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#####  Statistics Course - Descriptive statistics with dataset   ######
#########            Dr. Ilaria Benedetti                     #########
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#homework assignment: Ex_caschool_desc_stat.pdf

setwd()

data <- read.csv("caschool.csv")
# 1.	observe the data structure, 
str(data)
dim(data)
head(data)

# 2.	focusing on the test score variable (var.name= testscr), 
#calculate the main position indicators (the mean, quantiles, min, max, mode), range, interquartile difference, asymmety indicators; 
summary(data)

mean(data$testscr)

summary(data$testscr) # all the statistics togheter

quantile(data$testscr, 0.75 ) # q3
quantile(data$testscr, 0.50 ) # q2 (median)
quantile(data$testscr, 0.25 ) # q1 

min(data$testscr) 
max(data$testscr)

# mode -> we define a function in R 
Mode <- function(x) {
  ux <- unique(x)
  ux[which.max(tabulate(match(x, ux)))]
}

Mode(data$testscr)


# range
range<- max(data$testscr) - min(data$testscr)
range

# interquartile difference
diff(quantile(data$testscr, probs = c(0.25, 0.75)))

# symmetry - asimmetry of a distribution
install.packages("labstatR")
library(labstatR)
skew(data$testscr)

# mean or other statistics by group: 

# 3.	Compute the mean of the test score variable by Grades; 
#this is factor indicating grade span of district (var.name=gr_span)

# compute the mean of the variable "testscr" by Grades 
data$gr_span <-as.factor(data$gr_span )
tapply(data$testscr, data$gr_span , mean) 



# 4. Compute the variance, the standard deviation and coefficient of variation of the variable test score. 

# # compute variance of the variable age 
var(data$testscr) # sampling variance by default in R --> sampling variance (n-1 observations)
sqrt(var(data$testscr)) # sqrt st.deviation 


# variance  of the population
library(labstatR)
sigma2(data$testscr) #variance in the pop

#coefficient of variation

# CV of variable testscr
mean<-mean(data$testscr)
var<-var(data$testscr)
sd<-sqrt(var)

cv<-(sd/mean)*100
cv

# Cv with packages 
install.packages("ineq")
library(ineq)
var.coeff(data$testscr, square = FALSE) # not expressed in 100%

# 5. compute variance and standard deviation of the variable testscore by gr_span 
tapply(data$testscr, data$gr_span, var) # sampling variance by default in R 
tapply(data$testscr, data$gr_span, sd)


####### alternative command ######
install.packages("dplyr")
library(dplyr)

group_by(data, gr_span) %>%
  summarise(
    count = n(),
    mean = mean(testscr, na.rm = TRUE),
    sd = sd(testscr, na.rm = TRUE)
  )

# 6.Represent the variable test score graphically using a box-plot
# boxplot - test_score
boxplot(data$testscr)

#7. outliers -test_score
table(boxplot(data$testscr)$out) # for detailed outiers
outlier <- boxplot(data$testscr)$out
outlier.number <- length(boxplot(data$testscr)$out)
outlier.number # only 1 outlier

#8 histogram - variable income avginc
hist(data$avginc)