Session8_Deans Dilemma Dataset

Apurva (PGP32242)
04 October 2017

setwd("~/Downloads/IIM Lucknow/TERM 5/DAM")
library(readr)
DeansDilemmaData <- read_csv("~/Downloads/IIM Lucknow/TERM 5/DAM/DeansDilemmaData.csv")

Slide With Summary

summary(DeansDilemmaData)

      SlNo          Gender           Percent_SSC     Board_SSC        
 Min.   :  1.0   Length:391         Min.   :37.00   Length:391        
 1st Qu.: 98.5   Class :character   1st Qu.:56.00   Class :character  
 Median :196.0   Mode  :character   Median :64.50   Mode  :character  
 Mean   :196.0                      Mean   :64.65                     
 3rd Qu.:293.5                      3rd Qu.:74.00                     
 Max.   :391.0                      Max.   :87.20                     
  Board_CBSE         Board_ICSE         Percent_HSC    Board_HSC        
 Length:391         Length:391         Min.   :40.0   Length:391        
 Class :character   Class :character   1st Qu.:54.0   Class :character  
 Mode  :character   Mode  :character   Median :63.0   Mode  :character  
                                       Mean   :63.8                     
                                       3rd Qu.:72.0                     
                                       Max.   :94.7                     
  Stream_HSC        Percent_Degree  Course_Degree      Degree_Engg       
 Length:391         Min.   :35.00   Length:391         Length:391        
 Class :character   1st Qu.:57.52   Class :character   Class :character  
 Mode  :character   Median :63.00   Mode  :character   Mode  :character  
                    Mean   :62.98                                        
                    3rd Qu.:69.00                                        
                    Max.   :89.00                                        
 Experience_Yrs   Entrance_Test          S.TEST       Percentile_ET  
 Min.   :0.0000   Length:391         Min.   :0.0000   Min.   : 0.00  
 1st Qu.:0.0000   Class :character   1st Qu.:1.0000   1st Qu.:41.19  
 Median :0.0000   Mode  :character   Median :1.0000   Median :62.00  
 Mean   :0.4783                      Mean   :0.8286   Mean   :54.93  
 3rd Qu.:1.0000                      3rd Qu.:1.0000   3rd Qu.:78.00  
 Max.   :3.0000                      Max.   :1.0000   Max.   :98.69  
  S.TEST.SCORE    Percent_MBA    Specialization_MBA Marks_Communication
 Min.   : 0.00   Min.   :50.83   Length:391         Min.   :50.00      
 1st Qu.:41.19   1st Qu.:57.20   Class :character   1st Qu.:53.00      
 Median :62.00   Median :61.01   Mode  :character   Median :58.00      
 Mean   :54.93   Mean   :61.67                      Mean   :60.54      
 3rd Qu.:78.00   3rd Qu.:66.02                      3rd Qu.:67.00      
 Max.   :98.69   Max.   :77.89                      Max.   :88.00      
 Marks_Projectwork   Marks_BOCA     Placement             Salary      
 Min.   :50.00     Min.   :50.00   Length:391         Min.   :     0  
 1st Qu.:64.00     1st Qu.:57.00   Class :character   1st Qu.:172800  
 Median :69.00     Median :63.00   Mode  :character   Median :240000  
 Mean   :68.36     Mean   :64.38                      Mean   :219078  
 3rd Qu.:74.00     3rd Qu.:72.50                      3rd Qu.:300000  
 Max.   :87.00     Max.   :96.00                      Max.   :940000

Q1. Median Salary

median(DeansDilemmaData$Salary)

[1] 240000

Q2. What percentage of students were placed? Answer this after rounding off to 2 decimal places

table1 <- xtabs( ~Placement, data = DeansDilemmaData)
round(prop.table(table1) * 100, 2)

Placement
Not Placed     Placed 
      20.2       79.8

Q3. Create a dataframe called 'placed', containing only those students who were successfully placed?

