Carmi is a Hebrew name from scripture.  He appears to have shaved two or three years off his age by the 1900 census.

1.  Works Progress Administraton.  1938-40.  Index to Marriage Records: Indiana (online at Ancestry.com):

Carnies Stroup

Lida Balyeat

22 Mar 1900

Lagrange Co.

Bk. 7, p. 72

Surely this is Lydia's birth record, not Carmi's marriage record!

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

Eliza BALYEAT Birth: 1866, Ashland, Ohio Father: Moses BALYEAT (1831-1902); Mother: Eliza HERSHEY (1832-1892) Source: patron submission

2.  1880 Census Every-Name-Index/Images (online at Ancestry.com):  Carmi STROUP (æ 25, b. OH) is living in Wellington, Lorain Co., OH, with his parents (q.v.).  Eliza BALYEAT (æ 14, b. IN) is living in Bloomfield Twp., LaGrange Co., IN (p. 361D), with her parents, Moses BALYEAT (æ 48, b. OH) and his wife, Eliza (æ 48, b. OH).

3.  1900 Census Every-Name-Index/Images (online at Ancestry.com, Image #8 of 35):  [street name unreadable], La Grange, Bloomfield Twp., La Grange Co., IN, Roll T623_383, p. 15B, SN 4, SD 12, ED 70, enumerated 5 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):¤•

1900:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

19

20

22

23

24

25

26

27

109

110

Balyeat Moses

Head

W

M

Nov 1831

68

Wd

OH

PA

PA

Janitor

0

Y

Y

Y

O

F

H

Stroup Carni S

Son in law

W

F

Nov 1857

42

M

1

OH

PA

NY

Farm & Mill Laborer

0

Y

Y

Y

______ Eliza

Dau

W

F

Feb 1866

34

M

1

1

1

IN

OH

OH

Y

Y

Y

______ Lydia E

GDau

W

F

Mar 1900

3/12

S

IN

OH

IN

4.  1910 Census Index/Images (online at Ancestry.com, Image #6 of 9):  Central Ave., LaGrange Town (Ward 4), Bloomfield Twp., LaGrange Co., IN, Roll T624_361 (Part 1), p. 38B, SN 18B, SD 12, ED 94, enumerated 29 Apr 1910, official enumeration date 15 Apr 1910 (extracted by Diana Gale Matthiesen):¤•

1910:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	9	10	11	12	13	14	17	18	19	20	23	24	25	26	27	28
67	70	Stroup Carmi S	Head	M	W	54	M1	11			OH	PA	NY	Eng	Farmer	General farm	Emp	Y	Y		O	F	H
		______ Lisa	Wife	F	W	44	M1	11	1	1	IN	OH	OH	Eng	None			Y	Y
		______ Lidia E	Dau	F	W	10	S				IN	OH	IN	Eng	None			Y	Y	Y

Listed four households from Carmi's brother, Milo STROUP.

5.  1920 Census Index/Images (online at Ancestry.com, Image #26 of 34 — indexed "Eliga Strong"):  [street unreadable], La Grange (Ward 4), Bloomfield Twp., LaGrange Co., IN, Roll 443 (Book 1), p. 236A, SN14A, SD 12, ED 118, enumerated 13 Jan 1920, official enumeration date 1 Jan 1920 (extracted by Diana Gale Matthiesen):¤•

1920:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
3	4	5	6	7	8	9	10	11	12	17	18	19	21	23	25	26
382	397	Stroup Eliza	Head	O	M	M	W	53	W	Y	Y	IN	OH	OH	Y	none
		______ Lydia A	Dau			F	W	19	S	Y	Y	IN	OH	IN	Y	none

6.  1930 Census Index/Images (online at Ancestry.com, Image #11 of 35):  212 West Central Avenue, La Grange Town, Bloomfield Twp., La Grange Co., IN, Roll 595 (Book 1), p. 227A, SN 6A, ED 44-1, SD 3, enumerated 8 Apr 1930, official enumeration date 1 Apr 1930 (extracted by Diana Gale Matthiesen):¤•

1930:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	10	11	12	13	14	16	17	18	19	20	24	25	26	27	28
*	212	171	177	Stroup Eliza	Head	O	3,500	N	F	W	64	Wd	N	Y	IN	OH	OH	Y	None
				______ Lydia E	Dau				F	W	30	S	N	Y	IN	OH	IN	Y	Teacher	Public school	W	Y
*West Central Avenue

Apparently sharing domicile (171/178) with the WOODWORTH family who are renters.

7.  Anon.  1938-41.  Various Indiana County Death Records Indexed by the Indiana Works Projects Administration (online at Ancestry.com and Genealogy.com):

Name:	Carmi S. Stroup
Date:	Sept 20, 1917
Location:	Lagrange
Age:	61 yr
Gender:	Male
Race:	W
Source Location:	County Health Office, La Grange
Source Notes:	The source of this record is the book H-8 on page 70 within the serious produced by the Indiana Works Progress Administration.

8.  Anon.  Monday, 24 Sep 1917.  "Lagrange News." The Fort Wayne Daily News (Fort Wayne, Allen Co., IN), p. 15 (online at Ancestry.com):

LAGRANGE NEWS... The funeral of Carmi Stroup was held Saturday afternoon.  Mr. Stroup had been sick for several Months, and he suffered a stroke of apoplexy a few days ago, which was the immediate cause of his death.  Mr. Stroup was 62 years old and had been a resident of Lagrange for the past thirty-seven years.  He was active in public affairs and one of the working members of the Lagrange I.O.O.F. lodge and the Methodist Episcoal church.  He was also a member of the county council at the time of his death.  He is survived by his wife and one daughter, four brothers — D.M. Stroup and M.O. Stroup, of Lagrange; Dr. Charles Stroup, of Bloomington, and Ellsworth Stronp (sic), of California — and one sister — Mrs. Charles Carpenter, of Bloominton, Ind.