Question

		6-year Graduation Rate
	Status	All students	athletes
Duke	Private	95%	87%
UNC-CH	Public	86%	74%
NCSU	Public	71%	51%
Wake	Private	88%	80%
ECU	Public	54%	58%
UNC-C	Public	51%	59%
BC	Private	91%	90%
Clemson	Public	79%	66%
FSU	Public	70%	53%
Ga Tech	Public	77%	56%
U-MD	Public	82%	66%
Miami	Private	77%	70%
UVA	Public	93%	73%
Va Tech	Public	78%	72%
UC-Davis (D-II)	Public	81%	81%
Florida	Public	82%	61%
UGA	Public	79%	59%
Illinois	Public	82%	70%
Iowa St	Public	67%	79%
Michigan St	Public	75%	66%
Minnesota	Public	66%	71%
Ohio State	Public	73%	67%
Penn State	Public	85%	76%
	Public	72%	66%
Texas A&M	Public	78%	61%
Wisconsin	Public	81%	59%

The graduation rate of college students is a subject of considerable interest and is a frequent topic in the news. College/university administrators use the graduation rate as a barometer of student success at their respective institution. State legislators are interested in the graduation rate since most states subsidize the cost of educating each in-state student at public universities and colleges.

Graduation rates are also used to evaluate university athletic programs. Athletic directors do not relish the negative publicity that results when the graduation rate of athletes is significantly lower than that of the general student body.

This Excel file graduation rates shows recent 6-year graduation rates for athletes and the general student body at 26 universities. The institutions included are all ACC schools, NCSU peer-designated institutions, and two of the larger schools in the UNC system - ECU and UNC-Charlotte.

Question. Use the data above to find the quartiles and the median of the general student body graduation rates and the athlete graduation rates (use the method discussed in class for calculating quartiles; see the Tukey method on p.58 of the ebook/text or p. 23 in Lecture Unit 2 of the coursepack).

____% Q₁, first quartile for general student body graduation rate
_____ % Q₁, first quartile for athlete graduation rate

_____ % median, general student body graduation rate
_______% median, athlete graduation rate

_____% Q₃, third quartile for general student body graduation rate
_____% Q₃, third quartile for athlete graduation rate

Answer 1

To calculate the Quartiles and Median , we first need to arrange the given data in Ascending Order.

All students ( % ) :   Arranged Horizontally

51	54	66	67	70	71	72	73	75	77	77	78	78
79	79	81	81	82	82	82	85	86	88	91	93	95

Using Tukey's Method :

Second Quartile ( Q₂ ) :  Median is halfway between the middle two numbers i.e. 78 and 79

Median = 78.5 %

First Quartile ( Q₁ ) :   The Lower Quartile is the Median of the lower half i .e , :

Median of : ( 51 , 54 , 66 , 67 , 70 , 71 , 72 , 73 , 75 , 77 , 77 , 78 , 78 ) = 72

  First Quartile = 72 %

Third Quartile ( Q₃ ) :   The Upper Quartile is the Median of the upper half i .e , :

Median of : ( 79 , 79 , 81 , 81 , 82 , 82 , 82 , 85 , 86 , 88 , 91 , 93 , 95 ) = 82

Third Quartile = 82 %

Atheletes ( % ) :   Arranged Horizontally

51	53	56	58	59	59	59	61	61	66	66	66	66
67	70	70	71	72	73	74	76	79	80	81	87	90

Using Tukey's Method :

Second Quartile ( Q₂ ) :  Median is halfway between the middle two numbers i.e. 66 and 67

Median = 66.5 %

First Quartile ( Q₁ ) :   The Lower Quartile is the Median of the lower half i .e , :

Median of : ( 51 , 53 , 56 , 58 , 59 , 59 , 59 , 61 , 61 , 66 , 66 , 66 , 66 ) = 59

  First Quartile = 59 %

Third Quartile ( Q₃ ) :   The Upper Quartile is the Median of the upper half i .e , :

Median of : ( 67 , 70 , 70 , 71 , 72 , 73 , 74 , 76 , 79 , 80 , 81 , 87 , 90 ) = 74

Third Quartile = 74 %