(5) graphical presentation 1

7/30/2019 (5) Graphical Presentation 1

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Applied Statistics and Computing Lab

GRAPHICAL PRESENTATIONS 1(REPRESENTATION OF CATEGORICAL DATA)


Indian School of Business

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Learning Goals

Why we use Graphs?

Basic Graphs for Categorical Data

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Why use graphs? A market survey firm is conducting a survey on the popularity of different

makes of car in the USA. For this, it investigates various car showrooms andlists down the various car varieties in each showroom

Suppose it obtains the following data on the makes of 28 cars in one suchshowroom : Buick, Cadillac, Buick, Chevrolet, Buick, Buick, Buick, Pontiac,Cadillac, Chevrolet, SAAB, SAAB, SAAB, Cadillac, Chevrolet, Pontiac, Buick,Buick, Buick, SAAB, Cadillac, SAAB, Pontiac, SAAB, Chevrolet, Buick, SAAB,Cadillac.

Relevant Questions: Which is the most common car in the showroom?

Which is the least common car in the showroom?

How to answer these questions?

Probably the first thing you do, is count the observations for each car make

and note them down Once you note them down in a tabular form, that makes it a frequency table

Frequency Table for categorical data is a table that displays the possiblecategories along with the associated frequencies or relative frequencies.

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Table 1: Frequency Table

Color Frequency

Buick 9

Cadillac 5

Chevrolet 4

Pontiac 3

SAAB 7

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At one glance- the answers are there!

Buick is the most common brand in that showroom and Pontiac is

the least common brand A frequency table is the simplest representation of data in a tabular

form

This same data can be represented pictorially in a number of ways!


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Different types of graphs for representing

categorical data

Graphs for presenting categorical data:

Frequency Table

Bar Chart- Multiple Bar, Divided or Segmented

Bar

Pie Chart

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Table 2:Why different graphs-

Illustration through examples

Consider the following Frequency table of the population of

Andhra Pradesh in 2011:

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Category Population in 2011

Rural Male 28219760Rural Female 28092028

Urban Male 14290121

Urban Female 14063624


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Bar Chart Inferences

For policy reasons, one isinterested in the composition ofpopulation in Andhra Pradesh.

From a bar chart, we can get themost frequently and infrequently

occurring categories- Rural malehas the highest occurrence, urbanfemale the lowest.

However, one may also beinterested in the relative share ofeach category, rather than theabsolute figure

Visually, from the bar chart ruralmale and rural female seems

almost equal. So does urban maleand female

To analyze their relative share welook at pie chart

Bar chart is a graph of the frequencydistribution of categorical data.

Each category in the frequency

distribution is represented by a bar or

rectangle.

Area of each bar is proportional to thecorresponding frequency.

Bar chart maybe vertical or horizontal.

The following is vertical

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Pie Chart

A circle is used to represent the whole data set

Slices of the pie represent possible categories

Area of the slice for a particular category is proportional to the correspondingrelative frequency

When to use: categorical data with a relatively small number of categories

In case of many categories, merge a few categories into one

Most useful for illustrating proportions of the whole dataset for various categories

Criticism: Not an effective visual display if one doesnt specify the percentages8


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Multiple Bar Graph

Category Population in 2011 Population in 2001

Rural Male 28219760 27937204Rural Female 28092028 27463863

Urban Male 14290121 10590209

Urban Female 14063624 10218731

Suppose the government of AP is interested in population control.

They are interested to know how the population in each category has

changed in the decade from 2001 to 2011 so that they know which sectionto target

We have bar plot and Pie chart of population in 2011.

Draw the same for 2001. Can we compare graphically and readily answer the

questions? (Check!)

A pie chart and bar chart allow comparison between categories within a

year- but not across years

To facilitate such a comparison Multiple bar graph is used

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Multiple Bar GraphInferences:

Most marked increase in populationin the category of urban female,followed closely by urban male

Very slight increase in the categoriesrural male and rural female

Possible cause- rural to urbanmigration- needs investigation

Since increase in each category from2001 to 2011, hence total increase inpopulation from 2001 to 2011

However, cannot visualize exactlyhow much the population hasincreased from 2001 to 2011

Also, no information about the

relative contribution of each categoryto the total

For this, use segmented or stackedbar plot

What is a multiple bar graph?

