MATH1324 Assignment 1

Student Details

Jaimee Lee Lincoln (s3797303)

Problem Statement

This assignment will focus on investigating whether the variable “che.di” from the Body Measurements Dataset fits a normal distribution. “Che.di” is comprised of the chest diameter (measured in centimetres at mid-expiration) of survey respondents. Information about whether or not the measurements fit a normal distribution will be ascertained using a histogram of the data with a normal distribution overlay.

Load Packages

The packages used in this assignment have been loaded below.

library(readxl)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

Data

The data used for this assignment has been imported and prepared below.

setwd("C:/Users/Jaimee-Lee/Documents/R/Working Directory/Intro to Statistics/Assignment One")
bdims <- read_excel("bdims.csv.xlsx")
View(bdims)

class(bdims$sex)

## [1] "numeric"

bdims$sex <- factor(bdims$sex,
                    levels = c(0,1),
                    labels = c("Female", "Male"))
levels(bdims$sex)

## [1] "Female" "Male"

chest_diameter <- bdims[,c(5,22:25)]
glimpse(chest_diameter)

## Observations: 507
## Variables: 5
## $ che.di <dbl> 28.0, 30.8, 31.7, 28.2, 29.4, 31.3, 31.7, 28.8, 27.5, 2...
## $ age    <dbl> 21, 23, 28, 23, 22, 21, 26, 27, 23, 21, 23, 22, 20, 26,...
## $ wgt    <dbl> 65.6, 71.8, 80.7, 72.6, 78.8, 74.8, 86.4, 78.4, 62.0, 8...
## $ hgt    <dbl> 174.0, 175.3, 193.5, 186.5, 187.2, 181.5, 184.0, 184.5,...
## $ sex    <fct> Male, Male, Male, Male, Male, Male, Male, Male, Male, M...

Summary Statistics

Descriptive statistics for Chest Diameter such as mean, median, standard deviation, first and third quartile, interquartile range, minimum values and maximum values have been calculated by sex below. The mode was also calculated using a custom function, so that the figure could be used to determine whether the mean, median and mode were equal and thus representative of a normal distribution.

#CREATING A MODE FUNCTION
getmode <- function(v) {
   uniqv <- unique(v)
   uniqv[which.max(tabulate(match(v, uniqv)))]
}

# MALE
chest_diameter_male <- filter(chest_diameter, sex == "Male")
chest_diameter_male %>% summarize(Mean = mean(che.di, na.rm = TRUE), 
                                         Median = median(che.di, na.rm = TRUE),
                                         Mode = getmode(chest_diameter_male$che.di),
                                         Sd = sd(che.di, na.rm = TRUE),
                                         Q1 = quantile(che.di, probs = .25, na.rm = TRUE),
                                         Q3 = quantile(che.di, probs = .75, na.rm = TRUE),
                                         IQR = IQR(che.di,na.rm = TRUE),
                                         Min = min(che.di,na.rm = TRUE),
                                         Max = max(che.di,na.rm = TRUE)) %>% round(digits = 3)

#FEMALE
chest_diameter_female <- filter(chest_diameter, sex == "Female")
chest_diameter_female %>% summarize(Mean = mean(che.di, na.rm = TRUE),
                                    Median = median(che.di, na.rm = TRUE),
                                    Mode = getmode(chest_diameter_female$che.di),
                                    Sd = sd(che.di, na.rm = TRUE),
                                    Q1 = quantile(che.di, probs = .25, na.rm = TRUE),
                                    Q3 = quantile(che.di, probs = .75, na.rm = TRUE),
                                    IQR = IQR(che.di, na.rm = TRUE),
                                    Min = min(che.di, na.rm =TRUE),
                                    Max = max(che.di, na.rm = TRUE)) %>% round(digits = 3)

Distribution Fitting

The empirical distribution of Chest Diameter has been plotted separately for men and women in histograms below. Additionally, an overlay of a normal distribution has been added to both plots, to enable comparison.

#MALE
hist(chest_diameter_male$che.di, freq=FALSE, xlab="Chest Diameter (cm at mid-expiration)", main="Histogram of Male Chest Diameter", col="lightgreen")
curve(dnorm(x, mean=mean(chest_diameter_male$che.di), sd=sd(chest_diameter_male$che.di)), add=TRUE, col="red", lwd=2)

#FEMALE
hist(chest_diameter_female$che.di, freq=FALSE, xlab="Chest Diameter (cm at mid-expiration)", main="Histogram of Female Chest Diameter", col="mediumpurple1")
curve(dnorm(x, mean=mean(chest_diameter_female$che.di), sd=sd(chest_diameter_female$che.di)), add=TRUE, col="red", lwd=2)

Interpretation