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Mechanical Engineering
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Dec 6, 2023
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Discussion 2: Numeric and Graphical Summaries
Put Your Name Here
Warmup
Consider the
Week 2 Quiz Question 6
with your neighbor. Choose the answers you think make sense and
explain how you know. What improvement could be made to these graphs to make this question easier to
answer?
Comparison of Two Sets of Data
We will be looking at the salaries of 1000 recently graduated engineers from two schools: Regional Technical
Institute and the State Polytechnic. We are interested to compare the distribution of salaries according to
various factors.
1. Load the data into your environment by reading in the CSV file (Engineering_Undergraduates_sample_10
to the variable engineers
a.
Download the CSV file into the same folder as this Rmd file (drag and drop this file directly
to the folder as opening the .csv file in other programs such as Numbers can cause issues)
b.
Set the folder that holds both the Discussion 2 files as your working directory by (navigate
to that folder in the Files pane of RStudio, and select “Session > Set Working Directory >
To Files Pane Location” from the top RStudio menu))
c.
Run the code below to define the variable engineers. The engineers variable is a data frame
that has 1000 observations of 6 variables. Confirm that it shows up in the Environment tab
of RStudio. Click on the blue arrow next to the engineers name to see some information
about the 6 variables it contains.
engineers
<-
read.csv(
"Engineering_Undergraduates_sample_1000.csv"
,
header=
TRUE)
d.
View the data frame to see what the data looks like. Run
View(enginers)
in the console as
View()
can create issues when you knit the document. Or, click on the table icon in the
Environment tab. (This will run
View(enginers)
in the console for you.)
2. We will be focusing on the variables Salary.K., job, and School.
Salary.K.
: is the starting annual salary of the accepted job offer in thousands.
job
: is yes if the graduate got a starting job offer and no otherwise
School
: is a categorical variable recording the school the student graduated from
a.
Run the following code to see how R has identified the variables in engineers.
Identify
whether any of the 3 we are interested in are saved incorrectly.
1
str(engineers)
##
data.frame :
1000 obs. of
6 variables:
##
$ degree
: chr
"civil" "physics" "civil" "biomedical" ...
##
$ GPA
: num
2.53 3.67 3.58 3.45 2.71 3.59 2.7 3.67 3.47 3.7 ...
##
$ School
: chr
"Regional Technical Institute" "Regional Technical Institute" "State Polytechnic"
##
$ offers
: int
3 2 1 3 2 2 2 1 1 1 ...
##
$ Salary.K.: num
77.7 99.8 79.4 80.5 73.4 79.8 67.6 83.7 76.4 83.2 ...
##
$ job
: chr
"yes" "yes" "yes" "yes" ...
b.
Run the following code to resave School and job as categorical vectors in the engineers data
frame.
Notice the $ after the data frame name
engineers
pulls up a list of all of the columns that are defined in
engineers
. And the
as.factor()
function changes the variable type to categorical.
Reference the Environment tab or rerun
str(engineers)
to confirm School and job have been updated
correctly.
engineers$School
=
as.factor(engineers$School)
engineers$job
=
as.factor(engineers$job)
str(engineers)
##
data.frame :
1000 obs. of
6 variables:
##
$ degree
: chr
"civil" "physics" "civil" "biomedical" ...
##
$ GPA
: num
2.53 3.67 3.58 3.45 2.71 3.59 2.7 3.67 3.47 3.7 ...
##
$ School
: Factor w/ 2 levels "Regional Technical Institute",..: 1 1 2 1 2 1 1 1 2 2 ...
##
$ offers
: int
3 2 1 3 2 2 2 1 1 1 ...
##
$ Salary.K.: num
77.7 99.8 79.4 80.5 73.4 79.8 67.6 83.7 76.4 83.2 ...
##
$ job
: Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
3. First let’s only look at graduates who got a job
#Create a subset dataset where job == "yes"
engineers.jobs
=
subset(engineers, job==
"yes"
)
4. We will focus on the variable Salary.K. compared across the two schools.
a.
Create Side by Side boxplots and comparative histograms of the variable Salary.K. between
graduates where School==“Regional Technical Institute” and “State Polytechnic”
(i)
Save off two data frames, RTI and SP, to hold the data for those graduates from
the two schools
#First make a data frame RTI for just those graduates who went to Regional Technical Institute
RTI
=
subset(engineers.jobs, School==
"Regional Technical Institute"
)
#Then make a data frame SP for just the graduates of State Polytechnic
SP
=
subset(engineers.jobs, School==
"State Polytechnic"
)
#After the above two steps look at your environment tab to see what the variables have stored in them. (
2
(ii)
Then save off the two vectors of Salary.K. for those two dataframes into salary.RTI
and salary.SP
#define salary.RTI to be the salary values from engineers from RTI
salary.RTI
<-
RTI$Salary.K.
