriage: 11 Mar 1816; Place: Shenandoah Co VA Spouse: Mary Stroup Father: William Stroup

1b.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

David Houseman Birth: 1783, Virginia Death: 11 Apr 1857, Highland, Ohio Burial: Road's Cemetery, Highland, Ohio Marriage: 11 Mar 1816, Shenandoah, Virginia Spouse: Mary Stroop Birth: About 1785, Frederick, Virginia Death: 10 May 1854, Highland, Ohio Burial: Road's Cemetery, Highland, Ohio Source: patron submission

2.  1810

3.  1820 Census Index/Images (online at Ancestry.com; Image #11 of 13; extracted by Diana Gale Matthiesen):¤•

1820

VA

Shenandoah Co.

*

Roll M33_138

p. 28/163B

Ln. 17

David Housman

120010-23110-0-100

no slaves

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	9 or under	1810-1820	= Son C
2 males	10-15	1804-1810	= Son B = Son A
1 male	26-44	1775-1794	= David (b. 1782/3)
2 females	9 or under	1810-1820	= Daughter F = Daughter E
3 females	10-15	1804-1810	= Daughter D = Daughter C = Daughter B
1 female	16-25	1794-1804	= Daughter A
1 female	26-44	1775-1794	= Mary (b. 1781/2)
1	person engaged in agriculture

*Indexed as being in "Isabella Furnace," but I don't see anything on the census pages indicating the location beyond just Shenandoah County.
There are certainly more children here than the ones born after David & Mary were married in 1816.  This was a late marriage for both of them, so it appears either or both of them had a prior marriage.

4.  1830 Census Index/Images (online at Ancestry.com; Image #11 of 28; extracted by Diana Gale Matthiesen):¤•

1830

OH

Highland Co.

Paint Twp.

Roll M19_133

p. 85

Ln. 22

David Housman

021 000 100 - 011 000 100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	5-9	1820-1825	= Son E = Son D
1 male	10-14	1815-1820	= Son C
1 male	40-49	1780-1790	= David (b. 1782/3)
1 female	5-9	1820-1825	= Lydia (b. 1824/5)
1 female	10-14	1815-1820	= Daughter F
1 female	40-49	1780-1790	= Mary (b. 1781/2)

5.  1840 Census Index/Images (online at Ancestry.com, Image #11-12 of 44  — mis-indexed "Daniel"; extracted by Diana Gale Matthiesen):¤•

1840

OH

Highland Co.

Paint Twp.

Roll 704_403

pp. 48B-49A

Ln. 12

David Houseman

000 120 010 - 000 110 010

0400000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	15-19	1820-1825	= Son E
2 males	20-29	1810-1820	= Son D = Son C
1 male	50-59	1780-1790	= David (b. 1782/3)
1 female	15-19	1820-1825	= Lydia (b. 1824/5)
1 female	20-29	1810-1820	= Daughter F
1 female	50-59	1780-1790	= Mary (b. 1781/2)
4	persons employed in agriculture

I think the enumerator goofed with his tally because there should be at least two boys in the 10-14 age class.

6.  1850 Census Index/Images (online at Ancestry.com; Image #50 of 65):  Paint Twp., Highland Co., OH, Roll M432_694, p. 183B, 1968/1972, enumerated 24 Oct 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤•

David Houseman	67	M		Farmer	1250	Va
Mary      "	68	F				"
Lydia M   "	25	F				"
Wm H      "	23	M		Farmer		"
David G   "	22	M				"

Unless their ages here are incorrect, William and David are too young to be Mary's children, nor are any children this young in our subjects' household in the 1830 or 1840 censuses.