There's a 14/15 year gap here.  Are the younger children possibly adopted?

4.  John STROUP, b. 1906/7
5.  Arthur STROUP, b. 1907/8

1.  Marriage Record:

2.  1890 Census:  the 1890 Census Population Schedules were destroyed.

3.  1900 Census Every-Name-Index/Images (online at Ancestry.com, Image #9 of 28):  Nineveh Twp., Adair Co., MO, Roll T623_836 (Book 1), p. 152A, SN 5, SD 1, ED 11, enumerated 8-9 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

21

22

23

24

25

27

28

92

98

Stroup David

Head

W

M

Apr 1860

40

M

14

PA

PA

PA

Farming

N

N

Y

R

F

85

______ Sarah

Wife

W

F

Jan 1863

37

M

14

3

3

MO

IL

MO

Y

N

Y

______ James E

Son

W

M

Jan 1887

13

S

MO

PA

MO

at School

6

Y

Y

Y

______ Hubart A

Son

W

M

Mar 1889

11

S

MO

PA

MO

at School

6

Y

N

Y

______ Alta E

Dau

W

F

Dec 1892

7

S

MO

PA

MO

at School

6

N

N

Y

4.  1910 Census Index/Images (online at Ancestry.com, Image #18 of 23):  Benton Twp., Adair Co., MO, Roll T624_766 (Part 1), p. 17B, SN 9B, SD 1, ED 2, enumerated 28 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	21	22	23	24	26	28	29
209	213	Stroup Dave	Head	M	W	54	M1	24			PA	PA	PA	Eng	Miner	Coal mine	W	Y	40	N	N	R	F	186
		______ Sarah B	Wife	F	W	43	M1	24	3	3	MO	IL	IL	Eng	None					Y	N
		______ John	Son	M	W	3	S				MO	PA	MO		None
		______ Arthur	Son	M	W	2	S				MO	PA	MO		None

I wish this record were a better match with 1900, yet I don't see how it can be anyone but our subjects.

5.  1920 Census Index/Images (online at Ancestry.com, Image #21 of 22):  Cainsville (Ward 2), Madison Twp., Harrison Co., MO, Roll T625_920 (Book 1), p. 140A, SN 11A, SD 3, ED 110, enumerated 10 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).

2

3

4

5

6

7

9

10

11

12

13

16

17

18

19

21

23

25

26

27

28

X

259

261

Stroup Dave

Head

R

M

W

59

M

MH

N

N

PA

PA

PA

Y

Miner

Coal Mine

W

______ Sarah

Wife

F

W

49

M

Y

N

MO

IL

MO

Y

None

______ Rosie

GDau

F

W

11

S

Y

Y

Y

MO

MO

TN

Y

None

Rosie is the daughter of their son, James Edward STROUP.

6.  1930 Census Index/Images (online at Ancestry.com):  not found.