Stat 353 Project 1

1.Introduction

This report will analyze data from https://www.lock5stat.com specifically the CollegeScores4yr data set.

I propose the following 12 questions based on my own understanding of the data.

What is the mean of the average SAT scores for all the colleges in the data?
What is the standard deviation in the average SAT score for all the colleges the data set?
What is the range of the average SAT score for the entire data set?
What is the distribution of the average SAT scores for the entire data set?
What is the median of the average SAT scores for the entire data set?
What is the mean of the average SAT scores for private colleges in the data
What is the standard deviation of the average SAT scores for private colleges in the data
What is the median of the average SAT scores for private colleges in the data
What is the mean of the average SAT scores for public colleges in the data
What is the standard deviation of the average SAT scores for the public colleges in the data
What is the median of the average SAT scores for public colleges in the data
How do the performance and distribution of the average SAT scores differ between public and private schools

2.Analysis

Question 1: What is the mean of the average SAT score for all the colleges in the data?

## [1] 1135.25

The mean of the average SAT scores across the data set is 1135.25

Question 2: What is the standard deviation in the average SAT score for the data set?

## [1] 128.9077

The standard deviation in the average SAT score for the data set is 128.91

Question 3: What is the range of the average SAT score for the data set?

## [1]  564 1558

The range of the average SAT scores for the data set is 564-1558

Question 4: What is the distribution of the average SAT scores for the entire data set?

Question 5: What is the median of the average SAT score for the entire data set

## [1] 1121

The median of the average SAT score for the entire data set is 1121

Question 6: What is the mean of the average SAT scores for private colleges in the data set

## [1] 1145.839

The mean of the average SAT scores for private and profit colleges is 1145.84

Question 7: What is the standard deviation of the average SAT scores for private colleges in the data

## [1] 139.3497

The standard deviation of the average SAT scores for private and profit colleges in the data is 139.35

Question 8: What is the median of the average SAT scores for private colleges in the data

## [1] 1124

The median of the average SAT scores for private and profite colleges in the data is 1124

Question 9: What is the mean of the average SAT scores for public colleges in the data

## [1] 1118.91

The mean of the average SAT scores for public colleges in the data is 1118.91

Question 10: What is the standard deviation of the average SAT scores for public colleges in the data

## [1] 109.2472

The standard deviaton of the average SAT scores for public colleges in the data is 109.25

Question 11: What is the median of the SAT scores for public colleges in the data

## [1] 1105

The median of the SAT scores for public colleges in the data is 1105

Question 12: How do the performance and distribution of SAT scores differ between public and private schools

4.Appendix

Here is the code for the analysis

Reading Data

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

Mean SAT all

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

## [1] 128.9077

Standard deviation SAT all

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

## [1] 128.9077

Range of SAT all

range(college$AvgSAT, na.rm=TRUE)

## [1]  564 1558

Distribution SAT all

hist(college$AvgSAT, main="Histogram of average SAT scores", xlab="Average SAT Score")

Median SAT all

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

## [1] 1121

Mean SAT private

private_colleges <- college[college$Control %in% c("Private", "Profit"), ]
mean_private_sat <- mean(private_colleges$AvgSAT, na.rm = TRUE)
mean_private_sat

## [1] 1145.696

Standard deviation SAT private

sd_private_sat <- sd(private_colleges$AvgSAT, na.rm = TRUE)
sd_private_sat

## [1] 139.1025

Median SAT private

median_private_sat <- median(private_colleges$AvgSAT, na.rm=TRUE)
median_private_sat

## [1] 1124

Mean SAT public

public_colleges <- college[college$Control == "Public", ]
mean_public_sat <- mean(public_colleges$AvgSAT, na.rm = TRUE)
mean_public_sat

## [1] 1118.91

Standard deviation SAT public

sd_public_sat <- sd(public_colleges$AvgSAT, na.rm = TRUE)
sd_public_sat

## [1] 109.2472

Median SAT public

median_public_sat <- median(public_colleges$AvgSAT, na.rm = TRUE)
median_public_sat

## [1] 1105

Performance distribution public/private

college$Control <- factor(college$Control, levels = c("Public", "Private"))

boxplot(AvgSAT ~ Control, data = college, main = "SAT Scores by School Type", 
        ylab = "Average SAT Score", xlab = "School Type")