Data Presentation and Visualization
Data Visualization is a term used to describe the use of graphical displays to:
- summarize
- present
Data becomes more comprehensible and more useful when organized and presented
Data Patterns in Graphs
Data patterns are commonly described in terms of the:
- Center: data point where about half of the observations are on either side.
- Spread: variability of the data
- Shape: can be described by the characteristics:
Symmetry
Number of Peaks
Skewness
Other data patterns:
- Unusual Features: if there are gaps or if there are outliers.
Summarizing Qualitative and Quantitative Data for a Single Variable
FREQUENCY DISTRIBUTION TABLE
- Shows how often each value (or set of values) of the variable in question occurs in a data set.
- tabular summary of data showing frequency or number
Relative Frequency Distribution
- Gives tabular summary of data showing relative frequency of each class.
Percent Frequency Distribution
- presents percent frequency of the data for each class
Frequency Distribution Table
Example 1
Create a Frequency Distribution Table for the data on soft drink purchases presented on the following table.
| Purchase | Purchase | Purchase | Purchase |
|---|---|---|---|
| Coke Classic | Sprite | Pepsi | Diet Coke |
| Coke Classic | Coke Classic | Pepsi | Diet Coke |
| Coke Classic | Diet Coke | Coke Classic | Coke Classic |
| Coke Classic | Diet Coke | Pepsi | Coke Classic |
| Coke Classic | Dr. Pepper | Dr. Pepper | Sprite |
| Coke Classic | Diet Coke | Pepsi | Diet Coke |
| Pepsi | Coke Classic | Pepsi | Pepsi |
| Coke Classic | Pepsi | Coke Classic | Coke Classic |
| Pepsi | Dr. Pepper | Pepsi | Pepsi |
| Sprite | Coke Classic | Coke Classic | Coke Classic |
| Sprite | Dr. Pepper | Diet Coke | Dr. Pepper |
| Pepsi | Coke Classic | Pepsi | Sprite |
| Coke Classic | Diet Coke |
Frequency Distribution Table
The R Script:
#install.packages("readr")
#install.packages("pander")
library(readr)
Warning: package 'readr' was built under R version 4.1.1
library(pander)
Warning: package 'pander' was built under R version 4.1.1
# Import "purchase.csv" data and store it in 'pchase'.
pchase <- read.csv("purchase.csv")
# Determine the frequencies for each observation. pchase.freq = table(pchase) pander(pchase.freq)
| Coke Classic | Diet Coke | Dr. Pepper | Pepsi | Sprite |
|---|---|---|---|---|
| 19 | 8 | 5 | 13 | 5 |
# Create the Frequency Distribution Table.
freq.dist <- cbind(pchase.freq)
colnames(freq.dist) <-c("Frequency")The Frequency Distribution Table
The Tabular Output
# Generate created Frequency Distribution Table. pander(freq.dist)
| Frequency | |
|---|---|
| Coke Classic | 19 |
| Diet Coke | 8 |
| Dr. Pepper | 5 |
| Pepsi | 13 |
| Sprite | 5 |
Relative Frequency Distribution Table
The R script:
data.relfreq<-pchase.freq/nrow(pchase)
relfreq.dist<-cbind(data.relfreq)
colnames(relfreq.dist) <-c("Relative Frequency")Relative Frequency Distribution Table
The Tabular Output
pander(relfreq.dist)
| Relative Frequency | |
|---|---|
| Coke Classic | 0.38 |
| Diet Coke | 0.16 |
| Dr. Pepper | 0.1 |
| Pepsi | 0.26 |
| Sprite | 0.1 |
Relative Frequency Distribution Table
Example 2
A survey was taken in Aurora Avenue. In each of 20 homes, people were asked how many cars were registered to their households. The results were recorded as follows: 1, 2, 1, 0, 3, 4, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 1, 4, 0, 0
Relative Frequency Distribution Table
The R Script:
# Create the data vector. cars <- c(1, 2, 1, 0, 3, 4, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 1, 4, 0, 0)
# Determine the frequencies. # Compute for relative and percent frequencies, respectively. car.freq<-table(cars) car.relfreq<-car.freq/sum(car.freq) car.pctfreq<-car.relfreq*100
# Create the tabular output.
car.freqdist<-cbind(car.freq, car.relfreq, car.pctfreq)
colnames(car.freqdist) <-c("Frequency", "Relative Frequency", "Percent Frequency")Complete Frequency Distribution
# Generate the tabular output. pander(car.freqdist)
| Frequency | Relative Frequency | Percent Frequency | |
|---|---|---|---|
| 0 | 4 | 0.2 | 20 |
| 1 | 6 | 0.3 | 30 |
| 2 | 5 | 0.25 | 25 |
| 3 | 3 | 0.15 | 15 |
| 4 | 2 | 0.1 | 10 |
Grouped Frequency Distribution Table
- Individual data values are classified into categories called class intervals.
- Not advisable to create and use one for data analysis.
- Simply created as a convenient means of organizing and summarizing data.
Grouped Frequency Distribution Table
Steps in Creating a Grouped FDT:
- Determine the number of classes, k.
(Use Sturges’ formula.)
- Calculate the class size (or class width), c.
- Enumerate the class intervals.
- Tally the observations.
Grouped Frequency Distribution Table
Example
Consider the following data set presented in Example 3 of the module:
425, 430, 430, 435, 435, 435, 435, 435, 440, 440, 440, 440, 440, 445, 445, 445, 445, 445, 450, 450, 450, 450, 450, 450, 450, 460, 460, 460, 465, 465, 465, 470, 470, 472, 475, 475, 475, 480, 480, 480, 480, 485, 490, 490, 490, 500, 500, 500, 500, 510, 510, 515, 525, 525, 525, 535, 549, 550, 570, 570, 575, 575, 580, 590, 600, 600, 600, 600, 615, 615
Create a frequency distribution table with 7 class intervals.