table_Placed <- subset(DeansDilemmaData, DeansDilemmaData$Placement== "Placed")
summary(table_Placed)

      SlNo           Gender           Percent_SSC     Board_SSC        
 Min.   :  1.00   Length:312         Min.   :37.00   Length:312        
 1st Qu.: 92.75   Class :character   1st Qu.:58.00   Class :character  
 Median :182.50   Mode  :character   Median :65.92   Mode  :character  
 Mean   :186.45                      Mean   :65.58                     
 3rd Qu.:276.25                      3rd Qu.:74.45                     
 Max.   :390.00                      Max.   :87.20                     
  Board_CBSE         Board_ICSE         Percent_HSC    Board_HSC        
 Length:312         Length:312         Min.   :41.0   Length:312        
 Class :character   Class :character   1st Qu.:55.0   Class :character  
 Mode  :character   Mode  :character   Median :63.0   Mode  :character  
                                       Mean   :64.1                     
                                       3rd Qu.:72.0                     
                                       Max.   :94.7                     
  Stream_HSC        Percent_Degree  Course_Degree      Degree_Engg       
 Length:312         Min.   :35.50   Length:312         Length:312        
 Class :character   1st Qu.:57.61   Class :character   Class :character  
 Mode  :character   Median :63.00   Mode  :character   Mode  :character  
                    Mean   :63.22                                        
                    3rd Qu.:69.00                                        
                    Max.   :89.00                                        
 Experience_Yrs Entrance_Test          S.TEST       Percentile_ET  
 Min.   :0.0    Length:312         Min.   :0.0000   Min.   : 0.00  
 1st Qu.:0.0    Class :character   1st Qu.:1.0000   1st Qu.:47.29  
 Median :0.0    Mode  :character   Median :1.0000   Median :65.00  
 Mean   :0.5                       Mean   :0.8365   Mean   :56.99  
 3rd Qu.:1.0                       3rd Qu.:1.0000   3rd Qu.:80.00  
 Max.   :3.0                       Max.   :1.0000   Max.   :98.00  
  S.TEST.SCORE    Percent_MBA    Specialization_MBA Marks_Communication
 Min.   : 0.00   Min.   :51.24   Length:312         Min.   :50.00      
 1st Qu.:47.29   1st Qu.:57.64   Class :character   1st Qu.:53.00      
 Median :65.00   Median :61.30   Mode  :character   Median :58.00      
 Mean   :56.99   Mean   :61.90                      Mean   :60.59      
 3rd Qu.:80.00   3rd Qu.:66.28                      3rd Qu.:67.00      
 Max.   :98.00   Max.   :77.89                      Max.   :88.00      
 Marks_Projectwork   Marks_BOCA     Placement             Salary      
 Min.   :50.00     Min.   :50.00   Length:312         Min.   :120000  
 1st Qu.:64.00     1st Qu.:57.00   Class :character   1st Qu.:220000  
 Median :69.00     Median :63.00   Mode  :character   Median :260000  
 Mean   :68.74     Mean   :64.71                      Mean   :274550  
 3rd Qu.:74.00     3rd Qu.:73.00                      3rd Qu.:300000  
 Max.   :87.00     Max.   :96.00                      Max.   :940000

Q4. What is the median salary of students who were placed?

median(table_Placed$Salary)

[1] 260000

Q5. Create a table showing the mean salary of males and females, who were placed.

aggregate(table_Placed$Salary, by=list(Gender = table_Placed$Gender), FUN = mean)

  Gender        x
1      F 253068.0
2      M 284241.9

Q6. Generate the histogram as shown as below, showing a breakup of the MBA performance of the students who were placed

hist(table_Placed$Percent_MBA, 
        main="MBA Performance of Placed Students", 
        xlab="MBA percentage", ylab="Count", breaks = 3)

plot of chunk unnamed-chunk-10

Q7. Create a dataframe called 'notplaced', that contains a subset of only those students who were NOT placed after their MBA

