Student Details

Anna Krinochkina (s3712761)

Problem Statement

The problem of this investigation is to determine if one of the body measurements fits a normal didtribution. The invistigation will be taking into consideration the empirical distribution of the variable for men and women separately. The body measurement of choice is respondent’s wrist minimum girth in centimeters, measured as the average of right and left girths wri.gi. The approach taken for normal distribution fitting is plotting the empirical distrubution of the chosen variable with the normal distribution curve overlay.

Load Packages

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

Data

bdims <- read_csv('bdims.csv')
Parsed with column specification:
cols(
  .default = col_double()
)
See spec(...) for full column specifications.
bdims$sex <- factor(bdims$sex, levels = c(1,0), labels = c("Male","Female"))
head(bdims$sex)
[1] Male Male Male Male Male Male
Levels: Male Female
wri_m <- bdims[bdims$sex == "Male", c("wri.gi","sex")]
head(wri_m) 
wri_f <- bdims[bdims$sex == "Female", c("wri.gi","sex")]
head(wri_f)

Summary Statistics

bdims %>% 
  group_by(sex) %>% 
  summarise(mean = round(mean(wri.gi),2),median = median(wri.gi),st_dev = round(sd(wri.gi),3), '1st_Qu' = quantile(wri.gi,0.25), '3rd_Qu' = quantile(wri.gi,0.75), IQR = IQR(wri.gi), min = min(wri.gi), max = max(wri.gi))

Distribution Fitting

hist(wri_m$wri.gi, breaks = 20, freq = F, main = "Histogram of Wrist Girth\n (Men)", col = "azure", xlab = "Centimeters")
curve(dnorm(x,mean = mean(wri_m$wri.gi), sd = sd(wri_m$wri.gi)), add = T, col="red2", lwd=2)
grid()

hist(wri_f$wri.gi, breaks = 20, freq = F, main = "Histogram of Wrist Girth\n (Women)", col = "lavenderblush", xlab = "Centimeters", ylim = c(0,.7))
curve(dnorm(x,mean = mean(wri_f$wri.gi), sd = sd(wri_f$wri.gi)), add = T, col="red2", lwd=2)
grid()

Interpretation

The approach taken in the investigation allowed to assume that the theoretical normal distribution approximately fits the wrist girth variable empirical data for both men and women. The results obtained suggest that the wrist girth variable exhibits a more or less normal distribution shape. For further insight it will be reasonable to take a more reliable approach.



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