Grouped Frequency Distribution Table
The R script
# Load necessary packages. library(readr) library(pander)
# Import data into RStudio.
rent <-read.csv("rent.csv")
# Generate regular sequences of values breaks <-seq(425, 621, by =28) # Create the class intervals and assign data values to these. classint<-cut(rent$Rent, breaks, right =FALSE)
# Determine frequencies of each class interval.
freq<-table(classint)
# Transform table to column format.
freq.dist<-cbind(freq)
# Provide label to the column of frequencies.
colnames(freq.dist) <-c("Frequency")Grouped Frequency Distribution Table
The Tabular Output
# Generate the Grouped FDT. pander(freq.dist)
| Frequency | |
|---|---|
| [425,453) | 25 |
| [453,481) | 16 |
| [481,509) | 8 |
| [509,537) | 7 |
| [537,565) | 2 |
| [565,593) | 6 |
| [593,621) | 6 |
Bar Chart
- Used to display qualitative data summarized in a frequency, relative frequency, or percent frequency distribution.
- Vertical bar chart: horizontal axis - categories; vertical axis - value (freq., rel. freq., % freq.)
Bar Chart
Example for Data on Soft Drink Purchases
The R Script:
# install.packages(“tidyverse”)
# install.packages(“forcats”)
# Load necessary packages.
library(readr)
library(tidyverse)
library(forcats)
# Import "purchase.csv" file.
purchase <-read.csv("purchase.csv") Bar Chart
The Chart:
# Create the chart. Store it to 'bar1'.
bar1 <- ggplot(purchase, aes(x=Purchase)) + geom_bar(width=.5)+
ggtitle("Soft Drink Purchases")
# Present the generated chart.
bar1
Bar Chart
The Graphical Output (ordered bars):
bar2 <- ggplot(mutate(purchase, Purchase =fct_infreq(Purchase)))+
geom_bar(aes(x = Purchase), width = .5) + ggtitle("Soft Drink Purchases")
bar2
Pie Chart
- Provides another graphical device for presenting the frequency, relative frequency, or percent frequency distributions for qualitative data.
- The pie chart makes use of sectors of a circle where the numerical values presented by each sector could be the frequencies, relative frequencies or percent frequencies.
- The angle of a sector is proportional to the frequency of each of the categories of the variable.
The Dot Plot
- Similar to a bar graph.
- The height, represented by the number of dots, equals the number of items in a certain category.
Example (Data on the number of cars registered to each household).
Data: 1, 2, 1, 0, 3, 4, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 1, 4, 0, 0
The Dot Plot
The R Script
library(ggplot2)
library(readr)
# Import the "cars.csv" data file
cars <-read.csv("cars.csv")
# Generate the plot
dplot <-ggplot(cars, aes(cars)) + geom_dotplot(binwidth = 0.25)
The Dot Plot
The Output Plot
dplot
The Dot Plot
Using the “stripchart” function
The R Script
# Manually construct the data vector.
cars <- c(1, 2, 1, 0, 3, 4, 0, 1, 1, 1,2, 2, 3, 2, 3, 2, 1, 4, 0, 0)
# Creater the dotplot
dplot <- stripchart(cars, method = "stack", at = c(0.05),
pch = 20, cex = 3.2, las = 1, frame.plot = FALSE,
xlim = c(0,5), main = "Number of Cars Registered")
Stem-and-Leaf Plot
- It shows both rank order of data as well as the shape.
- Useful for numerous data.
Example 1
Data: 22, 29, 22, 31, 20, 12, 14, 24, 13, 4, 2, 1
Stem-and-Leaf Plot
The R Script
# Create the data vector data <- c(22, 29, 22, 31, 20, 12, 14, 24, 13, 4, 2, 1)
# Create the stem-and-leaf plot stem(data, scale = 1)
The decimal point is 1 digit(s) to the right of the | 0 | 124 1 | 234 2 | 02249 3 | 1
Stem-and-Leaf Plot
Example 2
Data: 8.6, 11.7, 9.4, 9.1, 10.2, 11.0, 8.8
Stem-and-Leaf Plot
The R Script
# Create the data vector data <- c(8.6, 11.7, 9.4, 9.1, 10.2, 11.0, 8.8)
# Create the stem-and-leaf plot stem(data, scale = 1)
The decimal point is at the | 8 | 68 9 | 14 10 | 2 11 | 07
Crosstabulation
A crosstabulation is a tabular summary of data for two variables.
It is also called a contingency table.
The two variables can be:
- both qualitative
- both quantitative
- combination
Crosstabulation
Example: Consider the data below:(named “example.csv”)
| Respondent | Gender | Age | Education |
|---|---|---|---|
| 1 | Male | 20 | Bachelor’s Degree |
| 2 | Male | 18 | Undergraduate |
| 3 | Female | 19 | Undergraduate |
| 4 | Male | 25 | Bachelor’s Degree |
| 5 | Female | 37 | Master’s Degree |
| 6 | Female | 15 | Undergraduate |
| 7 | Female | 40 | PhD |
| 8 | Male | 43 | Bachelor’s Degree |
| 9 | Male | 60 | Bachelor’s Degree |
| 10 | Female | 65 | Master’s Degree |
| 11 | Female | 42 | Bachelor’s Degree |
For the given data:
-
Create a crosstabulation of Gender vs Education
- . Create a crosstabulation of Age vs Education where for the age, classify each respondents as a “Teen” (from 15 to 19 years of age), an “Adult” (from 20 to 59 years of age), or a “Senior” (from 60 years of age and above).