Exercises 1,6,7,8,9,10,11

##Exercise 1

Level of measurement

library(knitr)

levels_table <- data.frame(
  Level_of_Measurement = c("Nominal", "Ordinal", "Ratio"),
  Examples = c(
    "Gender, Hair color, Blood type",
    "Education level, Satisfaction scale, Class rank",
    "Height, Weight, Age, Income"
  ),
  Description = c(
    "Categories used as labels only; no ranking or order possible",
    "Ordered categories; ranking matters but differences are not measurable",
    "Ordered, equal intervals, and has a true zero; allows meaningful ratios"
  ),
  Operations = c(
    "= (equal / not equal), Counting frequencies",
    "=, !=, <, >, Ranking",
    "=, !=, <, >, +, -, *, /, Ratios"
  )
)

kable(levels_table, caption = "Levels of Measurement Table")

Levels of Measurement Table

Level_of_Measurement	Examples	Description	Operations
Nominal	Gender, Hair color, Blood type	Categories used as labels only; no ranking or order possible	= (equal / not equal), Counting frequencies
Ordinal	Education level, Satisfaction scale, Class rank	Ordered categories; ranking matters but differences are not measurable	=, !=, <, >, Ranking
Ratio	Height, Weight, Age, Income	Ordered, equal intervals, and has a true zero; allows meaningful ratios	=, !=, <, >, +, -, *, /, Ratios

Import Students.txt into R

---

students<-read.delim("C:\\Users\\ahmad\\Downloads\\Datasets\\students.txt",stringsAsFactors=F)

Call library mosaic

library(mosaic)

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally

## The following object is masked from 'package:Matrix':
## 
##     mean

## The following object is masked from 'package:ggplot2':
## 
##     stat

## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum

##Exercise 6

Creating the table:

tab <- matrix(c(66, 53, 28, 28, 17,11,3), ncol=1, byrow=TRUE)
colnames(tab) <- c("Frequency")
rownames(tab) <- c("Industry","Master student","Acadamic Faculty","Researcher","Doctoral Student","Undergraduate Student","Non-profit")
tab <- as.table(tab)

Creating a data frame:

ex6 <- data.frame(Frequency = c(66, 53, 28, 28, 17,11,3), Background
= c("Industry","Master student","Acadamic Faculty","Researcher","Doctoral Student","Undergraduate Student","Non-profit"))

Creating a barchart:

par(mar = c(8, 5, 4, 2))  

barplot(
  ex6$Frequency,
  names.arg = ex6$Background,
  col = rainbow(7),
  las = 2,           # Rotate labels vertically for readability
  cex.names = 0.8,   # Adjust label size
  main = "Frequency by Background",
  ylab = "Frequency",
  ylim = c(0, 80)    # Add height space so labels fit
)

legend("topright", legend = ex6$Background, fill = rainbow(7), cex = 0.8)

Creating a barchart using ggplot2

library(ggplot2)

ggplot(ex6, aes(x = Background, y = Frequency, fill = Background)) +
  geom_col(width = 0.7, show.legend = FALSE) +
  coord_flip() +  # Flip chart to make long labels readable
  labs(title = "Frequency by Background", x = "Background", y = "Frequency") +
  theme_minimal(base_size = 12) +
  theme(
    plot.title = element_text(hjust = 0.5, face = "bold"),
    axis.text.y = element_text(size = 10),
    axis.text.x = element_text(size = 10)
  )

##Exercise 7

Absolute frequencies

tally(~Blood_group, data=students)

## Blood_group
##  0  A AB  B 
## 31 35  5 11

Relative frequencies

prop(~Blood_group, success = "0", data = students)

##    prop_0 
## 0.3780488

prop(~Blood_group, success = "A", data = students)

##    prop_A 
## 0.4268293

prop(~Blood_group, success = "AB", data = students)

##    prop_AB 
## 0.06097561

prop(~Blood_group, success = "B", data = students)

##    prop_B 
## 0.1341463

Create the pie chart using the absolute frequencies

 blood_pie_ex7 <- c(31,35,5,11)

Pie chart

pie(blood_pie_ex7, labels = c("Blood group 0", "A", "AB", "B"))

##Exercise 8

Bar chart of the variable ’points reached in the exam’

bargraph(~Points_exam, data=students)

##Exercise 9

Histogram of the variable ’body size’

histogram(~Size_cm, data = students)

##Exercise 10

Absolute frequencies

tally(~Grade, data=students)

## Grade
##  1  2  3  4  5 
## 14 12 27  8 21

Relative frequencies

prop(~Grade, success = "1", data = students)

##    prop_1 
## 0.1707317

prop(~Grade, success = "2", data = students)

##    prop_2 
## 0.1463415

prop(~Grade, success = "3", data = students)

##    prop_3 
## 0.3292683

prop(~Grade, success = "4", data = students)

##     prop_4 
## 0.09756098

prop(~Grade, success = "5", data = students)

##    prop_5 
## 0.2560976

Create the pie chart using the absolute frequencies

 blood_pie_ex10 <- c(14, 12, 27,  8, 21)

Pie chart

pie(blood_pie_ex10, labels = c("Grade 1", "2", "3", "4","5"))

Bar chart of the variable “Grade”

bargraph(~Grade, data=students)

##Exercise 11

Histogram of the variable ’body weight’

histogram(~Weight_kg, data = students)