Table_notplaced <- subset(DeansDilemmaData, DeansDilemmaData$Placement== "Not Placed")
summary(Table_notplaced)

      SlNo          Gender           Percent_SSC     Board_SSC        
 Min.   : 11.0   Length:79          Min.   :37.30   Length:79         
 1st Qu.:136.0   Class :character   1st Qu.:54.03   Class :character  
 Median :266.0   Mode  :character   Median :59.20   Mode  :character  
 Mean   :233.7                      Mean   :60.99                     
 3rd Qu.:327.0                      3rd Qu.:68.00                     
 Max.   :391.0                      Max.   :85.80                     
  Board_CBSE         Board_ICSE         Percent_HSC     Board_HSC        
 Length:79          Length:79          Min.   :40.00   Length:79         
 Class :character   Class :character   1st Qu.:52.10   Class :character  
 Mode  :character   Mode  :character   Median :62.00   Mode  :character  
                                       Mean   :62.61                     
                                       3rd Qu.:71.92                     
                                       Max.   :90.00                     
  Stream_HSC        Percent_Degree  Course_Degree      Degree_Engg       
 Length:79          Min.   :35.00   Length:79          Length:79         
 Class :character   1st Qu.:58.00   Class :character   Class :character  
 Mode  :character   Median :63.00   Mode  :character   Mode  :character  
                    Mean   :62.06                                        
                    3rd Qu.:67.40                                        
                    Max.   :85.00                                        
 Experience_Yrs   Entrance_Test          S.TEST       Percentile_ET  
 Min.   :0.0000   Length:79          Min.   :0.0000   Min.   : 0.00  
 1st Qu.:0.0000   Class :character   1st Qu.:1.0000   1st Qu.:21.48  
 Median :0.0000   Mode  :character   Median :1.0000   Median :56.15  
 Mean   :0.3924                      Mean   :0.7975   Mean   :46.83  
 3rd Qu.:1.0000                      3rd Qu.:1.0000   3rd Qu.:71.10  
 Max.   :2.0000                      Max.   :1.0000   Max.   :98.69  
  S.TEST.SCORE    Percent_MBA    Specialization_MBA Marks_Communication
 Min.   : 0.00   Min.   :50.83   Length:79          Min.   :50.00      
 1st Qu.:21.48   1st Qu.:56.10   Class :character   1st Qu.:54.00      
 Median :56.15   Median :60.29   Mode  :character   Median :59.00      
 Mean   :46.83   Mean   :60.74                      Mean   :60.35      
 3rd Qu.:71.10   3rd Qu.:65.04                      3rd Qu.:66.50      
 Max.   :98.69   Max.   :75.71                      Max.   :79.00      
 Marks_Projectwork   Marks_BOCA     Placement             Salary 
 Min.   :50.00     Min.   :50.00   Length:79          Min.   :0  
 1st Qu.:62.50     1st Qu.:56.50   Class :character   1st Qu.:0  
 Median :66.00     Median :63.00   Mode  :character   Median :0  
 Mean   :66.86     Mean   :63.06                      Mean   :0  
 3rd Qu.:73.00     3rd Qu.:68.50                      3rd Qu.:0  
 Max.   :79.00     Max.   :82.00                      Max.   :0

Q8. Create a dataframe called 'notplaced', that contains a subset of only those students who were NOT placed after their MBA

par(mfrow=c(1,2))
hist(table_Placed$Percent_MBA, xlab="MBA Percentage", ylab = "Count", main="MBA performance- placed students", breaks=3)
hist(Table_notplaced$Percent_MBA, xlab="MBA Percentage", ylab = "Count", main="MBA performance- not placed students", breaks=3)

plot of chunk unnamed-chunk-13

Q9. Generate two boxplots, one below the other, comparing the distribution of salaries of males and females who were placed

placed_gender.f<-factor(table_Placed$Gender,levels = c("M","F"),labels = c("Male","Female"))
boxplot(table_Placed$Salary~placed_gender.f, horizontal=TRUE, xlab="Salary", ylab="Gender", main="Comparison of Salaries of Males and Females")

plot of chunk unnamed-chunk-15

Q10. Create a dataframe called 'placedET', representing students who were placed after the MBA and who also gave some MBA entrance test before admission into the MBA program

placedET <- subset(table_Placed, S.TEST== "1")
summary(placedET)

