STAT 2450
Recitation Activity #3
Numerical Summary Measures
OBJECTIVES
• Students will compute measures of central tendency and variability.
• Students will understand the connection between graphical displays & numerical summaries.
• Students will identify statistics that are resistant to outliers through exploration.
Measures of Central Tendency and Variability for a Sample vs. Population:
The measures of central tendency discussed here (sample statistics) have corresponding measures in the population (population parameters). One goal of this course is to use sample statistics to estimate population parameters.
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Measure
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Sample
Statistic
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Population
Parameter
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x
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μ
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x
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μ
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tr(p)
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M
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^(p)
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p
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2 s
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2 σ
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s
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σ
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PART I: VOCABULARY Complete the sentence.
1. [1 point] skewed data has a sample mean that is larger than its median.
2. [1 point] What are the 3 primary ‘calculations’ used in describing the center of a data set? Briefly define each of them.
PART II: DATA ANALYSIS
3. The perceived stress levels of 30 employees are listed below.
55 35 43 40 46 58
12 37 40 32 46 48
39 74 43 52 35 29
28 43 34 3 63 29
71 62 30 60 61 27
a. [2 points] Create a frequency distribution of the data.
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Class
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Frequency
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Relative
frequency
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Cumulative
rel. freq.(CRF)
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b. [2 points] Sketch a relative frequency histogram based upon the frequency distribution in part(a).
c. [1 point] Describe the center of the data.
d. [2 points] Enter the data into R. Title the column Stress. Compare this histogram to the one created earlier.
Create a histogram by using the following code in R:
Open a excel file and input data under the column name “Stress” . Save the data set in
.csv format (Stress.csv).
Click the “import dataset” button on the environment pane. Click the “From
Text(base)” option in the import dataset menu and select your dataset file.
Type “Stressdata” on Name field. Click “import” .
Or
Run the following code:
#download the Stress data set from Carmen site
# use file.choose("stress.csv") to locate the place you saved the dataset and copy and paste that place inside the read.csv() function
stressdata=read.csv("/Users/sanjeewaniweerasingha/Library/CloudStorage/OneDrive- TheOhioStateUniversity/OSUteaching/AAASTAT 2450/Summer 2025/Week 01 and
2/recitation/Rec 2/stressdata.csv")
Copy and paste the created histogram here.
hist(stressdata$Stress, main="Frequency Distribution of Stress data", xlab="class", ylab="Frequency")
PART III: Understanding visualization options in R
4. Let’s start with the States data in the library carData This data set contains information regarding
each state’s (and the District of Columbia’s) population, verbal and math SAT scores, proportion of high school students taking the SAT, dollars ($1000) in state public education spending, and average teacher salary ($1000) in 1992.
Step I: Install the carData package by using the code install.packages(“carData”)
Package installation you have to do onetime, and then you may comment the above code with # symbol as follows
#install. Packages(“carData”)
Step II: Keep open the carData library in your working environment with the following code library(carData); you are not supposed to comment this code
Step III: Import the States data set by using the code data(State)
Step IV: Look at the details of the data set either by using View(State) or head(State) code.
(a). [1 point] Use the code ?States() to get the description of States data set on Help pane. What is the real meaning of dollar variable in this dataset.
(b). [3 points] Use the code class(States$pop) to determine the format in which R has stored this
variable. Then, find the variable type/format for the following variables and state whether these variables are categorical, numerical discrete, or numerical continuous type variables.
Region:
Percent:
Dollars:
(c) [3 points] Draw the histogram and make modifications using the following code for the SATV
variable. Don't forget to label the x-axis and y-axis, and to add a title to the histogram. Arrange all these histograms in a grid of (1,3).
par(mfrow = c(1, 3)) # 1 rows, 3 columns
hist(States$SATV)
#You may change the default class with by using break option inside hist function
hist(States$SATV, breaks=10)
# Or you may control more the starting and ending points in x axis by using
hist(States$SATV, breaks = seq(300, 600, by = 25))
# Here we used the seq() function to create a sequence of values from 300 to 600,
# increasing by 25. Run seq(300, 600, by = 25) to see the generated sequence.
(d). [3 points] Run the following code to create a pie chart of the region variable and paste it here.
pie(table(States$region))
If you want to include the calculated percentages in your plot, please follow the following code
region_counts <- table(States$region) #Create a frequency table
percentages <- round(100 * region_counts / sum(region_counts), 1) #Calculate percentages
labels <- paste(names(region_counts), ":", percentages, "%") #Create labels with percent
pie(region_counts, labels = labels, main = "Region Distribution with Percentages") #Draw pie chart with labels
5. [1 point] The following data are the blood types (A, B, AB, O) of 15 individuals. Find the
distribution of blood types. Express the distribution in terms of frequencies and percents. Why would a distribution of blood types be useful to a hospital?