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## Statistics Assignment

•Business Analytics

•Chapter 3

•Graphical descriptive techniques – Nominal data

•Chapter outline

3.1 Graphical techniques to describe nominal data3.2 Selecting the appropriate chart: Which chart is best?

3.3 Graphical techniques to describe ordinal data

3.4 Describing the relationship between two nominal variables

•Learning Objectives

LO1 Construct charts to summarise nominal dataLO2 Use excel to draw appropriate charts for nominal data

LO3 Determine which chart is best for nominal data under a given circumstance

LO4 Use charts to describe ordinal data

LO5 Use various tabular and graphical techniques to analyse the relationships between two nominal variables.

•Introduction

In this chapter, we introduce graphical and tabular statistical methods that allow managers to summarise data visually in order to produce useful information – a technique often used in decision makingWe also discuss ways to use the techniques introduced in an effective and accurate way.

•3.1 Graphical techniques to describe nominal data

The graphical presentations shown here are used primarily for nominal data.These graphical tools are most appropriate when the raw data can be naturally categorised in a meaningful manner.

•3.1 Graphical techniques to describe nominal data

The only allowable calculation on nominal data is to count the frequency of each value of the variable.We can summarise the data in a table that presents the categories and their

__counts__called a frequency distribution.

A relative frequency distribution lists the categories and the

__proportion__with which each occurs.

The methods presented apply to both

•the entire population, and

•a sample selected from the population.

•Example 4 - Newspaper Readership Survey

(Example 3.7, p68)

XM03-07 In a major Australian city there are four competing newspapers: N1, N2, N3 and N4.(Example 3.7, p68)

To help design advertising campaigns, the managers of the newspapers need to know which segments of the market are reading their newspapers.

A survey was conducted to determine whether the newspaper readership and occupation are related.

A sample of newspaper readers was asked to report which newspaper they read: N1, N2, N3, N4, and to indicate whether they were blue-collar worker (1), white-collar worker (2), or professional (3).

•Example 1

•Solution: Example 1

•Counting the No’s of 1s. 2s, 3s and 4s manually or using the ‘countif’ command in excel gives

•Types of Graphical charts used to describe nominal data

•Bar charts

–A bar chart graphically represents the frequency of each category as a bar rising vertically from the horizontal axis.

–The height of each bar is proportional to the frequency of the corresponding category.

•Pie charts

–A pie chart is a circle that is subdivided into slices whose areas are proportional to the frequencies (or relative frequencies), thereby displaying the proportion of occurrences of each category.

–The pie chart is a very popular tool used to represent the proportions of appearance for nominal data.

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Example: Pie ChartUsing the frequency distribution table in example 1, we can draw a pie chart

•Pie charts

Pie chart - Calculating manuallyIn constructing a pie chart, the size of a slice of the circle is proportional to the percentage corresponding to that category.

For example, the angle between the lines demarcating N1 readers is

25.1 × 3.6 = 90.4o.

The angles of the pie chart for the other four categories are calculated similarly, as shown in the table below:

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•3.2 Selecting the appropriate chart:

Which chart is best?

Which chart is best – bar or pie chart?Which chart is best?

•Depends on what you want to emphasize

–If the focus is to compare the size or frequency of various categories, a bar chart may be appropriate

–If the focus is on the distribution (or share) of each category, use a pie chart

•Example 2

(Table 3.5, page 53)

If the focus is to compare the size of frequency of various categories, a bar chart is more appropriate.(Table 3.5, page 53)

•Example 2…

If the focus is on the distribution of each category either pie or bar chart may be appropriate.
•Example 2…

If the focus is on the change in market share, a bar chart may be appropriate.
•Component bar chart

A component bar chart represents all categories within a single bar.The bar is partitioned into components, with the height of each component proportional to the frequency of the category that it represents.

Component bar charts offer a good alternative to using two pie charts, when a comparison of two breakdowns is desired.

•Example 3

(Table 3.8, page 59)

(Table 3.8, page 59)

•Example 3…

The shares of likelihood in 2008 and 2010 can be compared by displaying them in a component bar chart.
•3.3 Graphical techniques to describe ordinal data

When the data are ordinal (or ranked), treat the data as nominal and use a bar or pie chart.For example, consider the average weekly household income for the 5 income quintiles (Example 3.6, page 60).

•3.4 Describing the relationship between two nominal variables

So far we’ve looked at tabular and graphical techniques for one nominal variable.Now we will look at the relationship between two nominal variables using either tabular or graphical techniques.

•Describing the relationship between two nominal variables…

Two ways to describe
•A cross-classification table (or contingency table or cross-tabulation table)

•A variation of a bar chart

•Describing the relationship between two nominal variables…

A cross-classification table is used to describe the relationship between two nominal variables.A cross-classification table lists the frequency of each combination of the values of the two nominal variables.

•Example 4 - Newspaper Readership Survey

(Example 3.7, p68)

XM03-07 In a major Australian city there are four competing newspapers: N1, N2, N3 and N4 as in Example 1.(Example 3.7, p68)

To help design advertising campaigns, the managers of the newspapers need to know which segments of the market are reading their newspapers.

A survey was conducted to determine whether the newspaper readership and occupation are related.

A sample of newspaper readers was asked to report which newspaper they read: N1, N2, N3, N4, and to indicate whether they were blue-collar worker (1), white-collar worker (2), or professional (3).

•Example 4…

Newspaper readership and occupation
•Example 4 – Solution

By counting the number of times each of the 12 combinations occurs, we produce Table 3.9.
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•Example 4 – Solution…

The frequencies can be depicted in graphical form using a bar chart.
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•Example 4 – Solution…

If occupation and newspaper readership are related, then there will be differences in the newspapers read among the occupations.An easy way to see this is to convert the frequencies in each row (or column) to relative frequencies using each row (or column) total.

That is, compute the row (or column) totals and divide each frequency by its row (or column) total.

•Example 4 – Solution…

•Example 4 – Solution…

Interpretation:Notice that the relative frequencies in the rows 2 (white-collar) and 3 (Professionals) are similar and that there are large differences between row 1 (blue-collar) and rows 2 and 3.

This tells us that

•blue collar workers tend to read different newspapers from both white-collar workers and professionals; and

•white-collar workers and professionals are quite similar in their newspaper choices.

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