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A Statistical Paper

by Morgan M. Smith

Management 215-03

Professor Kirchner

18 April 2007

The top business schools in America are becoming more difficult to get accepted to. It seems almost impossible to get into schools like Harvard, University of Pennsylvania, Stanford, without having a parent who attended, or having a high socioeconomic status. The demographics of the top 50 business school in the United States are the topic of interest in this paper. The following demographics that were found, gathered, and analyzed were in-state vs. out-of-state students, gender, race, class ranking, and overall high school grade point average of the student population at these top schools. The top 50 business school in the United States are the following: Harvard, Stanford, UPenn, MIT, Northwestern, University of Chicago, Dartmouth College, University of California-Berkeley, Columbia University, NYU, University of Michigan-Ann Arbor, Duke University, UVA, Cornell University, Yale, UCLA, Carnegie Mellon, University of North Carolina-Chapel Hill, University of Texas-Austin, Emory, USC, Ohio State, Purdue University, Indiana University-Bloomington, Georgetown University, Georgia Institute of Technology, University of Maryland-College Park, University of Minnesota-Twin Cities, Michigan State University, Texas A&M University, University of Washington, University of Wisconsin-Madison, Washington University in St. Louis, Pennsylvania State University Park, Vanderbilt University, University of Rochester, University of Florida, University of Illinois at Urbana-Champaign, Boston College, University of Notre Dame, Arizona State University, Babson College, Boston University, Brigham Young University, Tulane University, University of California-Davis, University of Georgia, Rice University, Wake Forest University, University of Iowa (U.S. News). The information provided in this paper can give the reader insight into the academic caliber of the students, diversity on campus, etc. The demographics of these first tier business schools are distributed in several ways. The statistics gathered is in the form of percentages, of the student population at a particular university/college. Once all the values were collected and grouped according to the demographic, it then became raw data, which is defined as unorganized information (Basic Statistics 25). The data found can be categorized as descriptive statistics. The data that I’ve collected is qualitative and quantitative statistics. The two levels of measurement that are present in the raw data collected are nominal-level, and interval level. Nominal-level data is observations of a qualitative variable that can only be classified and counted. Nominal-level data is mutually exclusive, and exhaustive. Mutual exclusivity is defined as a property of a set of categories such that an individual or object is included in only one category (Basic Statistics 10). Exhaustive is a characteristic of a set of categories such that each individual or object must appear in a category (Basic Statistics 10). Several demographics found in my research are nominal-level data: gender, race/nationality, and in-state vs. out-of-state students. In addition to interval-level data also being mutually exclusive, and exhaustive; data classifications are ranked or ordered according to the particular trait they possess (Basic Statistics 10). Overall high school grade point average, and class rank are considered to be interval-level data. After grouping the data from lowest to highest, it was quite easy to find several different measures that are very helpful in making inferences. With characteristics like gender, race, and in-state vs. out-of-state students being of nominal-level, I constructed pie charts for each demographic. The amount of students who attend school out-of-state compared to those who attend school in-state is very close; 51% of the student population at the top 50 business schools are out-of-state students, compared to the 49% of students who chose to attend school in-state. It doesn’t come as a surprise that there are more women than men attending these first tier schools. About 52% of the student population at these schools is women; the remaining 48% are (of course) men. The numbers are considerably different at lower tier schools, i.e. Historically Black Colleges and Universities. The set of nominal-level data that was not evenly distributed like the previous two demographics was race/nationality. More than half of the student population at these post-secondary institutions is White/Non-Hispanic. To be more specific, 60% of the student population is Caucasian. The second most prominent race on these campuses is Asian/Pacific Islander, who makes up 15% of the student population. Surprisingly, Hispanics are the third largest race attending these top business schools, which is 7% of the student population. Making up only 6% of the student population at these first tier schools are Blacks/Non-Hispanics. American Indian/Alaskan Native are a measly 1% of the student population. The remaining 11% are non-resident aliens, and those who chose not to report their race/ethnicity. The number of students who attend school in-state compared to those who don’t, is fairly even, in addition to gender ratios at top tier schools in the United States. I believe that Caucasians will always be the majority at ivy leagues, and first tier schools. One demographic in particular that was somewhat difficult to construct a graph for was, class rank. Class ranking is demographic that is a cumulative or in statistical terms, a continuous variable. A continuous variable can assume any value within a specific range (Basic Statistics 9). The percentiles that were used when identifying class rank were 10%, 25%, and 50%. The average amount of students that were ranked in the top 10% of their graduating class in high school was 69.5%. About 95% of the student population at these schools of such high-caliber was in the top 25% of their high school graduating class. Almost the entire student population, exactly 99% of the students is ranked in the top 50% in their class. The class rankings show that these schools are very competitive, and accept only the best. The most important demographic being discussed in this paper is grade point average. The overall high school grade point average was divided into six classes: 3.75 and higher, 3.5-3.74, 3.25-3.49, 3.0-3.24, 2.5-2.99, 2.49 and below. With this particular characteristic, I was able to calculate the mean, median, mode, and range, which are measures of location (Basic Statistics 69). The percentage of students with a G.P.A. of 3.75 and higher is 58.34%. About 20.5% of the student population graduated high school with an overall grade point average between 3.5 and 3.74. Only 10.54% of students attending the top business schools had a grade point average between 3.25 and 3.49. The average of each class is decreasing at a decreasing rate. A low average, 6.66% of the college students earned a G.P.A. between 3.0 and 3.24. A measly 3.5% of the student population attending the top business schools had a high school grade point average between 2.5 and 2.99. Not even 1% of the student population had a high school G.P.A. of 2.49 and below. Four out of six of the classes have positively skewed distributions, meaning that the mean was the largest measure, median was second largest, and mode being the smallest of the three (Basic Statistics 69). One class has a negatively skewed distribution, which is caused when the mean is the lowest of the three measures (Basic Statistics 70). The median is usually the second lowest, and the mode is the largest of the three. More than half of the student population had a high school G.P.A. of a 3.75 or higher. What I found to be most shocking was that the most competitive schools in this country admitted students with a grade point average of a 2.49 or lower. Not only is the topic of this research paper important, but just the assignment itself has significance in relation to management. A manager is somebody who controls, directs, or organizes business affairs. A successful manager should have great organizational skills. In my opinion, this research paper has improved my organizational skills tremendously. When I began collecting data for this paper, I found and gathered over 500 values of raw data, which I turned into meaningful measures like mean, median, mode, range, frequency, etc. I categorized each percentage, and arranged them numerically. I’ve also drawn several conclusions from the data collected over the past two weeks. An effective manager should be able to turn raw data into meaningful numbers, which is important when making business decisions. An individual, who is in the business industry, can find this research to be of significance if they considered making the typical college student a consumer of theirs. Like any manager, more specifically an entrepreneur, should study the demographics of their potential consumers to determine what type of good or service to provide. This information can also be helpful to a college student, considering attending a school mentioned in this paper, i.e. myself. Upon completion of this paper, I’ve have a greater knowledge of what the top business schools in the United States expect from their applicants.