#define salary.SP to be the salary values for graduates from SP
salary.SP
<-
SP$Salary.K.
#After the above two steps look at your environment tab to see what the variables have stored in them.
(iii)
Update the following boxplot code to include labels that show which data is which.
You’ll need to change
eval = TRUE
for the code to run when you knit.
boxplot(salary.RTI, salary.SP,
horizontal =
TRUE,
names=
c(
"RTI"
,
"SP"
),
main=
"Salary Comparison"
,
xlab=
"Salary (thousands $)"
)
RTI
SP
65
70
75
80
85
90
95
100
Salary Comparison
Salary (thousands $)
#or using the original engineers data frame:
boxplot(Salary.K. ~ School,
data=
engineers.jobs,
horizontal =
TRUE,
main=
"Salary Comparison"
,
ylab=
""
,
xlab=
"Salary (thousands $)"
)
3
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Regional Technical Institute
65
70
75
80
85
90
95
100
Salary Comparison
Salary (thousands $)
(iv)
Update the following frequency and relative frequency histogram code so that both
histograms have x axis classes from 50 to 100 with a width of 5. Also, choose a
more useful y axis for both graphs. Again, you’ll need to change
eval = TRUE
.
Why is it important that the x and y axis are consistent across the two histograms?
(Skip relative frequency if short on time)
#this makes two rows and 1 column for graphs
par(
mfrow =
c(
2
,
1
),
mar =
c(
4
,
4
,
1.5
,
1.5
))
#frequency histograms ok since the sample sizes are similar
hRTI
<-
hist(salary.RTI,
breaks =
seq(
50
,
100
,
5
),
ylim=
c(
0
,
200
),
plot=
TRUE)
hSN
<-
hist(salary.SP,
breaks =
seq(
50
,
100
,
5
),
ylim=
c(
0
,
200
),
plot=
TRUE)
4
Histogram of salary.RTI
salary.RTI
Frequency
50
60
70
80
90
100
0
100
200
Histogram of salary.SP
salary.SP
Frequency
50
60
70
80
90
100
0
100
200
#Relative Frequency Histogram Code takes more messing around
hRTI
<-
hist(salary.RTI,
breaks =
seq(
50
,
100
,
5
),
plot=
FALSE)
hRTI$counts
<-
hRTI$counts / length(salary.RTI)
plot(hRTI,
ylab=
"Relative Frequency"
,
main =
"Graduates of RTI"
,
xlab =
"Salary (thousands)"
,
ylim=
c(
0
,
1
))
hSN
<-
hist(salary.SP,
breaks =
seq(
50
,
100
,
5
),
plot=
FALSE)
hSN$counts
<-
hSN$counts/length(salary.SP)
plot(hSN,
ylab =
"Relative Frequency"
,
ylim =
c(
0
,
1
),
main =
"Graduates of SP"
,
xlab=
"Salary (thousands)"
,
axes=
TRUE)
5
Graduates of RTI
Salary (thousands)
Relative Frequency
50
60
70
80
90
100
0
1
Graduates of SP
Salary (thousands)
Relative Frequency
50
60
70
80
90
100
0
1
par(
mfrow=
c(
1
,
1
),
mar=
c(
5.1
,
4.1
,
4.1
,
2.1
))
#this makes one row and one column for graphing
b.
Compare the center, variability and shape of the two groups’ data using the graphs and
numeric summaries.
mean(salary.SP)
## [1] 77.84685
mean(salary.RTI)
## [1] 76.83511
median(salary.SP)
## [1] 76.9
median(salary.RTI)
## [1] 75.85
IQR(salary.SP,
type=
2
)
## [1] 8
IQR(salary.RTI,
type=
2
)
## [1] 6.4
sd(salary.SP)
## [1] 5.567901
6
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sd(salary.RTI)
## [1] 5.973521
Mean and median salary is slightly higher for SP graduates. IQR for SP graduates is also higher, since data
is more spread out between median and Q3. RTI has slightly higher sd (and lower IQR) since middle 50% is
more tightly packed with more “outlying” values. Both distributions look to be slightly right skewed.
7
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