Variant of the bar diagram

Used to compare one or more series of data

on the same variable or for showing

different components of an item Several sets of bars are drawn so that bars

for a particular period (here 2001 and

2011) or related phenomenon are put

together and uniform gap is maintained

between any two sets of bars10


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Segmented Bar Graph:

Year wise

Inferences

Gives an idea about the total increase in populationfrom 2001 to 2011

Also, the relative share of each category in each year

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Segmented Bar Graph uses a

rectangular bar rather than a circle to

represent the entire dataset

The bar is then divided into segments,with different segments representing

different categories

Size of the segment for a particular

category is proportional to the relative

frequency for that category


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Segmented Bar Graph: Category-wise

Rural male is the most dominant category, followed by rural female

From 2001 to 2011, there has been a relative increase in the urban male

and urban female population (relative to rural male and rural female)

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Suppose we want to

compare each category-

Rural male vs. rural female,urban male vs. urban female

in both the years

Simple trick- switch the

row/column in your data so

that you have segmentedbar graph, category wise


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Pictorial Presentation or Table? The objective of a frequency table is to provide insights about the data that cannot

be quickly obtained by looking only at the original data- like the cars example

Here if you make a pictorial presentation of the data, no extra gain in information

But Pictorial Presentation sometimes necessary to depict some features of data-not readily readable from table- refer table 2, slide 11

Recall some questions we have asked-

What is the relative share of urban male, urban female, rural male and rural

female in the population of Andhra Pradesh in 2011?

By how much did the total population increase from 2001 to 2011?

What was the combined urban male, urban female, rural male and rural

female populations for the years 2001 and 2011?

You cannot readily answer such questions by looking at just the frequency table

which only gives information about the frequency of each category. However, you will be able to answer questions like-

Which one is the most frequently occurring category in 2001 and in 2011?

Was there an increase in the frequency of urban male, urban female, rural

male and rural female from 2001 to 2011?13


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R-Codes#Creating Data

APPopulation = cbind(c(28219760,28092028,14290121,14063624),

c(27937204,27463863,10590209,10218731))

rownames(APPopulation) = c("RuralMale","RuralFemale","UrbanMale","UrbanFemale")

colnames(APPopulation) = c("2011","2001")

#barplot

colors=c("red", "bisque", "darkslategray", "violet")

barplot(APPopulation[,"2011"]/1000000,col=colors)

title(main="Barplot of AP Population in 2011 (in millions)")

# Multiple Bar Graph:A = matrix(

c(10218731,10590209,27463863,27937204,14063624,14290121,28092028,28219760), # the dataelements

nrow=2, # number of rows

ncol=4, # number of columns

byrow = TRUE) # fill matrix by rows

colors=c("red", "bisque")

barplot(A/1000000,names.arg=rev(rownames(APPopulation)),legend.text=c(2001,2011),beside=TRUE,main="Distribution ofpopulation by category",xlab="Categories", ylab="population, in millions",ylim=c(0,80),col=colors)

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R-Codes (Continued)# Segmented bar graph (yearwise)

colors=c("red", "bisque", "darkslategray", "violet","red","yellow")

barplot(APPopulation/1000000, main="Distribution of population by category yearwise",

xlab="Year", ylab="population, in millions",col=colors,

legend = rownames(APPopulation))

# Segmented bar graph (categorywise)

colors=c("red", "bisque")

A = matrix(

c(10218731,10590209,27463863,27937204,14063624,14290121,28092028,28219760), # the data elements

nrow=2,

ncol=4,

byrow = TRUE)barplot(A/1000000,names.arg =rev(rownames(APPopulation)),legend.text=c(2001,2011),beside=FALSE,main="Distribution

of population by category",xlab="Categories", ylab="population, in millions",ylim=c(0,90),col=colors)

# Pie Chart

colors=c("red", "bisque", "darkslategray", "violet")

slices


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Thank you

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