Question

Sportswriters and football fans expressed surprise when the Seattle Seahawks named Russell Wilson as their starting quarterback at the beginning of the 2012 season, both because he was a rookie recently drafted after playing college football, and because at 5 feet 11 inches he was the shortest starting quarterback in the National Football League. The table below contains the last name, team, conference (NFC or AFC) and height (in feet and inches) of each starting quarterback in the NFL as of September 24m 2012.

1. Compute the median height of all quarterback:

2. Compute the IQR of all quarterback heights:

3. Draw a boxplot of all quarterback heights:

4. Draw two box plots comparing the quarterback heights for the AFC and NFC:

name   team conf height
Wilson   Seattle NFC 5'11"
Bradford   St.Louis NFC 6'5"
Kolb   Arizona NFC 6'3"
Smith   San Francisco NFC 6'4"
Rodgers   Green Bay NFC 6'2"
Stafford   Detroit NFC 6'3"
Ponder   Minnesota  NFC 6'2"
Cutler   Chicago NFC 6'3"
Vick   Philadelphia NFC 6'0"
Romo   Dallas NFC 6'2"
Manning   New York Giants NFC 6'4"
Griffin   Washington NFC 6'2"
Brees   New Orleans NFC 6'0"
Ryan   Atlanta NFC 6'4"
Newton   Carolina NFC 6'5"
Freeman   Tampa Bay NFC 6'6"
Brady   New England AFC 6'4"
Tannehill   Miami AFC 6'4"
Sanchez   New York Jets AFC 6'2"
Fitzpatrick   Buffalo AFC 6'2"
Flacco   Baltimore AFC 6'6"
Roethlisberger   Pittsburgh AFC 6'5"
Dalton   Cincinatti AFC 6'2"
Weeden   Cleveland AFC 6'4"
Schaub   Houston AFC 6'5"
Luck   Indianapolis AFC 6'4"
Gabbert   Jacksonville AFC 6'5"
Locker   Tennesse AFC 6'3"
Manning   Denver AFC 6'5"
Rivers   San Diego AFC 6'5"
Palmer   Oakland AFC 6'5"
Cassel   Kansas City AFC 6'4"

Answer 1

Given data is

name	team	conf	height
Wilson	Seattle	NFC	5'11"
Bradford	St.Louis	NFC	6'5"
Kolb	Arizona	NFC	6'3"
Smith	San Francisco	NFC	6'4"
Rodgers	Green Bay	NFC	6'2"
Stafford	Detroit	NFC	6'3"
Ponder	Minnesota	NFC	6'2"
Cutler	Chicago	NFC	6'3"
Vick	Philadelphia	NFC	6'0"
Romo	Dallas	NFC	6'2"
Manning	New York Giants	NFC	6'4"
Griffin	Washington	NFC	6'2"
Brees	New Orleans	NFC	6'0"
Ryan	Atlanta	NFC	6'4"
Newton	Carolina	NFC	6'5"
Freeman	Tampa Bay	NFC	6'6"
Brady	New England	AFC	6'4"
Tannehill	Miami	AFC	6'4"
Sanchez	New York Jets	AFC	6'2"
Fitzpatrick	Buffalo	AFC	6'2"
Flacco	Baltimore	AFC	6'6"
Roethlisberger	Pittsburgh	AFC	6'5"
Dalton	Cincinatti	AFC	6'2"
Weeden	Cleveland	AFC	6'4"
Schaub	Houston	AFC	6'5"
Luck	Indianapolis	AFC	6'4"
Gabbert	Jacksonville	AFC	6'5"
Locker	Tennesse	AFC	6'3"
Manning	Denver	AFC	6'5"
Rivers	San Diego	AFC	6'5"
Palmer	Oakland	AFC	6'5"
Cassel	Kansas City	AFC	6'4"

We will use R-Software for calculation purpose .

1 . Compute the median height of all quarterback

height=scan("clipboard")

> ardt=sort(height)
> ardt
[1] 5.11 6.00 6.00 6.20 6.20 6.20 6.20 6.20 6.20 6.20 6.30 6.30 6.30 6.30 6.40
[16] 6.40 6.40 6.40 6.40 6.40 6.40 6.40 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.50
[31] 6.60 6.60

MED = (ardt[16]+ardt[17])/2
> MED                # Median
[1] 6.4

median(dt)           # R -function for meaian

Thus Median is 6.4 .

2. Compute the IQR of all quarterback heights

IQR = Q3 - Q1

Where Q3 third quartile and Q1 is 1st quartile

quantile(ardt)
0% 25% 50% 75% 100%
5.11 6.20 6.40 6.50 6.60

Thus 25% is 1st quartile and 75% is third quartile

0%	25%	50%	75%	100%
5.11	6.20	6.40	6.50	6.60

Therefore   , IQR = Q3 - Q1 = 6.50 - 6.20

                                               = 0.3

3.Draw a boxplot of all quarterback heights

br=boxplot(height,main="Boxplot", col = "orange")
br
> br
$stats
     [,1]
[1,] 6.0
[2,] 6.2
[3,] 6.4
[4,] 6.5
[5,] 6.6

$n
[1] 32

$conf
         [,1]
[1,] 6.316208
[2,] 6.483792

$out
[1] 5.11

$group
[1] 1

$names
[1] ""

4. Draw two box plots comparing the quarterback heights for the AFC and NFC

For NFC Observation are from 1 - 16

For AFC Observation are from 17 - 32

nfc=height[1:16]
afc=height[17:32]
nfc
[1] 5.11 6.50 6.30 6.40 6.20 6.30 6.20 6.30 6.00 6.20 6.40 6.20 6.00 6.40 6.50
[16] 6.60
afc
[1] 6.4 6.4 6.2 6.2 6.6 6.5 6.2 6.4 6.5 6.4 6.5 6.3 6.5 6.5 6.5 6.4

quantile(nfc)
0%    25%   50% 75%    100%
5.11    6.20    6.30    6.40    6.60

quantile(afc)
   0%     25%      50%      75% 100%
6.200    6.375    6.400    6.500    6.600

Draw two box plot

We can conclude that there is more variability in heights in NFC as compare to AFC.

50 % of NFC have height less than 6.3 or 6'3

where as only 25% of AFC have height less than 6.375 or 6'375