Name and Surname
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
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 ...
#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 = mean)
## Exam Time
## 66.22581 91.58065
mean(mydata$Exam)
## [1] 66.22581
hist(mydata$Exam,
main = "Distribution of points on exam",
xlab = "Points",
ylab = "Frequency",
breaks = seq(from = 0, to = 200, by = 10))
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)
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(mydata[ , -1])
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
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