School

York UniversityDepartment

Operations Management and Information SystemCourse Code

OMIS 2010Professor

Alan MarshallChapter

1This

**preview**shows pages 1-3. to view the full**24 pages of the document.**Chapter 1

Descriptive Statistics

Deals with methods of organizing, summarizing, and presenting data in a convenient and

informative way

Forms:

−graphical techniques for easy extraction of useful information (Histogram)

−Numerical techniques to describe different features of data

−Actual technique depends on the specific information that we would like to extract

Measure of central location (Mode, mean, median)

Measure of variability (Range)

Inferential Statistics

Is a body of methods used to draw conclusions or inferences about characteristics of population

based on sample data

A sample that is only a small fraction of the size of the population can lead to correct inferences

only a certain percentages of the time

1.1 Key Statistical Concepts

Population

Is the group of all items of interest to a statistics practitioner

Descriptive measure: parameter

−represents the information we need (in most applications)

Sample

Set of data drawn from a studied population

Descriptive measure: Statistic

−Used to make inferences about parameter

Statistical Inference

Process of making an estimate, prediction, or decision about a population based on sample data

Populations = almost always VERY large, impractical to investigate each member

Easier and cheaper to take sample from population and draw conclusions or make estimates

Not always correct

Thus statistical inference measure of reliability

−Confidence level: proportion of times that an estimating procedure will be correct

−Significance level: Measures how frequently the conclusion will be wrong

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Chapter 2

2.1 Types of Data and Information

Variable: Some characteristic of a population or sample

−Varies from person to person, thus the name

Values of the variable: Possible observations of the variable

Data: Observed values of a variable (Plural form of datum)

−Three types

•Interval: Real numbers, referred to as quantitative or numerical

•Nominal: Categories, also called qualitative or categorical

•Ordinal: Appear to be nominal, but order of their values has meaning, and thus must be

maintained.

−Magnitude no important, as long as they are in order

Difference between ordinal and interval:

−Intervals or differences between values of interval are consistent and meaningful (can

calculate or interpret), while the intervals or differences between ordinal values hold no

meaning (cannot calculate or interpret)

Calculations for Types of Data

Interval Data

−All calculations are permitted

Nominal Data

−Cannot perform any calculations

−Calculations based on codes used to store this type of data are meaningless

−Can only count or compute percentages of the occurrences of each category

Ordinal Data

−Most important aspect = order of the values

−Only permissible calculations are those involving a ranking process

Hierarchy of Data

Placed in order of permissible calculations

Higher-level data types may be treated as lower-level ones

−Conversion leads to loss of information

−Do not convert data unless necessary

CANNOT treat lower-level data as higher-level

Summary

−Interval

•Values are real numbers

•All calculations are valid

•Data may be treated as ordinal or nominal

−Ordinal

•Values must represent the ranked order of the data

•Calculations based on an ordering process are valid

•Data may be treated as nominal but not as interval

−Nominal

•Values are the arbitrary numbers that represent categories

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•Only calculations based on the frequencies or percentages of occurrences are valid

•Data may not be treated as ordinal or interval

Interval, Ordinal, and Nominal Variables

Variables are given the same name as the type of data which they constitute

2.2 Describing a Set of Nominal Data

Frequency Distribution: Summarized data in a table, which presents the categories and their

counts

Relative Frequency Distribution: Lists the categories and the proportion with which each

occurs

Bar Chart and Pie chart are used to present a picture of the data

Bar chart = frequencies

Pie chart = relative frequencies

Used to enhance the readers’ ability to grasp the substance of the data

Describing Ordinal Data

No specific graphical techniques

When describing, treat as if nominal

Only criterion = the bars in bar charts should be arranged in ascending or descending ordinal

values, in pie charts the wedges are typically arranged clockwise

Factors That Identify Where to Use Frequency and Relative Frequency Tables, Bar and Pie Charts

Objective: Describe a single set of data

Data type: Nominal or ordinal

2.3 Describing the Relationship between Two Nominal Variables and Comparing Two or More

Nominal Data Sets

Univariate: Techniques applied to single sets of data

Bivariate: Techniques that depict relationship between variables

Cross-classification table: Used to describe the relationship between two nominal variables

(Table 2.5)

−A variation of bar chart is used to describe the information graphically (Page 35)

−Same technique used to compare two or more sets of nominal data

Tabular Methods of Describing the Relationship between Two Nominal Variables

Must remember permitted only to determine the frequency of the values (Table 2.5)

Comparing Two or More Sets of Nominal Data

Consider one category as defining population (variables are different populations)

−Then compare the bar charts or individual bars

Data Formats

Several ways to store data to produce a table or a bar/pie chart

1. Data in two columns (Example 2.4)

−First column categories for first variable, second column categories for second variable

−Each row represents one observation of the two variables

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