Chapter 4: Descriptive Statistical Measures

Exercise 7: Compute the Range (Pg. 152)

Compute descriptive statistics for liberal arts colleges and research universities in the Excel file Colleges and Universities. Compare the two types of colleges. What can you conclude?

df <- read.csv("./data/colleges-and-universities.csv")
df
summary(df[df$Type == "Lib Arts", ])
##        School           Type      Median.SAT   Acceptance.Rate 
##  Amherst  : 1   Lib Arts  :25   Min.   :1170   Min.   :0.2200  
##  Barnard  : 1   University: 0   1st Qu.:1230   1st Qu.:0.3300  
##  Bates    : 1                   Median :1255   Median :0.3800  
##  Bowdoin  : 1                   Mean   :1257   Mean   :0.4056  
##  Bryn Mawr: 1                   3rd Qu.:1290   3rd Qu.:0.4900  
##  Carleton : 1                   Max.   :1336   Max.   :0.6700  
##  (Other)  :19                                                  
##  Expenditures.Student   Top.10..HS     Graduation..  
##  Min.   :15904        Min.   :47.00   Min.   :72.00  
##  1st Qu.:18847        1st Qu.:61.00   1st Qu.:80.00  
##  Median :20377        Median :68.00   Median :85.00  
##  Mean   :21612        Mean   :67.24   Mean   :84.12  
##  3rd Qu.:24718        3rd Qu.:76.00   3rd Qu.:88.00  
##  Max.   :27879        Max.   :86.00   Max.   :93.00  
## 
summary(df[df$Type == "University", ])
##              School           Type      Median.SAT   Acceptance.Rate 
##  Berkeley       : 1   Lib Arts  : 0   Min.   :1109   Min.   :0.1700  
##  Brown          : 1   University:24   1st Qu.:1223   1st Qu.:0.2400  
##  Cal Tech       : 1                   Median :1280   Median :0.3150  
##  Carnegie Mellon: 1                   Mean   :1270   Mean   :0.3554  
##  Columbia       : 1                   3rd Qu.:1330   3rd Qu.:0.4550  
##  Cornell        : 1                   Max.   :1400   Max.   :0.6400  
##  (Other)        :18                                                  
##  Expenditures.Student   Top.10..HS     Graduation..  
##  Min.   : 19365       Min.   :52.00   Min.   :61.00  
##  1st Qu.: 26098       1st Qu.:76.25   1st Qu.:75.75  
##  Median : 37867       Median :83.50   Median :86.00  
##  Mean   : 38861       Mean   :81.46   Mean   :82.33  
##  3rd Qu.: 46139       3rd Qu.:90.25   3rd Qu.:89.25  
##  Max.   :102262       Max.   :98.00   Max.   :93.00  
## 
par(mfrow = c(2,3))
boxplot(Median.SAT ~ Type, data = df, main = "Median.SAT")
boxplot(Acceptance.Rate ~ Type, data = df, main = "Acceptance.Rate")
boxplot(Expenditures.Student ~ Type, data = df, main = "Expenditures.Student")
boxplot(Top.10..HS ~ Type, data = df, main = "Top.10..HS")
boxplot(Graduation.. ~ Type, data = df, main = "Graduation..")

Kết luận:

Có sự khác biệt giữa 2 nhóm Lib Arts và University. - Về điểm SAT: University cao hơn (1270 > 1257) - Về tỉ lệ đậu: Lib Art cao hơn (40% > 35%) - Về chi phí học: University cao hơn 1.8 lần ($38,861 > $21,612) - Về tỉ lệ sv nằm trong top 10% ở trường trung học: University cao hơn 1.2 lần (81 > 67) - Về tỉ lệ tốt nghiệp: Lib Art cao hơn (84% > 82%)

Tóm lại, University thu hút được nhiều sv giỏi hơn, có tỉ lệ đậu khắt khe hơn và tỉ lệ tốt nghiệp thấp hơn. Lib Arts là sự lựa chọn dễ dàng hơn cho sinh viên.