Data import

mydata <- read.table("./ME.csv", 
                     header = TRUE, 
                     sep = ";", 
                     dec = ",")

  
  
head(mydata) #Showing the first 6 rows of an object, called mydata
##   ID Exam Time
## 1  1   50  120
## 2  2   48  120
## 3  3   48   90
## 4  4   47   50
## 5  5   52   70
## 6  6   50  120

Explanation of dataset

mydata2 <- mydata[   , -3  ] #Removing the third column

mydata3 <- mydata[  ,  c(1, 2)  ] #Keeping the first and second column

Create mydata4 which exclude unit ID 5

mydata4 <- mydata[-5, ] #Excluding the 5th row

head(mydata4)
##   ID Exam Time
## 1  1   50  120
## 2  2   48  120
## 3  3   48   90
## 4  4   47   50
## 6  6   50  120
## 7  7   50  120
str(mydata[ , -1])
## 'data.frame':    31 obs. of  2 variables:
##  $ Exam: int  50 48 48 47 52 50 50 54 57 50 ...
##  $ Time: int  120 120 90 50 70 120 120 65 95 100 ...

Parameter estimation

#install.packages("psych")
library(psych)
describe(mydata[ , -1])
##      vars  n  mean    sd median trimmed   mad min max range  skew kurtosis   se
## Exam    1 31 66.23 28.84     60   63.24 17.79  20 189   169  2.32     8.00 5.18
## Time    2 31 91.58 25.73     95   94.76 37.06  15 120   105 -0.92     0.61 4.62
#install.packages("pastecs")
library(pastecs)
round(stat.desc(mydata[ , -1]), 2)
##                 Exam    Time
## nbr.val        31.00   31.00
## nbr.null        0.00    0.00
## nbr.na          0.00    0.00
## min            20.00   15.00
## max           189.00  120.00
## range         169.00  105.00
## sum          2053.00 2839.00
## median         60.00   95.00
## mean           66.23   91.58
## SE.mean         5.18    4.62
## CI.mean.0.95   10.58    9.44
## var           831.91  662.05
## std.dev        28.84   25.73
## coef.var        0.44    0.28
summary(mydata[ , -1])
##       Exam             Time       
##  Min.   : 20.00   Min.   : 15.00  
##  1st Qu.: 50.00   1st Qu.: 77.50  
##  Median : 60.00   Median : 95.00  
##  Mean   : 66.23   Mean   : 91.58  
##  3rd Qu.: 75.00   3rd Qu.:115.00  
##  Max.   :189.00   Max.   :120.00
sapply(mydata[ , -1], FUN = sd)
##     Exam     Time 
## 28.84292 25.73036
mean(mydata$Exam)
## [1] 66.22581
mean(mydata$Exam)
## [1] 66.22581
library(modeest)
## Registered S3 method overwritten by 'rmutil':
##   method         from 
##   plot.residuals psych
mlv(mydata$Exam)
## [1] 50
hist(mydata$Exam, 
     main = "Distribution of points on exam", 
     xlab = "Points", 
     ylab = "Frequency", 
     breaks = seq(from = 0, to = 200, by = 10))

Normal distribution

pnorm(80, mean = 62.13, sd = 17.99, 
      lower.tail = FALSE)
## [1] 0.1602747
mean = 62.13; sd = 17.99
lb = 80; ub = Inf

x <- seq(-4,4,length=100)*sd + mean
hx <- dnorm(x,mean,sd)

plot(x, hx, type="n", xlab="Točke", ylab="",
  main="", axes=FALSE)

i <- x >= lb & x <= ub
lines(x, hx)
polygon(c(lb,x[i],ub), c(0,hx[i],0), col="blue") 

area <- pnorm(ub, mean, sd) - pnorm(lb, mean, sd)
result <- paste("P(",lb,"< Points <",ub,") =",
   signif(area, digits=3))
mtext(result,3)
axis(1, at=seq(0, 100, 20), pos=0)

Interval estimate

ybar = mean(mydata$Exam); sd = sd(mydata$Exam); n = nrow(mydata)

se = sd/sqrt(n)

ybar_lower_z = ybar + qnorm(0.025)*se
ybar_upper_z = ybar + qnorm(0.975)*se

cat(c("95-% CI:", round(ybar_lower_z, 3), "< Mu <", round(ybar_upper_z, 3)))
## 95-% CI: 56.073 < Mu < 76.379
ybar = mean(mydata$Exam); sd = sd(mydata$Exam); n = nrow(mydata)

se=sd/sqrt(n)

ybar_lower_t = ybar + qt(0.025, df=n-1)*se
ybar_upper_t = ybar + qt(0.975, df=n-1)*se

cat(c("95-% CI:", round(ybar_lower_t, 3), "< Mu <", round(ybar_upper_t, 3)))
## 95-% CI: 55.646 < Mu < 76.805

Boxplot

boxplot(mydata[ , -1])

Cleaning the data

mydata <- read.table("./ME.csv", 
                     header = TRUE, 
                     sep = ";", 
                     dec = ",")

head(mydata)
##   ID Exam Time
## 1  1   50  120
## 2  2   48  120
## 3  3   48   90
## 4  4   47   50
## 5  5   52   70
## 6  6   50  120
tail(mydata)
##    ID Exam Time
## 26 26   74   95
## 27 27   74   95
## 28 28   76  120
## 29 29   44   45
## 30 30   52   92
## 31 31  189  110

¸

boxplot(mydata[ , -1])

library(psych)
describe(mydata[ , -1])
##      vars  n  mean    sd median trimmed   mad min max range  skew kurtosis   se
## Exam    1 31 66.23 28.84     60   63.24 17.79  20 189   169  2.32     8.00 5.18
## Time    2 31 91.58 25.73     95   94.76 37.06  15 120   105 -0.92     0.61 4.62
head(mydata[order(-mydata$Exam),    ])
##    ID Exam Time
## 31 31  189  110
## 24 24   95  120
## 16 16   92  120
## 23 23   92  120
## 22 22   85   90
## 15 15   80   95
mydata_new <- mydata[-31, ]
mydata[31, 2] <- 89

head(mydata[order(-mydata$Exam), ])
##    ID Exam Time
## 24 24   95  120
## 16 16   92  120
## 23 23   92  120
## 31 31   89  110
## 22 22   85   90
## 15 15   80   95
boxplot(mydata[ , -1])

library(psych)
describe(mydata[ , -1])
##      vars  n  mean    sd median trimmed   mad min max range  skew kurtosis   se
## Exam    1 31 63.00 18.33     60   63.12 17.79  20  95    75 -0.07    -0.66 3.29
## Time    2 31 91.58 25.73     95   94.76 37.06  15 120   105 -0.92     0.61 4.62