Introduction

We use data from the “CollegeScores4yr” section of the statistics page provided on D2L.

I propose the following 10 questions based on my own understanding of the data.

Analysis

We will explore the questions in detail, below is the data set provided.

##                                  Name State     ID Main
## 1            Alabama A & M University    AL 100654    1
## 2 University of Alabama at Birmingham    AL 100663    1
## 3                  Amridge University    AL 100690    1
## 4 University of Alabama in Huntsville    AL 100706    1
## 5            Alabama State University    AL 100724    1
## 6           The University of Alabama    AL 100751    1
##                                                                Accred
## 1 Southern Association of Colleges and Schools Commission on Colleges
## 2 Southern Association of Colleges and Schools Commission on Colleges
## 3 Southern Association of Colleges and Schools Commission on Colleges
## 4 Southern Association of Colleges and Schools Commission on Colleges
## 5 Southern Association of Colleges and Schools Commission on Colleges
## 6 Southern Association of Colleges and Schools Commission on Colleges
##   MainDegree HighDegree Control    Region Locale Latitude Longitude AdmitRate
## 1          3          4  Public Southeast   City 34.78337 -86.56850    0.9027
## 2          3          4  Public Southeast   City 33.50570 -86.79935    0.9181
## 3          3          4 Private Southeast   City 32.36261 -86.17401        NA
## 4          3          4  Public Southeast   City 34.72456 -86.64045    0.8123
## 5          3          4  Public Southeast   City 32.36432 -86.29568    0.9787
## 6          3          4  Public Southeast   City 33.21187 -87.54598    0.5330
##   MidACT AvgSAT Online Enrollment White Black Hispanic Asian Other PartTime
## 1     18    929      0       4824   2.5  90.7      0.9   0.2   5.6      6.6
## 2     25   1195      0      12866  57.8  25.9      3.3   5.9   7.1     25.2
## 3     NA     NA      1        322   7.1  14.3      0.6   0.3  77.6     54.4
## 4     28   1322      0       6917  74.2  10.7      4.6   4.0   6.5     15.0
## 5     18    935      0       4189   1.5  93.8      1.0   0.3   3.5      7.7
## 6     28   1278      0      32387  78.5  10.1      4.7   1.2   5.6      7.9
##   NetPrice  Cost TuitionIn TuitonOut TuitionFTE InstructFTE FacSalary
## 1    15184 22886      9857     18236       9227        7298      6983
## 2    17535 24129      8328     19032      11612       17235     10640
## 3     9649 15080      6900      6900      14738        5265      3866
## 4    19986 22108     10280     21480       8727        9748      9391
## 5    12874 19413     11068     19396       9003        7983      7399
## 6    21973 28836     10780     28100      13574       10894     10016
##   FullTimeFac Pell CompRate Debt Female FirstGen MedIncome
## 1        71.3 71.0    23.96 1068   56.4     36.6      23.6
## 2        89.9 35.3    52.92 3755   63.9     34.1      34.5
## 3       100.0 74.2    18.18  109   64.9     51.3      15.0
## 4        64.6 27.7    48.62 1347   47.6     31.0      44.8
## 5        54.2 73.8    27.69 1294   61.3     34.3      22.1
## 6        74.0 18.0    67.87 6430   61.5     22.6      66.7

Q1: What is the mean admission rate from the colleges in the data?

## [1] 0.6702025

The mean admission rate is 67.02025%.

Q2: What is the correlation between admission rate and cost?

## [1] -0.3036798

The correlation between admission rate and cost is -0.3036798.

Q3: What is the distribution of admission rate?

The histogram above shows the distribution for admission rate.

Q4: What is the median average SAT score for the colleges in the data?

## [1] 1121

The median SAT score is 1,121 for the colleges in the data.

Q5: What is the standard deviation for the average SAT score among the colleges in the data?

## [1] 128.9077

The standard deviation for the average SAT scores from the given colleges is 128.9077.

Q6: What is the variance in cost for the colleges in the given data?

## [1] 233433900

The variance in cost for the given colleges is 233,433,900.

Q7: What is the median percent of female stuedents at the colleges in the data?

## [1] 59.15

The median percent of female student at the colleges in the data is 59.15%.

Q8: What is the correlation between enrollment and cost for the given colleges?

## [1] -0.1914363

The correlation between enrollment and cost is -0.1914363.

Q9: What is the distribution for completion rates at the colleges in the data set?

The histogram above shows the distribution of completion rates for the colleges in the data.

Q10: What is the mean debt for students from the colleges in the data?

## [1] 2365.655

The mean debt among students from the colleges in the data is $2,365.655.

Summary of Data

This is a summary of the provided college data set by looking at the analysis above. The average admission rate across the colleges is approximately 67%, showing a relatively high overall acceptance rate. This might then show that these institutions have less strict admission criteria. The distribution of admission rates, as shown in the histogram, show that the majority of the colleges in the data have relatively high admission rates. The majority are located between 60% and 80% admission rates. A negative correlation of -0.3036798 exists between admission rates and cost. This shows that colleges with higher admission rates tend to have lower costs, and vice versa. However, the correlation is very small, and may not be the leading cause for costs or admissions of these colleges. The variance in cost is fairly high, at 233,433,900, which can show a large range of costs between the colleges. Another cost related statistic is that the mean student debt is $2,365.655. The median average SAT score for the given colleges is 1,121 and this score can be anywhere from, 400 to 1,600, so 1,121 is a reasonable median. The standard deviation of SAT scores is 128.9077, indicating the spread of scores among the students from each college. The median percentage of female students is 59.15%, which means that the given colleges are leaning towards a female majority in most cases. The correlation between enrollment and cost is a negative correlation of -0.1914363, indicating a slight trend that shows higher enrollment correlates to lower costs. The distribution of completion rates, illustrated in the provided histogram, shows that most colleges were between 40% and 60% completion rates.

Appendix

# Q1 Code: mean(college$AdmitRate, na.rm = TRUE)
# Q2 Code: cor(college$AdmitRate, college$Cost, use = "complete.obs")
# Q3 Code: hist(college$AdmitRate, main = "Histogram of Admission Rate", xlab = "Admission Rate", col = "turquoise")
# Q4 Code: median(college$AvgSAT, na.rm = TRUE)
# Q5 Code: sd(college$AvgSAT, na.rm = TRUE)
# Q6 Code: var(college$Cost, na.rm=TRUE)
# Q7 Code: median(college$Female, na.rm = TRUE)
# Q8 Code: cor(college$Cost, college$Enrollment, use = "complete.obs")
# Q9 Code: hist(college$CompRate, main = "Histogram of Completion Rate", xlab = "Completion Rate", col = "gray")
# Q10 Code: mean(college$Debt, na.rm = TRUE)