      SlNo          Gender           Percent_SSC     Board_SSC        
 Min.   :  1.0   Length:261         Min.   :37.00   Length:261        
 1st Qu.: 95.0   Class :character   1st Qu.:58.00   Class :character  
 Median :183.0   Mode  :character   Median :66.00   Mode  :character  
 Mean   :188.8                      Mean   :65.80                     
 3rd Qu.:276.0                      3rd Qu.:74.44                     
 Max.   :390.0                      Max.   :87.20                     
  Board_CBSE         Board_ICSE         Percent_HSC     Board_HSC        
 Length:261         Length:261         Min.   :41.00   Length:261        
 Class :character   Class :character   1st Qu.:55.00   Class :character  
 Mode  :character   Mode  :character   Median :63.00   Mode  :character  
                                       Mean   :64.03                     
                                       3rd Qu.:72.00                     
                                       Max.   :94.70                     
  Stream_HSC        Percent_Degree  Course_Degree      Degree_Engg       
 Length:261         Min.   :38.00   Length:261         Length:261        
 Class :character   1st Qu.:57.80   Class :character   Class :character  
 Mode  :character   Median :63.00   Mode  :character   Mode  :character  
                    Mean   :63.33                                        
                    3rd Qu.:69.30                                        
                    Max.   :89.00                                        
 Experience_Yrs   Entrance_Test          S.TEST  Percentile_ET  
 Min.   :0.0000   Length:261         Min.   :1   Min.   : 0.00  
 1st Qu.:0.0000   Class :character   1st Qu.:1   1st Qu.:58.00  
 Median :0.0000   Mode  :character   Median :1   Median :68.71  
 Mean   :0.4904                      Mean   :1   Mean   :68.12  
 3rd Qu.:1.0000                      3rd Qu.:1   3rd Qu.:83.00  
 Max.   :3.0000                      Max.   :1   Max.   :98.00  
  S.TEST.SCORE    Percent_MBA    Specialization_MBA Marks_Communication
 Min.   : 0.00   Min.   :51.24   Length:261         Min.   :50.00      
 1st Qu.:58.00   1st Qu.:57.90   Class :character   1st Qu.:53.00      
 Median :68.71   Median :61.63   Mode  :character   Median :59.00      
 Mean   :68.12   Mean   :62.09                      Mean   :60.87      
 3rd Qu.:83.00   3rd Qu.:66.22                      3rd Qu.:67.00      
 Max.   :98.00   Max.   :77.89                      Max.   :88.00      
 Marks_Projectwork   Marks_BOCA     Placement             Salary      
 Min.   :50.00     Min.   :50.00   Length:261         Min.   :120000  
 1st Qu.:64.00     1st Qu.:57.00   Class :character   1st Qu.:220000  
 Median :70.00     Median :63.00   Mode  :character   Median :260000  
 Mean   :69.26     Mean   :64.93                      Mean   :274860  
 3rd Qu.:74.00     3rd Qu.:73.00                      3rd Qu.:300000  
 Max.   :87.00     Max.   :96.00                      Max.   :940000

Q11. Draw a Scatter Plot Matrix for 3 variables -- {Salary, Percent_MBA, Percentile_ET} using the dataframe placedET, as shown below

library(car)
scatterplotMatrix(~Salary+Percent_MBA+Percentile_ET, data = placedET, main="Scatter Plot Matrix")

plot of chunk unnamed-chunk-18

Analyzing the Salaries of Men versus Women MBA students who were placed

Q12. What is mean salary of all the students who were placed?

