Stat 353 Project 1: Exploring College Data

1. Introduction

We use the data from Statistics: Unlocking the Power of Data
by Lock, Lock, Lock, Lock, and Lock

I propose the following 10 questions based on my curiosity

What is the average annual cost for four-year colleges in the US?
Which region (Midwest, South, Northeast, West) tends to have higher average faculty salaries?
How spread out are student loan amounts across all colleges?
What is the median graduation rate among private vs. public colleges?
What is the range of average SAT scores across all institutions?
Which region has the largest variation in student population size?
What proportion of colleges have an admission rate below 50%?
How does the average tuition differ between in-state and out-of-state students?
What is the distribution shape (histogram) of graduation rates?
Do colleges with higher average SAT scores tend to have higher graduation rates?

The 10 questions proposed by CHATGPT:

What is the mean, median, and standard deviation of average student debt?
What is the average admission rate for colleges with graduation rates above 70%?
Which region has the highest average earnings 10 years after graduation?
What is the variance of tuition among private four-year institutions?
Create a histogram of average SAT scores to show their distribution.
Compare average faculty salaries between public and private colleges using a boxplot.
Is there a correlation between average student debt and average earnings 10 years after graduation?
What percentage of colleges charge more than $30,000 in annual tuition?
Create a pie chart showing the proportion of colleges by region.
Compare admission rate and average student loan using a scatterplot.

The final 10 questions:

What is the average annual cost for four-year colleges?
What is the median graduation rate among private vs. public colleges?
Which region has the highest average faculty salary?
What is the average admission rate across all colleges?
What is the correlation between SAT score and graduation rate?
How variable are student loan amounts?
Create a histogram of average earnings 10 years after graduation.
Compare tuition between in-state and out-of-state students.
Show the distribution of graduation rates by region.
Is there a relationship between tuition and earnings 10 years after graduation?

Analysis

We will explore the questions in detail

college = read.csv("https://www.lock5stat.com/datasets3e/CollegeScores4yr.csv")
head(college)

##                                  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 average annual cost for four-year colleges?

mean(college$Cost, na.rm = TRUE)

## [1] 34277.31

median(college$Cost, na.rm = TRUE)

## [1] 30699

sd(college$Cost, na.rm = TRUE)

## [1] 15278.54

hist(college$Cost,
     main = "Distribution of Annual Cost",
     xlab = "Average Annual Cost ($)",
     col = "Blue",
     border = "white")

Q2. What is the median graduation rate among private vs. public colleges?

aggregate(CompRate ~ Control, data = college, median, na.rm = TRUE)

##   Control CompRate
## 1 Private   56.240
## 2  Profit   26.390
## 3  Public   48.575

boxplot(CompRate ~ Control,
        data = college,
        main = "Completion Rate by College Type",
        xlab = "College Type",
        ylab = "Completion Rate (%)",
        col = c("White", "Black"))

Q3. Which region has the highest average faculty salary?

aggregate(FacSalary ~ Region, data = college, mean, na.rm = TRUE)

##      Region FacSalary
## 1   Midwest  7113.745
## 2 Northeast  8305.674
## 3 Southeast  6820.719
## 4 Territory  4333.978
## 5      West  7837.133

barplot(tapply(college$FacSalary, college$Region, mean, na.rm = TRUE),
        main = "Average Faculty Salary by Region",
        xlab = "Region",
        ylab = "Average Faculty Salary ($)",
        col = "red",
        las = 2)

Q4. What proportion of colleges have an admission rate below 50 %?

mean(college$AdmitRate, na.rm = TRUE)

## [1] 0.6702025

median(college$AdmitRate, na.rm = TRUE)

## [1] 0.69505

sd(college$AdmitRate, na.rm = TRUE)

## [1] 0.208179

hist(college$AdmitRate,
     main = "Distribution of Admission Rates",
     xlab = "Admission Rate (%)",
     col = "lightblue")

Q5. What is the correlation between SAT score and graduation rate?

cor(college$AvgSAT, college$CompRate, use = "complete.obs")

## [1] 0.8189495

plot(college$AvgSAT, college$CompRate,
     main = "SAT vs Completion Rate",
     xlab = "Average SAT Score",
     ylab = "Completion Rate (%)",
     col = "red",
     pch = 19)

Q6. How variable are student loan amounts?

mean(college$Debt, na.rm = TRUE)

## [1] 2365.655

sd(college$Debt, na.rm = TRUE)

## [1] 5360.986

var(college$Debt, na.rm = TRUE)

## [1] 28740171

hist(college$Debt,
     main = "Distribution of Student Debt",
     xlab = "Debt Amount ($)",
     col = "yellow",
     border = "white")

Q7. Create a histogram of average earnings 10 years after graduation

hist(college$MedIncome,
     main = "Distribution of Median Family Income",
     xlab = "Median Family Income ($)",
     col = "dark green",
     border = "white")

mean(college$MedIncome, na.rm = TRUE)

## [1] 46.51453

sd(college$MedIncome, na.rm = TRUE)

## [1] 22.85785

Q8. Compare tuition between in-state and out-of-state students

boxplot(college$TuitionIn, college$TuitonOut,
        names = c("In-State", "Out-of-State"),
        main = "Tuition Comparison: In-State vs Out-of-State",
        ylab = "Tuition ($)",
        col = c("white", "orange"))

