Dean’s Dillemma:Slection of Students for the MBA Program
Ayan Ghosh
9 December 2017
this is HBR Case Study “Dean’s Dilemma: Selection of Students for the MBA Program”
dean.df <- read.csv(paste("Data - Deans Dilemma.csv", sep=""))
View(dean.df)
summary(dean.df)## SlNo Gender Gender.B Percent_SSC Board_SSC
## Min. : 1.0 F:127 Min. :0.0000 Min. :37.00 CBSE :113
## 1st Qu.: 98.5 M:264 1st Qu.:0.0000 1st Qu.:56.00 ICSE : 77
## Median :196.0 Median :0.0000 Median :64.50 Others:201
## Mean :196.0 Mean :0.3248 Mean :64.65
## 3rd Qu.:293.5 3rd Qu.:1.0000 3rd Qu.:74.00
## Max. :391.0 Max. :1.0000 Max. :87.20
##
## Board_CBSE Board_ICSE Percent_HSC Board_HSC
## Min. :0.000 Min. :0.0000 Min. :40.0 CBSE : 96
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:54.0 ISC : 48
## Median :0.000 Median :0.0000 Median :63.0 Others:247
## Mean :0.289 Mean :0.1969 Mean :63.8
## 3rd Qu.:1.000 3rd Qu.:0.0000 3rd Qu.:72.0
## Max. :1.000 Max. :1.0000 Max. :94.7
##
## Stream_HSC Percent_Degree Course_Degree
## Arts : 18 Min. :35.00 Arts : 13
## Commerce:222 1st Qu.:57.52 Commerce :117
## Science :151 Median :63.00 Computer Applications: 32
## Mean :62.98 Engineering : 37
## 3rd Qu.:69.00 Management :163
## Max. :89.00 Others : 5
## Science : 24
## Degree_Engg Experience_Yrs Entrance_Test S.TEST
## Min. :0.00000 Min. :0.0000 MAT :265 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.0000 None : 67 1st Qu.:1.0000
## Median :0.00000 Median :0.0000 K-MAT : 24 Median :1.0000
## Mean :0.09463 Mean :0.4783 CAT : 22 Mean :0.8286
## 3rd Qu.:0.00000 3rd Qu.:1.0000 PGCET : 8 3rd Qu.:1.0000
## Max. :1.00000 Max. :3.0000 GCET : 2 Max. :1.0000
## (Other): 3
## Percentile_ET S.TEST.SCORE Percent_MBA
## Min. : 0.00 Min. : 0.00 Min. :50.83
## 1st Qu.:41.19 1st Qu.:41.19 1st Qu.:57.20
## Median :62.00 Median :62.00 Median :61.01
## Mean :54.93 Mean :54.93 Mean :61.67
## 3rd Qu.:78.00 3rd Qu.:78.00 3rd Qu.:66.02
## Max. :98.69 Max. :98.69 Max. :77.89
##
## Specialization_MBA Marks_Communication Marks_Projectwork
## Marketing & Finance:222 Min. :50.00 Min. :50.00
## Marketing & HR :156 1st Qu.:53.00 1st Qu.:64.00
## Marketing & IB : 13 Median :58.00 Median :69.00
## Mean :60.54 Mean :68.36
## 3rd Qu.:67.00 3rd Qu.:74.00
## Max. :88.00 Max. :87.00
##
## Marks_BOCA Placement Placement_B Salary
## Min. :50.00 Not Placed: 79 Min. :0.000 Min. : 0
## 1st Qu.:57.00 Placed :312 1st Qu.:1.000 1st Qu.:172800
## Median :63.00 Median :1.000 Median :240000
## Mean :64.38 Mean :0.798 Mean :219078
## 3rd Qu.:72.50 3rd Qu.:1.000 3rd Qu.:300000
## Max. :96.00 Max. :1.000 Max. :940000
## library(psych)
describe(dean.df)## vars n mean sd median trimmed
## SlNo 1 391 196.00 113.02 196.00 196.00
## Gender* 2 391 1.68 0.47 2.00 1.72
## Gender.B 3 391 0.32 0.47 0.00 0.28
## Percent_SSC 4 391 64.65 10.96 64.50 64.76
## Board_SSC* 5 391 2.23 0.87 3.00 2.28
## Board_CBSE 6 391 0.29 0.45 0.00 0.24
## Board_ICSE 7 391 0.20 0.40 0.00 0.12
## Percent_HSC 8 391 63.80 11.42 63.00 63.34
## Board_HSC* 9 391 2.39 0.85 3.00 2.48
## Stream_HSC* 10 391 2.34 0.56 2.00 2.36
## Percent_Degree 11 391 62.98 8.92 63.00 62.91
## Course_Degree* 