Answer:
The question you are asking is too vague to be anwsered.
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I will say that 6'2" is the preferred height among teams around the league
Times have changed as the 60's had only allowed giants on the gridiron to present an idea of toughness, while the height averages have decreased among reason years due to the will of shorter players to prove they are just as good, if not better, then the giants on the field.
Here is a researched estimation of all positions on the field
Quarterbacks
Preferred Height: 6'2"-6'5"
-Quarterbacks need to be tall to be able to see downfield. Great Quarterbacks like Drew Brees, and Steve McNair were not criticized for their great play, but their lack of ability to see downfield openings due to height.
Halfbacks
Preferred Height: 5'10"-5'11"
-Most Halfbacks Nowadays are around the area of 5'9", and this may be due to the grating of legplates because of excess running. However, big backs like Brandon Jacobs prove statements like this false. No matter how much one person can prove a stereotype wrong, smaller backs are still the majority in the league.
Fullbacks
Preferred Height: 5'11"-6'1"
-Fullbacks are usually former Linebackers or Offensive Lineman with "Fullback Play", therefore most Fullbacks are much taller then the preferred height.
Wide Receivers
Preferred Height: 6'0"-6'2"
-Most Coaches in the NFL are looking for a fast downfield threat with sure hands and a build that is tall enough to catch jump balls (EX: Randy Moss and Plaxico Burress)
but because of "Leg-Plate Theory" a tall, fast, and sure handed wide receiver is hard to come by.
Tight Ends
Preferred Height:6'3"-6'5"
-Tights Ends, like Fullbacks, are usually former Offensive Lineman who possess better speeds and catching ability so the height range for Tight Ends is usually higher then the preferred Height.
Offensive Tackles
Preferred Height: 6'5"-6'10"
-Not much of a Conversation here, Tall Tackles are highly valued so that their big sizes can sustain the pocket, contain Defensive Ends, and protect the Quarterback's blind side. (They still need skill mind you).
Offensive Guards
Preferred Height: 6'3"-6'6"
-Guards also need to have size because Interior Lineman are usually the strongest of the Defensive Core.
Offensive Centers
Preferred Height: 6'1"-6'4"
-In olden days, a Center was a Lineman who needed to have the ability to snap the ball. That's it. The expectations for height were carried. However, since that time, interior defensive lineman have become more valued so Tall Centers have also become somewhat of a demand.
Defensive
Defensive Ends
Preferred Height: 6'2"-6'6"
-Defensive Ends were usually the biggest and fastest Lineman on the team. Now (proven by Elvis Dumervil and Dwight Freeney) they are only needed to be fast to be dominant and outrun Tackles to the Quarterback, making the need for skilled Tackles even more valuable.
Defensive Tackles
Preferred Height: 6'3"-6'6"
Interior Lineman have increased in size over the years to collapse the pocket right in the face of Quarterback and possibly predict snap counts to rush the Quarterback.
Outside Linebackers
Preferred Height: 6'2"-6'4"
-No Comment (ability over size)
Inside Linebackers
Preferred Height: 6'3"-6'5"
-More Helpful on Goaline Situations more then anything, the size of an Inside Linebacker to stop the Goaline Dive is very crucial. With Inside Linebackers being worked into Zone Schemes nowadays, the ability to jump high and intercept in zone is also very helpful.
Strong Safeties
Preferred Height: 6'0"-6'2"
-Strong Safeties are usually more Linebacker then Defensive Back, so Size and Strength matter.
Free Safeties
Preferred Height: 5'11"-6'2"
-A Free Safety is basically a Cornerback who covers whatever is open. Ability is valued over height.
Cornerbacks
Preferred Height: 5'11"-6'1"
-Cornerbacks are usually extremely fast. The ability of makeup speed, breakaway speed, and acceleration are crucial in a shutdown Corner's abilities. Cornerbacks are usually shorter (again, the leg-plate theory), and short Cornerbacks are usually put in uncompromised situations with taller Wide Receivers, however some Cornerbacks have dominated under this situation (DeAngelo Hall V. Chad Johnson). In short ability over size, but a Taller Cornerback with shutdown capabilities will always be of more value. (Antonio Cromartie).
Special Teams
Punters
No preferred Height
Kickers
No preferred Height
Long Snappers
Preferred Height: 5'10"-6'7"
-Height is not an issue, but being too short can cause a collapse in the blocking during punts/field goals.