MATH1324 Assignment 1

Modeling Body Measurements

Student Details

Xiyue Shu (s3705474)

Problem Statement

This investigation aims to determine whether body measurement in female and male follows normal distribution. The chosen body measurment for below is respondent’s hip grids in centimetere (hip.gi). The normal distribution fitting will be done by overlaying normal distribution curves over the histogram obtained from analysis.

Load Packages

library(readr)
library(dplyr)
library(ggplot2)
library(magrittr)

Data

Firstly, set working directory by “session” –> “setting working directory” –> “choose directory” –> folder

bdims <- read_csv('bdims.csv')

Parsed with column specification:
cols(
  .default = col_double(),
  age = col_integer(),
  sex = col_integer()
)
See spec(...) for full column specifications.

bdims$sex <- factor(bdims$sex, levels=c(1,0), labels =c("male","female"))
hipw <- bdims %>% filter(sex == 'female') %>% select(hip.gi)
hipm <- bdims %>% filter(sex == 'male') %>% select(hip.gi)

Summary Statistics

bdims %>%
  group_by(sex) %>%
  summarise(mean=mean(hip.gi), median=median(hip.gi),sd= sd(hip.gi), '1st_Qu'=quantile(hip.gi,0.25),'3rd_Qu'=quantile(hip.gi, 0.75),IQR=IQR(hip.gi), min=min(hip.gi), max=max(hip.gi))

Distribution Fitting

hist(hipw$hip.gi, density=100, breaks=20, prob=TRUE, xlab = 'hip girth', col = 'cornflowerblue', ylim=c(0,0.08), main = 'normal curve over histogram female')
curve(dnorm(x, mean=mean(hipw$hip.gi), sd=sd(hipw$hip.gi)), add = TRUE, col='red')

hist(hipm$hip.gi, density=100, breaks=20, prob=TRUE, xlab = 'hip girth', col = 'cornflowerblue', ylim=c(0,0.08), main = 'normal curve over histogram male')
curve(dnorm(x, mean=mean(hipm$hip.gi), sd=sd(hipm$hip.gi)), add = TRUE, col='red')

Interpretation

Based on the normal distribution fitting, the body measurement hip grids is normally distributed in male and right skewed in female. The shape of the histogram is aligns with the normal curve. However, the peak of the curve and histogram does not always match.