########################## Students dataset - exercise solutions ###################

# - set your working directory (w.d.) and open students.xlxs dataset 
setwd( ... ) # set your w.d.
library(readxl)
stud <- read_excel("students.xlsx")
str(stud)

# 1- n.row and n. coloumns
dim(stud)

# 2 - 	How many students study at least 5 weekley hours? 
# legend (1=- <2 hours, 2 = 2 to 5 hours, 3 = 5 to 10 hours,  4 = >10 hours)

# at least 5 hours --> 5 or more  
table <- table(stud$studytime)
# students who study at least 5 weekley hours are the sum of the freq. included in modalities 3 and 4. 

# 3 - mode of the reasons for chosing this school 
table(stud$reason) 
# the main reason is "course" this is the mode

# 4. 4.	Plot the rel.freq. distribution of free time after school and provide a comment on this distribution  
nj<-table(stud$freetime)
fj<-prop.table(nj)
fj
barplot(fj*100, main=" Bar Plot of free time",
        xlab="free time after school", ylab="% Frequency", col="lightblue") 

# 38% of student have a score equal to 3 ((label from 1 to 5, 3 could be an intermediate  free time) 3 is the mode. 
# 10% have very high free time (modality equal to 5), while only 6.9% have very low free time (modality equal to 1)


# 5.	Plot weekend alcohol consumption weekend alcohol consumption (numeric: from 1 - very low to 5 - very high)
table<-table(stud$Walc)
freq<-prop.table(table)
freq

# labels weekend alcohol consumption (numeric: from 1 - very low to 5 - very high)
# 38% of distrib very low alchool cons. 

# barplot 
barplot(freq,
        main=" Bar Plot",
        xlab="weekend alchool consumption", ylab="Frequency", col="blue") # col add colour to the bars 

#5.	Compute summary statistics of the number of school absences. 
summary(stud$absences)
hist(stud$absences) 
# asimmetric distribution (positive skewness)


# 6.	Compute a box plot of the variable absences. Can you detect the presence of any outliers? 
# if yes,  Identify the n. of outliers and compute a new boxplot without outliers. 

boxplot(stud$absences) 
# yes!! there are outliers! 

#outliers identification
outlier <- boxplot(stud$absences)$out
outlier.number <- length(boxplot(stud$absences)$out)
outlier.number # 21 outlier

boxplot(stud$absences, outline=FALSE) 


#7.	Compute a box plot of the variable absences by alcohol consumption. Provide a comment of this graphical representation
boxplot(stud$absences ~ stud$Dalc, outline=FALSE, xlab="Alcool consumpt", ylab=" absences distrib")
# comment?? 

# 8. variability indicators of variable absence 
var(stud$absences)
sd<-sd(stud$absences)
mean<-mean(stud$absences, rm.na=TRUE)
cv<-sd/mean 


# 9.	Compute the mean and sdeviation of day absences by workday alcohol consumption
mean<-tapply(stud$absences, stud$Dalc, mean)
sd<-tapply(stud$absences, stud$Dalc, sd)
cv<-mean/sd
cv