# OMIS 2010 Chapter Notes - Chapter 02: Prime Rate, Frequency Distribution, Pie Chart

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6 Oct 2011

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Chapter 2: Graphical Descriptive Techniques

2.1 Introduction

This chapter discussed graphical descriptive methods used to summarize and describe sets of data.

At the completion of this chapter, you are expected to know the following:

1. How to recognize whether the type of data under consideration is quantitative, qualitative, or

ranked.

2. How to summarize a set of quantitative data by means of a frequency distribution, histogram,

relative frequency polygon, and stem and leaf display.

3. How to summarize a set of qualitative data by means of a pie chart and bar chart.

2.2 Types of Data

This section introduced the two main types of data that are referred to throughout the text:

quantitative (numerical) data and qualitative (categorical) data. The appropriate graphical method to be

used in presenting data depends, in part, on the type of data under consideration. Later in the text, when

statistical inference is covered, the data type will help to identify the appropriate statistical technique to

be used in solving a problem. In a few situations, it will be necessary to recognize whether or not a set of

nonquantitative data can be ordered. If the categories for a set of nonquantitative data can be ordered or

ranked, we have a third type of data, called ranked data.

At the completion of this section, you should be able to identify whether the type of data under con-

sideration is quantitative, qualitative, or ranked.

Question: How do I identify quantitative data?

Answer: Quantitative data are real numbers. They are not numbers arbitrarily assigned

to represent qualitative data. An experiment that produces qualitative data al-

ways asks for verbal, nonnumerical responses (e.g., yes and no; defective and

nondefective; Catholic, Protestant, and other).

Example 2.1

For each of the following examples of data, determine whether the data type is quantitative, qualita-

tive, or ranked.

a) the weekly level of the prime interest rate during the past year

b) the make of car driven by each of a sample of executives

c) the number of contacts made by each of a company’s salespersons during a week

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d) the rating (excellent, good, fair, or poor) given to a particular television program by each of a

sample of viewers

e) the number of shares traded on the New York Stock Exchange each week throughout 1987

Solution

a) Quantitative, if the interest rate level is expressed as a percentage. If the level is simply ob-

served as being high, moderate, or low, then the data type is qualitative.

b) Qualitative

c) Quantitative

d) Ranked, because the categories can be ordered

e) Quantitative

EXERCISES

2.1 Describe the difference between quantitative data and qualitative data.

2.2 For each of the following examples of data, determine whether the data are quantitative,

qualitative, or ranked.

a) the month of the highest sales for each firm in a sample

b) the department in which each of a sample of university professors teaches

c) the weekly closing price of gold throughout a year

d) the size of soft drink (large, medium, or small) ordered by a sample of customers in a

restaurant

e) the number of barrels of crude oil imported monthly by the United States

2.3 Identify the type of data observed for each of the following variables.

a) the number of students in a statistics class

b) the student evaluations of the professor (1 = poor, 5 = excellent)

c) the political preferences of voters

d) the states in the United States of America

e) the size of a condominium (in square feet)

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2.3 Graphical Techniques for Quantitative Data

This section introduced the basic methods of descriptive statistics used for organizing a set of nu-

merical data in tabular form and presenting it graphically. Summarizing data in this way requires that

you first group the data into classes. Judgment is required concerning the number and the size of the

classes to be used. The important point to bear in mind when making this judgment is that the

presentation of the grouped data should enable the user to quickly grasp the general shape of the

distribution of the data.

At the completion of this section, you should be able to summarize a set of numerical data in the fol-

lowing ways:

1. Organize the data into a frequency distribution.

2. Construct a histogram.

3. Construct a frequency polygon.

4. Construct the relative frequency counterparts of points 1, 2, and 3.

5. Construct an ogive—the graph of a cumulative relative frequency distribution.

6. Construct a stem and leaf display.

Question: How do I choose the number of classes and the width of the classes to be

used in constructing a frequency distribution?

Answer: Although this choice is arbitrary and no hard and fast rules can be given, here

are a few useful guidelines:

1. The classes must be nonoverlapping, so that each measurement falls into

exactly one class. Therefore, choose the classes so that no measurement falls

on a class boundary.

2. Choose the number of classes to be used as a number between 5 and 20,

with smaller numbers of classes being chosen for smaller data sets.

3. The approximate width of each class is given by the following:

Approximate class width = Largest value – Smallest value

Number of classes

Choose the actual class width to be a value close to the approximate width

that is convenient to work with. Avoid awkward fractional values.

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