Q9. Show the distribution of graduation rates by region

boxplot(CompRate ~ Region,
        data = college,
        main = "Completion Rate by Region",
        xlab = "Region",
        ylab = "Completion Rate (%)",
        las = 2)

Q10. Is there a relationship between tuition and earnings 10 years after graduation?

cor(college$Cost, college$MedIncome, use = "complete.obs")

## [1] 0.589288

plot(college$Cost, college$MedIncome,
     main = "Cost vs Median Family Income",
     xlab = "Average Cost ($)",
     ylab = "Median Family Income ($)",
     pch = 19,
     col = "darkgreen")

Summary

This project helped me understand how to use descriptive statistics in R to explore real college data. I used measures like the mean, median, standard deviation, and correlation, along with visual tools such as histograms, boxplots, and scatterplots. From the results, I noticed that the average annual cost for four-year colleges is around the mid-$20,000s, but some private schools are much higher. Private colleges tend to have higher graduation rates, while for-profit ones have the lowest. The Northeast region showed the highest average faculty salaries compared to other areas.

Most colleges have admission rates between 50% and 90%, meaning they’re not extremely selective. There was also a clear positive relationship between SAT scores and graduation rates. Student debt and family income were both skewed, showing that most students fall within lower ranges. Out-of-state tuition was much higher than in-state, and family income was higher for students attending more expensive schools. Overall, this project helped me practice using R and understand how data analysis can reveal interesting patterns about U.S. colleges.

Appendix

# Load dataset
college <- read.csv("https://www.lock5stat.com/datasets3e/CollegeScores4yr.csv")

# Q1. What is the average annual cost for four-year colleges?

mean(college$Cost, na.rm = TRUE)

## [1] 34277.31

median(college$Cost, na.rm = TRUE)

## [1] 30699

sd(college$Cost, na.rm = TRUE)

## [1] 15278.54

hist(college$Cost,
     main = "Distribution of Annual Cost",
     xlab = "Average Annual Cost ($)",
     col = "blue",
     border = "white")

# Q2. What is the median graduation rate among private vs. public colleges?


aggregate(CompRate ~ Control, data = college, median, na.rm = TRUE)

##   Control CompRate
## 1 Private   56.240
## 2  Profit   26.390
## 3  Public   48.575

boxplot(CompRate ~ Control,
        data = college,
        main = "Completion Rate by College Type",
        xlab = "College Type",
        ylab = "Completion Rate (%)",
        col = c("White", "black"))

# Q3. Which region has the highest average faculty salary?

aggregate(FacSalary ~ Region, data = college, mean, na.rm = TRUE)

##      Region FacSalary
## 1   Midwest  7113.745
## 2 Northeast  8305.674
## 3 Southeast  6820.719
## 4 Territory  4333.978
## 5      West  7837.133

barplot(tapply(college$FacSalary, college$Region, mean, na.rm = TRUE),
        main = "Average Faculty Salary by Region",
        xlab = "Region",
        ylab = "Average Faculty Salary ($)",
        col = "red",
        las = 2)

# Q4. What proportion of colleges have an admission rate below 50 %?

mean(college$AdmitRate, na.rm = TRUE)

## [1] 0.6702025

median(college$AdmitRate, na.rm = TRUE)

## [1] 0.69505

sd(college$AdmitRate, na.rm = TRUE)

## [1] 0.208179

hist(college$AdmitRate,
     main = "Distribution of Admission Rates",
     xlab = "Admission Rate (%)",
     col = "lightblue")

# Q5. What is the correlation between SAT score and graduation rate?

cor(college$AvgSAT, college$CompRate, use = "complete.obs")

## [1] 0.8189495

plot(college$AvgSAT, college$CompRate,
     main = "SAT vs Completion Rate",
     xlab = "Average SAT Score",
     ylab = "Completion Rate (%)",
     col = "red",
     pch = 19)

# Q6. How variable are student loan amounts?

mean(college$Debt, na.rm = TRUE)

## [1] 2365.655

sd(college$Debt, na.rm = TRUE)

## [1] 5360.986

var(college$Debt, na.rm = TRUE)

## [1] 28740171

hist(college$Debt,
     main = "Distribution of Student Debt",
     xlab = "Debt Amount ($)",
     col = "yellow",
     border = "white")

# Q7. Create a histogram of average earnings 10 years after graduation

hist(college$MedIncome,
     main = "Distribution of Median Family Income",
     xlab = "Median Family Income ($)",
     col = "darkgreen",
     border = "white")

mean(college$MedIncome, na.rm = TRUE)

## [1] 46.51453

sd(college$MedIncome, na.rm = TRUE)

## [1] 22.85785

# Q8. Compare tuition between in-state and out-of-state students

boxplot(college$TuitionIn, college$TuitonOut,
        names = c("In-State", "Out-of-State"),
        main = "Tuition Comparison: In-State vs Out-of-State",
        ylab = "Tuition ($)",
        col = c("white", "orange"))

# Q9. Show the distribution of graduation rates by region

boxplot(CompRate ~ Region,
        data = college,
        main = "Completion Rate by Region",
        xlab = "Region",
        ylab = "Completion Rate (%)",
        las = 2)

# Q10. Is there a relationship between tuition and earnings 10 years after graduation?

cor(college$Cost, college$MedIncome, use = "complete.obs")

## [1] 0.589288

plot(college$Cost, college$MedIncome,
     main = "Cost vs Median Family Income",
     xlab = "Average Cost ($)",
     ylab = "Median Family Income ($)",
     pch = 19,
     col = "darkgreen")