Homework_One

#Problem 1
## c Set
#A
modified_mortar <- c(16.85,16.40,17.21,16.35,16.52,17.04,16.96,17.15,16.59,16.57)
unmodified_mortar <- c(16.62,16.75,17.37,17.12,16.98,16.87,17.34,17.02,17.08,17.27)
print(modified_mortar)

##  [1] 16.85 16.40 17.21 16.35 16.52 17.04 16.96 17.15 16.59 16.57

print(unmodified_mortar)

##  [1] 16.62 16.75 17.37 17.12 16.98 16.87 17.34 17.02 17.08 17.27

## Mean B
mean_modified <- mean(modified_mortar)
mean_unmodified <- mean(unmodified_mortar)

print(mean_modified)

## [1] 16.764

print(mean_unmodified)

## [1] 17.042

## Median B
median_modified <- median(modified_mortar)
median_unmodified <- median(unmodified_mortar)

print(median_modified)

## [1] 16.72

print(median_unmodified)

## [1] 17.05

## SD C
sd_modified <- sd(modified_mortar)
sd_unmodified <- sd(unmodified_mortar)

print(sd_modified)

## [1] 0.3164455

print(sd_unmodified)

## [1] 0.2479158

## var

var_modified <- var(modified_mortar)
var_unmodified <- var(unmodified_mortar)

print(var_modified)

## [1] 0.1001378

print(var_unmodified)

## [1] 0.06146222

## IQR 

iqr_modified <- IQR(modified_mortar)
iqr_unmodified <- IQR(unmodified_mortar)

print(iqr_modified)

## [1] 0.4875

print(iqr_unmodified)

## [1] 0.335

#D
hist(modified_mortar, xlab = "Modified Mortar ", col = "blue", border = "black")

# Modified Mortar
# has a gap between 16.6 - 16.8
# shape is bi model
hist(unmodified_mortar, xlab = "Unmodified Mortar ", col = "red", border = "black")

# Unmodified mortar 
# symmetrical 
# shape is left shape skew
#E
boxplot(modified_mortar, unmodified_mortar, names = c("Modified Mortar", "Unmodified Mortar"),
      main = "Mortar Types",
      ylab = "Tension Bond Strength", col = c("blue", "red"))

#modified median is lower than unmodified 
# the IQR is slightly higher for modified

#Problem 2
#a
survey <- c(4, 2, 3, 3, 1, 5, 4, 2, 2, 4,
          5, 6, 4, 3, 3, 4, 4, 5, 6, 1,
          2, 2, 3, 4, 3, 3, 5, 2, 1, 3)
#b
survey_table <- table(survey)
print(survey_table)

## survey
## 1 2 3 4 5 6 
## 3 6 8 7 4 2

#Pie problem problem c
survey_pie <- pie(survey_table, main="Pie Chart of Courses")

print(survey_pie)

## NULL

#bar plot
#d
survey_barplot <- barplot(survey_table, main="Bar Plot of Courses Taken",
      xlab = "Number of Courses",
      ylab = "Frequency",
      col= "blue")

print(survey_barplot)

##      [,1]
## [1,]  0.7
## [2,]  1.9
## [3,]  3.1
## [4,]  4.3
## [5,]  5.5
## [6,]  6.7

#e
more_than_four_class <- sum(survey > 4)
print(more_than_four_class)

## [1] 6

#Problem 3
#a
data <- seq(2,50, by = 2)
print(data)

##  [1]  2  4  6  8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

#b
log_data <- log(data)
print(log_data)

##  [1] 0.6931472 1.3862944 1.7917595 2.0794415 2.3025851 2.4849066 2.6390573
##  [8] 2.7725887 2.8903718 2.9957323 3.0910425 3.1780538 3.2580965 3.3322045
## [15] 3.4011974 3.4657359 3.5263605 3.5835189 3.6375862 3.6888795 3.7376696
## [22] 3.7841896 3.8286414 3.8712010 3.9120230

#c
log_modified <- log_data[-(3:10)]
print(log_modified)

##  [1] 0.6931472 1.3862944 3.0910425 3.1780538 3.2580965 3.3322045 3.4011974
##  [8] 3.4657359 3.5263605 3.5835189 3.6375862 3.6888795 3.7376696 3.7841896
## [15] 3.8286414 3.8712010 3.9120230

#d
data_log_modified <- length(log_modified)
print(data_log_modified)

## [1] 17

#e
sort_data <- sort(log_modified, decreasing = TRUE)
print(sort_data)

##  [1] 3.9120230 3.8712010 3.8286414 3.7841896 3.7376696 3.6888795 3.6375862
##  [8] 3.5835189 3.5263605 3.4657359 3.4011974 3.3322045 3.2580965 3.1780538
## [15] 3.0910425 1.3862944 0.6931472