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|G.P.A |Schools With 0% of Population in Given Range |Relative Frequency |Found by |

|3.75 and higher |0 |0 |0/50 |

|3.5 - 3.74 |0 |0 |0/50 |

|3.25 - 3.49 |0 |0 |0/50 |

|3.0 - 3.24 |2 |4.00% | |

|2.5 - 2.99 |8 |16.00% | |

|2.49 and lower |40 |80.00% |40/50 |

|Total |50 |100.00% |50/50 |

| | | | |

[pic]

[pic]

|Student Population's Secondary School G.P.A. |

| | | | | | | | |

|G.P.A. |Measure of Location |Value | | | | | |

|3.75 and higher |Mean |58.34 | | | | | |

| |Median |58.5 | | | | | |

| |Mode |36 | | | | | |

| |Range |74 | | | | | |

| | | | | | | | |

|3.5 - 3.74 |Mean |20.5 | | | | | |

| |Median |20 | | | | | |

| |Mode |23 | | | | | |

| |Range |90 | | | | | |

| | | | | | | | |

|3.25 - 3.49 |Mean |10.54 | | | | | |

| |Median |11.5 | | | | | |

| |Mode |16 | | | | | |

| |Range |28 | | | | | |

| | | | | | | | |

|3.0 - 3.24 |Mean |6.66 | | | | | |

| |Median |6 | | | | | |

| |Mode |1 | | | | | |

| |Range |23 | | | | | |

| | | | | | | | |

|2.5 - 2.99 |Mean |3.5 | | | | | |

| |Median |2 | | | | | |

| |Mode |2 | | | | | |

| |Range |23 | | | | | |

| | | | | | | | |

|2.49 and below |Mean |0.46 | | | | | |

| |Median |0 | | | | | |

| |Mode |0 | | | | | |

| |Range |6 | | | | | |

Works Cited

“America’s Best Schools 2008.” U.S. News & World Report. 2007. US. News & World

Report. 1 Apr. 2007 .

CollegeBoard.com 2007. College Board. 1 Apr. 2007 .

Lind, Douglas, William Marchal, Samuel Wathen. Basic Statistics for Business &

Economics. New York: McGraw Hill, 2006.…...

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