mean(table_Placed$Salary)

[1] 274550

Q13. Test whether the distribution of the salaries is normal

shapiro.test(table_Placed$Salary)


    Shapiro-Wilk normality test

data:  table_Placed$Salary
W = 0.84168, p-value < 2.2e-16

 # P value < 0.05; hence we reject the null hypothesis that the data are normally distributed

Q14. Create a table giving the mean salary of the men and the women MBAs who were placed?

aggregate(table_Placed$Salary, by=list(Gender = table_Placed$Gender), FUN = mean)

  Gender        x
1      F 253068.0
2      M 284241.9

Q15. Visualize the mean salary of men and women who were placed, using plotmeans()

library(gplots)
plotmeans(table_Placed$Salary~table_Placed$Gender,mean.labels =TRUE)

plot of chunk unnamed-chunk-23

Q16. Create a table giving the variance of the salary of the men and women MBAs who were placed?

aggregate(table_Placed$Salary, by=list(Gender = table_Placed$Gender), FUN = var)

  Gender          x
1      F 5504236572
2      M 9886408520

Q17. Use a suitable statistical test to compare whether the variances are significantly different?

var.test(table_Placed$Salary~table_Placed$Gender)


    F test to compare two variances

data:  table_Placed$Salary by table_Placed$Gender
F = 0.55675, num df = 96, denom df = 214, p-value = 0.00135
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.3999212 0.7927360
sample estimates:
ratio of variances 
         0.5567478 

# We reject the null hypothesis; variances are statistically significantly different

Q18. Use a suitable statistical test to compare whether there is a significant difference between the salaries of men and women? 

t.test(Salary~Gender,data = table_Placed)


    Welch Two Sample t-test

data:  Salary by Gender
t = -3.0757, df = 243.03, p-value = 0.00234
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -51138.42 -11209.22
sample estimates:
mean in group F mean in group M 
       253068.0        284241.9 

# We reject the null hypothesis that the means are equal

Analyzing the Salaries of placed MBA students who are Engineers, versus the Salaries of placed MBA students who are not Engineers

Q19. Create a table giving the mean salary of the engineers and the non-engineers MBAs who were placed?

aggregate(table_Placed$Salary, by=list(Gender = table_Placed$Degree_Engg), FUN = mean)

  Gender        x
1     No 269161.7
2    Yes 325200.0

Q20. Visualize the mean salary of the engineers and the non-engineers who were placed, using plotmeans()

library(gplots)
plotmeans(table_Placed$Salary~table_Placed$Degree_Engg, mean.labels =TRUE)

plot of chunk unnamed-chunk-29

Q21. Create a table giving the variance of the salary of the engineers and the non-engineers MBAs who were placed?

aggregate(table_Placed$Salary, by=list(Gender = table_Placed$Degree_Engg), FUN = var)

  Gender           x
1     No  7996660450
2    Yes 12994648276

Q22. Use a suitable statistical test to compare whether the variances are significantly different?

var.test(table_Placed$Salary~table_Placed$Degree_Engg)


    F test to compare two variances

data:  table_Placed$Salary by table_Placed$Degree_Engg
F = 0.61538, num df = 281, denom df = 29, p-value = 0.05124
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.3341346 1.0025622
sample estimates:
ratio of variances 
         0.6153811 

# We fail to reject the null hypothesis that the variances are equal

Q23. Use a suitable statistical test to compare whether there is a significant difference between the salaries of the engineers and the non-engineers? 

t.test(Salary~Degree_Engg, data = table_Placed)


    Welch Two Sample t-test

data:  Salary by Degree_Engg
t = -2.6085, df = 32.907, p-value = 0.01357
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -99750.14 -12326.45
sample estimates:
 mean in group No mean in group Yes 
         269161.7          325200.0 

# We reject the null hypothesis that the means are equal

THANK YOU