12 391 3.85 1.61 4.00 3.81
## Degree_Engg 13 391 0.09 0.29 0.00 0.00
## Experience_Yrs 14 391 0.48 0.67 0.00 0.36
## Entrance_Test* 15 391 5.85 1.35 6.00 6.08
## S.TEST 16 391 0.83 0.38 1.00 0.91
## Percentile_ET 17 391 54.93 31.17 62.00 56.87
## S.TEST.SCORE 18 391 54.93 31.17 62.00 56.87
## Percent_MBA 19 391 61.67 5.85 61.01 61.45
## Specialization_MBA* 20 391 1.47 0.56 1.00 1.42
## Marks_Communication 21 391 60.54 8.82 58.00 59.68
## Marks_Projectwork 22 391 68.36 7.15 69.00 68.60
## Marks_BOCA 23 391 64.38 9.58 63.00 64.08
## Placement* 24 391 1.80 0.40 2.00 1.87
## Placement_B 25 391 0.80 0.40 1.00 0.87
## Salary 26 391 219078.26 138311.65 240000.00 217011.50
## mad min max range skew kurtosis
## SlNo 145.29 1.00 391.00 390.00 0.00 -1.21
## Gender* 0.00 1.00 2.00 1.00 -0.75 -1.45
## Gender.B 0.00 0.00 1.00 1.00 0.75 -1.45
## Percent_SSC 12.60 37.00 87.20 50.20 -0.06 -0.72
## Board_SSC* 0.00 1.00 3.00 2.00 -0.45 -1.53
## Board_CBSE 0.00 0.00 1.00 1.00 0.93 -1.14
## Board_ICSE 0.00 0.00 1.00 1.00 1.52 0.31
## Percent_HSC 13.34 40.00 94.70 54.70 0.29 -0.67
## Board_HSC* 0.00 1.00 3.00 2.00 -0.83 -1.13
## Stream_HSC* 0.00 1.00 3.00 2.00 -0.12 -0.72
## Percent_Degree 8.90 35.00 89.00 54.00 0.05 0.24
## Course_Degree* 1.48 1.00 7.00 6.00 0.00 -1.08
## Degree_Engg 0.00 0.00 1.00 1.00 2.76 5.63
## Experience_Yrs 0.00 0.00 3.00 3.00 1.27 1.17
## Entrance_Test* 0.00 1.00 9.00 8.00 -2.52 7.04
## S.TEST 0.00 0.00 1.00 1.00 -1.74 1.02
## Percentile_ET 25.20 0.00 98.69 98.69 -0.74 -0.69
## S.TEST.SCORE 25.20 0.00 98.69 98.69 -0.74 -0.69
## Percent_MBA 6.39 50.83 77.89 27.06 0.34 -0.52
## Specialization_MBA* 0.00 1.00 3.00 2.00 0.70 -0.56
## Marks_Communication 8.90 50.00 88.00 38.00 0.74 -0.25
## Marks_Projectwork 7.41 50.00 87.00 37.00 -0.26 -0.27
## Marks_BOCA 11.86 50.00 96.00 46.00 0.29 -0.85
## Placement* 0.00 1.00 2.00 1.00 -1.48 0.19
## Placement_B 0.00 0.00 1.00 1.00 -1.48 0.19
## Salary 88956.00 0.00 940000.00 940000.00 0.24 1.74
## se
## SlNo 5.72
## Gender* 0.02
## Gender.B 0.02
## Percent_SSC 0.55
## Board_SSC* 0.04
## Board_CBSE 0.02
## Board_ICSE 0.02
## Percent_HSC 0.58
## Board_HSC* 0.04
## Stream_HSC* 0.03
## Percent_Degree 0.45
## Course_Degree* 0.08
## Degree_Engg 0.01
## Experience_Yrs 0.03
## Entrance_Test* 0.07
## S.TEST 0.02
## Percentile_ET 1.58
## S.TEST.SCORE 1.58
## Percent_MBA 0.30
## Specialization_MBA* 0.03
## Marks_Communication 0.45
## Marks_Projectwork 0.36
## Marks_BOCA 0.48
## Placement* 0.02
## Placement_B 0.02
## Salary 6994.72median of salary of all students
median(dean.df$Salary)## [1] 240000the required proportions and percentages of placed students are shown
mytable <- with(dean.df, table(Placement))
mytable # frequencies## Placement
## Not Placed Placed
## 79 312prop.table(mytable) # proportions## Placement
## Not Placed Placed
## 0.202046 0.797954round(prop.table(mytable)*100,digits = 2) # percentages## Placement
## Not Placed Placed
## 20.2 79.8dataframe for placed students
placed <- dean.df[ which(dean.df$Placement=='Placed'),]median of salary of all placed students
median(placed$Salary)## [1] 260000mean of salary of all placed students
