Others census' in the Bible are supported by the fact that figures for all the other tribes are also listed and totaled. Hense an actual census.
Numbers 1The Census of Israel's Warriors
1 Then the LORD spoke to Moses in the wilderness of Sinai, in the tent of meeting, on (1) the first of the second month, in the second year after they had come out of the land of Egypt, saying,
2 " (2) Take a [1] census of all the congregation of the sons of Israel, by their families, by their fathers' households, according to the number of names, every male, head by head
3 from (3) twenty years old and upward, whoever is able to go out to war in Israel, you and Aaron shall [2] number them by their armies.
4 "With you, moreover, there shall be a man of each tribe, (4) each one head of his father's household.
5 "These then are the names of the men who shall stand with you: (5) of Reuben, Elizur the son of Shedeur;
6 of Simeon, Shelumiel the son of Zurishaddai;
7 of Judah, (6) Nahshon the son of Amminadab;
8 of Issachar, Nethanel the son of Zuar;
9 of Zebulun, Eliab the son of Helon;
10 of the sons of Joseph: of Ephraim, Elishama the son of Ammihud; of Manasseh, Gamaliel the son of Pedahzur;
11 of Benjamin, Abidan the son of Gideoni;
12 of Dan, Ahiezer the son of Ammishaddai;
13 of Asher, Pagiel the son of Ochran;
14 of Gad, Eliasaph the son of (7) Deuel;
15 of Naphtali, Ahira the son of Enan.
16 "These are they who were (8) called of the congregation, the leaders of their fathers' tribes; they were the (9) heads of [3] divisions of Israel."
17 So Moses and Aaron took these men who had been designated by name,
18 and they assembled all the congregation together on the (10) first of the second month. Then they registered by (11) ancestry in their families, by their fathers' households, according to the number of names, from twenty years old and upward, head by head,
19 just as (12) the LORD had commanded Moses. So he numbered them in the wilderness of Sinai.
20 (13) Now the sons of Reuben, Israel's firstborn, their genealogical registration by their families, by their fathers' households, according to the number of names, head by head, every male from twenty years old and upward, whoever was able to go out to war,
21 their numbered men of the tribe of Reuben were 46,500.
22 (14) Of the sons of Simeon, their genealogical registration by their families, by their fathers' households, their numbered men, according to the number of names, head by head, every male from twenty years old and upward, (15) whoever was able to go out to war,
23 their numbered men of the tribe of Simeon were 59,300.
24 (16) Of the sons of Gad, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
25 their numbered men of the tribe of Gad were 45,650.
26 (17) Of the sons of Judah, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
27 their numbered men of the tribe of Judah were 74,600.
28 (18) Of the sons of Issachar, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
29 their numbered men of the tribe of Issachar were 54,400.
30 (19) Of the sons of Zebulun, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
31 their numbered men of the tribe of Zebulun were 57,400.
32 (20) Of the sons of Joseph, namely, of the sons of Ephraim, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
33 their numbered men of the tribe of Ephraim were 40,500.
34 (21) Of the sons of Manasseh, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
35 their numbered men of the tribe of Manasseh were 32,200.
36 (22) Of the sons of Benjamin, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
37 their numbered men of the tribe of Benjamin were 35,400.
38 (23) Of the sons of Dan, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
39 their numbered men of the tribe of Dan were 62,700.
40 (24) Of the sons of Asher, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
41 their numbered men of the tribe of Asher were 41,500.
42 (25) Of the sons of Naphtali, their genealogical registration by their families, by their fathers' households, according to the number of names, from twenty years old and upward, whoever was able to go out to war,
43 their numbered men of the tribe of Naphtali were 53,400.
44 These are the ones who were numbered, whom Moses and Aaron numbered, with the leaders of Israel, twelve men, each of whom was of his father's household.
45 So all the numbered men of the sons of Israel by their fathers' households, from twenty years old and upward, whoever was able to go out to war in Israel,
46 even all the numbered men were (26) 603,550.
From counts here it shows that the number of militarily capable men during the time of the Exodus was 603,550. This does not mean that they ware a standing army though, but only that they were "able to go out to war" Also a later count in the book of Numbers gives slightly higher figures for each of the tribes adding up to slightly higher number due to population growth between the two censuses. Thus the book of numbers gives two specific censuses (each one broken down by tribes).