It appears the median record for Missouri's last 90 years of college football is a smidge over .500. Which, I guess, is better than a smidge below, now isn't it?
#90-86
#85-81
#80-76
#75-71
#70-66
#65-61
#60-56
#55-51
#50: Mizzou 1972 (6-6)

Best Win: Mizzou 30, #8 Notre Dame 26, which was preceded by...
Worst Loss: #6 Nebraska 62, Mizzou 0
More on this season here, here and here.
In 13 seasons in Columbia, Dan Devine suffered only one losing season (his last). In the first season post-Dan, Al Onofrio's Tigers went a startling 1-10. Mizzou went from competing for national titles to woeful in just two years, but they would bounce back a bit in 1972, making the Fiesta Bowl (it wasn't as meaningful then as it is now, but still) and registering one of the biggest one-week turnarounds in team history. They limped through the early portion of the season, and an embarrassing 62-0 loss to Nebraska knocked them to just 2-3 with a trip to South Bend on the horizon. But in the first of many inexplicable Onofrio road upsets, the Tigers knocked off #8 Notre Dame, kick-starting a streak in which they won four of five and became bowl-eligible.
Considering where they were in 1971, and taking into account the Notre Dame upset, this season was an absolute success ... but the team certainly wasn't very good. Mizzou was outscored 311-219 for the season, gave up 60+ points to Nebraska, and 700+ yards to Arizona State in the Fiesta Bowl. But after a season in the abyss, Mizzou mattered again thanks to the '72 squad.
#49: Mizzou 1952 (5-5)

Best Win: Mizzou 27, Colorado (6-2-2) 7
Worst Loss: Oklahoma State (3-7) 14, Mizzou 7
If point margins are your thing, the 1952 Mizzou squad was one of the more baffling in Mizzou history. They began the season 1-4 despite just a -16 point margin ... and they finished the season 4-1 despite just a +4 margin.
This was really the typical 1950s Mizzou team -- hard-nosed and tough in conference play ... with little to show for it in the W-L columns. As was normal, Faurot's Tigers struggled in non-conference action. Actually, that's not true -- they played pretty well, but their ambitious schedule was a bit too much. They took #2 Maryland to the wire before falling, 13-0; then they had to travel to #8 California and put up a solid fight before falling, 28-14. They pelted Kansas State, 26-0, then played host to a solid SMU squad. Mizzou was dominated by the Mustangs, 25-7, then upset by Oklahoma State in Stillwater. The team seemed to be regressing, but they perked back up when conference play got going full-steam.
With an October 25 19-0 win over Iowa State, Mizzou moved to just 2-4 for the season, but 2-0 in conference. Then they knocked off two teams that would finish with winning records -- Nebraska (10-6 in Lincoln) and Colorado (27-7 in Columbia) -- and moved to 4-0 in conference. All that stood in the way of a Big 7 title was a trip to Norman to take on the #8 Sooners, who had just lost to Notre Dame. As was the case throughout the '50s (and, to be honest, just about every decade since then), however, OU had no trouble wrecking Mizzou's hopes. The Sooners dominated, 47-7, and all Mizzou had left to play for was a .500 record and runner-up status in conference. They locked that down with a super-exciting win over Kansas -- a Tony Scardino touchdown late in the game gave Mizzou a 20-19 victory.
As with all the other teams in this portion of the list, the 1952 wasn't particularly great, but they peaked at the right time and almost scored a surprising Orange Bowl bid ... if only OU weren't so damn good.
#48: Mizzou 1945 (6-4)