aggregate(placed$Salary, by=list(placed$Gender), FUN=mean)## Group.1 x
## 1 F 253068.0
## 2 M 284241.9the average salary of male MBAs who were placed is 284241.9 the average salary of female MBAs who were placed is 253068.0
Use R to generate the following histogram showing a breakup of the MBA performance of the students who were placed
hist(placed$Percent_MBA,
main = "MBA Performance of students ",
xlab = "MBA percentage",
ylab = "Count",
xlim = c(50,80),
ylim = c(0,80), #add limits to axes
breaks = 10, #more columns
col = "lightblue") #color to the axes
dataframe for NOT placed students
notplaced <- dean.df[ which(dean.df$Placement=='Not Placed'),]Use R to generate the following histogram showing a breakup of the MBA performance of the students who were notplaced
hist(notplaced$Percent_MBA,
main = "MBA Performance of students ",
xlab = "MBA percentage",
ylab = "Count",
xlim = c(50,80),
ylim = c(0,80), #add limits to axes
breaks = 10, #more columns
col = "lightblue") #color to the axes
Draw two histograms side-by-side, visually comparing the MBA performance of Placed and Not Placed students
par(mfrow=c(1, 2))
hist(placed$Percent_MBA,
main = "MBA Performance of placed students. ",
xlab = "MBA percentage",
ylab = "Count",
xlim = c(50,80),
ylim = c(0,100), #add limits to axes
breaks = 05, #more columns
col = "yellow") #color to the axes
hist(notplaced$Percent_MBA,
main = "MBA Performance of not placed students ",
xlab = "MBA percentage",
ylab = "Count",
xlim = c(50,80),
ylim = c(0,100), #add limits to axes
breaks = 5, #more columns
col = "red") #color to the axes
Use R to draw two boxplots, one below the other, comparing the distribution of salaries of males and females who were placed:
boxplot(Salary~Gender, data=placed,horizontal=TRUE,yaxt="n",
ylab="Gender",xlab="Salary",
main="comparison of Salaries of Males and Females ")
axis(side=2, at=c(1,2), labels=c("Female","Male"))
dataframe for students who were placed after the MBA and who also gave some MBA entrance test before admission into the MBA program.
placedET <- dean.df[ which(dean.df$Placement=='Placed' & dean.df$Entrance_Test != 'None'),]
View(placedET)Draw a Scatter Plot Matrix for 3 variables – {Salary, Percent_MBA, Percentile_ET} using the dataframe placedET.
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplotMatrix(formula = ~ Salary + Percent_MBA + Percentile_ET , cex=1, data=placedET ,reg.line="" )
Hypothesis 1 H1: The average salary of the male MBAs is higher than the average salary of female MBAs. Independent t-test
A two-group independent t-test can be used to test the hypothesis that the two population means are equal. Here, we assume that the two groups are independent and that the data is sampled from normal populations. #t-test
t.test(Salary ~ Gender, data=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 284241.9Result of Independent t-test The p-value = 0.00234(>0.001) Based on the above output of the t-test, we can’t reject the hypothesis that, The average salary of the male MBAs is higher than the average salary of female MBAs as (p>0.001).(Ans)