title: “Example 6”

output: html_document

Example 6: Comparing the Standard Deviation

If necessary, install the Mosaic package.

install.packages("mosaic")

Table7 <- read.csv("https://sullystats.github.io/Statistics6e/Data/Chapter3/Table7.csv")
head(Table7,n=4)

##   University  IQ
## 1          A 136
## 2          A  81
## 3          A  80
## 4          A  85

First, let’s draw a side-by-side histogram of the IQ data by university.

library(mosaic)
mean(IQ ~ University,data=Table7)

##      A      B 
## 100.00 100.01

gf_histogram(~IQ|University,data=Table7,binwidth=10,boundary=60,color='black',fill='skyblue',title="IQ Score by University")

Notice that both universities have the same mean IQ of 100.0. However, based on the histograms, University A appears to have more dispersion.

We will determine the standard deviation of each schools’ IQ score to verify University A has more dispersion.

sd(IQ ~ University,data=Table7)

##         A         B 
## 16.080605  8.357535

The standard deviation for University A is 16.1 and the standard deviation for University B is 8.4. University A has more dispersion in IQ scores.