Best Win: Mizzou 14, Oklahoma (5-5) 6
Worst Loss: Minnesota (4-5) 34, Mizzou 0
However, if you're in the market for a surprise conference champ, then look no further than the 1945 squad. While Faurot was still off to war, his assistants (led by Chauncey Simpson) led Mizzou to a wonderful finish ... after one of the more unimaginably bad starts anybody can imagine. As has been mentioned before, Faurot (with his Athletic Director hat on) paid for the entire athletic department's budget by taking on brutal non-conference slates against multiple top-tier programs, and the Tigers started the season with games against Minnesota (the country's best program in the pre-war '40s) and Ohio State. In those two games, they were outscored 81-6. From that point on, Mizzou outscored their opponents 164-93.
After the ridiculousness of the first two games, Mizzou licked their wounds and made some improvements. They upset SMU on the road, 10-7, then stole a win in Ames, 13-7. They returned home to romp over a terrible Kansas State team (41-7) and held steady against a decent Nebraska team (19-0). They were 3-0 in conference, 4-2 overall, when they took on another tough foe in Michigan State. The Spartans were rumored to be the tenth team in the new-fangled Big Ten around this time, and they were making mighty improvements on the field. They struggled to put away Mizzou, however, settling for just a 14-7 win.
Missouri then returned home with a conference title on their mind. The 1945 college football world was still in a bit of upheaval because of the war (in other words, OU wasn't dominant yet), and the conference was ripe for the taking. They knocked off OU in Columbia, 14-6, then wrapped up the conference title with a 33-12 romp over KU in Kansas City, clinching their third bowl bid in seven years.
Their bowl assignment was less than ideal. They had to travel to Dallas to play #10 Texas (9-1) in the Cotton Bowl, but against an explosive Longhorns offense, they held their own ... with more offense. An inordinate amount of offensive records fell in Dallas that day -- points scored (Texas - 40), first downs (Mizzou - 22), passing yards (Texas - 234), rushing yards (Mizzou - 408), completion percentage (Texas - 0.934, 13-for-14), total yards (Mizzou - 514), and total combined yards (950). Texas' Bobby Layne was 11-for-12 passing for two touchdowns, rushed for three short touchdowns, and caught a 50-yard touchdown pass. Meanwhile, Mizzou did their best to match them, drive for drive, but after a short Robert Hopkins touchdown cut Texas' lead to 33-27 (which would be like 56-49 today), Layne capped off the clinching drive with a 2-yard plunge. Texas won 40-27, but Mizzou's Split-T was still unique and effective ... until Faurot, Jim Tatum and Bud Wilkinson came back from war and the knowledge of the T spread.
#47: Mizzou 1958 (5-4-1)

Best Win: Mizzou 33, Colorado 9
Worst Loss: Oklahoma 39, Mizzou 0 the next week
Most Amazing Tie: Mizzou 13, Kansas 13 (explanation here)
More on this season here, here, here and here.
Dan Devine's first season in Columbia played out almost exactly like Frank Broyles' the year before. Mizzou started slow 1-3, with losses to Vanderbilt, Texas A&M and SMU), got hot in mid-October (easy wins over Kansas State, Iowa State, Nebraska and a good Colorado squad by a combined 110-23), and saw their conference title hopes get murdered at the hands of Oklahoma. As Mizzou left Norman's Memorial Stadium after the killer 39-0 defeat, he vowed to his team that they would win on their next trip to Norman. They did just that. Apparently he should have vowed that Mizzou would win their next 40.
As referenced above, Mizzou's season ended with the most amazing tie of all-time (the most classic of Mizzou's Forgotten Classics), with Kansas, down 13-7, completing a miraculous 89-yard touchdown pass in the game's closing seconds to tie the game ... and Mizzou blocking the PAT to preserve the tie. Mizzou had outplayed KU all game, but they had to settle for a tie and a 5-4-1 record identical to that of Broyles the season before. This team was better -- the 1957 squad was outscored by 8, the 1958 squad was +23 against an almost identical schedule -- but barely.
#46: Mizzou 1982 (5-4-2)

Best Win: Mizzou 16, Kansas 10
Worst Loss: Oklahoma State 30, Mizzou 20
By 1982, Warren Powers' Mizzou squads had established a pretty clear pattern: win early, build up the fanbase's hopes, fall into an October funk, rally late. They were 11-3 in September under Powers, 9-7 in October (6-6 after the 1978 season), and 11-7 in November and bowls. They were a solid program by all means, but the October fades were discouraging and disheartening to what was once a growing fanbase. The 1982 season played out almost exactly the same, only without the payoff of a bowl game.
When Powers got to Columbia, he tried to take the non-conference schedule down a couple of notches, simply because it was exhausting to the team. The 1982 non-con slate still featured a really good Texas team but also had manageable home games against Colorado State, Army and East Carolina. Predictably, Mizzou went 3-1 against those teams, beating the mid-majors 28-14, 23-10, and 28-9, respectively, and losing 21-0 to Texas. However, this year's October fade was worse than normal, even though the team couldn't blame the exhausting September. Against average-at-best Kansas State (in Manhattan) and Iowa State (at home) squads, Mizzou managed just two ties, 7-7 and 17-17. Offense was this team's Achilles heel, and it cost them.
Even a split of the two games would have been more beneficial, as now with games remaining against Nebraska and Oklahoma, Mizzou would need to sweep their three other lesser opponents to qualify for a bowl game. They did not. They lost a 23-19 heartbreaker at Nebraska then fell to an improving-but-still-not-great Oklahoma State team in Stillwater, 30-20. With a 3-3-2 record, Mizzou would need to beat Colorado (they did), Kansas (they did) and Oklahoma (they very much did not) to make a bowl, and they fell short. The 5-4-2 season was Powers' first without bowl eligibility, and it assured that, even after a nice bounceback campaign in 1983, Powers was not given a lot of rope when his Tigers underachieved again in 1984.