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© 2012 McGraw-Hill Ryerson Limited 1© 2009 McGraw-Hill Ryerson Limited
© 2012 McGraw-Hill Ryerson Limited 2
LindMarchalWathenWaite
© 2012 McGraw-Hill Ryerson Limited 3
Explain why we study statistics.
Explain what is meant by descriptive statistics
and inferential statistics.
Distinguish between a qualitative variable and a
quantitative variable.
Describe how a discrete variable is different from
a continuous variable.
Distinguish among the nominal, ordinal, interval,
and ratio levels of measurement.
Learning Objectives
LO 1
LO 2
LO 3
LO 4
LO 5
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Why Study Statistics?LO 1
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Three main reasons:
1. Data are everywhere.
2. Statistical techniques are used to make many decisions that affect our lives.
3. No matter what your career, you will make decisions that involve data.
An understanding of statistical methods will help you make these decisions more effectively.
Why Study Statistics?
LO 1
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Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.
What Is Meant By Statistics?
LO 1
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Types of StatisticsLO 2
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Descriptive Statistics
Methods of organizing, summarizing, and presenting data in an informative way.
1. Frequency distributions2. Chart forms3. Central tendency 4. Measures5. Data clustering
Types of Statistics
LO 2
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Inferential Statistics
The methods used to determine something about a population, based on a sample:
1. A population is the entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.
2. A sample is a portion, or part, of the population of interest.
Types of Statistics
LO 2
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1. Prohibitive cost of surveying the whole population2. Destructive nature of some tests3. Physical impossibility of capturing the population
Types of Statistics
LO 2
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Descriptive Statistics:
1. Population census data2. Weekly earnings of hospitality workers3. Individual responses of registered voters regarding their
choice of Prime Minister of Canada
Inferential Statistics:
1. 46% of high school students can solve fractions, decimals, and percentages.
2. 77% of high school students can correctly total a restaurant menu.
Types of Statistics
LO 2
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You Try It Out!
LO 2
The Wooden Furniture Company asked a sample of 2564 consumers to try out a newly developed living room set in a showroom. Of the 2564 sampled, 2126 said they would purchase the furniture if it were marketed.
a)What should the Wooden Furniture Company report to its Board of Directors regarding the percentage of acceptance of the living room set?
b)Is this an example of descriptive statistics or inferential statistics? Explain.
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Types of VariablesLO 3
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Types of Variables
Qualitative
The characteristic being studied is non-numeric.
Examples:
Gender, religious affiliation, type of automobile owned, country of birth, eye colour
Quantitative
Information is reported numerically.
Examples:
The balance in your chequing account, the ages of company CEOs, the life of a battery, the number of children in a family
LO 3
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A Discrete Variable is Different from a Continuous Variable
LO 4
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Quantitative Variables: Classifications
Discrete Variables
Can only assume certain values and there are usually “gaps” between values
Examples:
Number of bedrooms in a house, number of cars arriving at a shopping centre, number of students in a statistics course section
Continuous Variables
Can assume any value within a specified range
Examples:
Tire pressure, weight of shipment of grain, amount of cereal in a box, duration of a flight
LO 4
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Summary of the Variable Types
Types of Variables
LO 3
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Mutually Exclusive
a property of a set of categories such that an individual or object is included in only one category
Exhaustive
a property of a set of categories such that each individual or object must appear in at least one category
Important Properties
LO 3
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Level of MeasurementLO 5
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Levels of Measurement
NominalThe variable of interest is divided into mutually exclusive categories or outcomes. There is no natural order to the outcomes.Examples: colour of M&Ms, gender
OrdinalData classifications are represented by labels or names (high, medium, low) that are mutually exclusive. Data classifications are ranked or ordered according to the particular trait they possess.Examples: professor ratings, terrorist attack risk levels
LO 5
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Levels of Measurement
LO 5
IntervalData classifications are mutually exclusive and exhaustive.Data classifications are ordered according to the amount of the characteristic they possess.Equal differences in the characteristic are represented by equal differences in the measurement.Examples: temperature, shoe size, IQ scores
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Levels of Measurement
LO 5
RatioData classifications are mutually exclusive and exhaustive.Data classifications are ordered according to the amount of the characteristics they possess.Equal differences in the characteristic are represented by equal differences in the numbers assigned to the classifications.The zero point is the absence of the characteristic and the ratio between two numbers is meaningful.Examples: wages, weight, height
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Levels of Measurement:
Summary of Major Characteristics
LO 5
Levels of Data
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You Try It Out!
LO 5
What level of measurement is reflected in the following data?
a) A sample number of books read in a year by 50 readers is given below:
b) In a survey of 300 television viewers, 100 were from a low income group, 150 from a middle income group, and 50 from a high income group.
15 4 3 11 17 3 1 7 14 14
10 6 6 10 18 13 4 17 16 11
5 13 8 16 9 4 5 18 16 12
7 11 9 14 11 12 5 12 17 13
8 12 12 6 2 1 6 13 15 9
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“There are three kinds of lies: lies, damn lies, and statistics”.
-- Benjamin Disraeli
“Figures don’t lie: liars figure”.
Statistics can be misused and data can be presented in misleading ways.
Ethics and Statistics
LO 5
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can provide accurate information in seconds
reduce the likelihood of an error
include options such as Excel, Excel add-ins (such as Megastat), or MINITAB
Computer Applications
LO 5
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I. Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.
II There are two types of statistics.
A Descriptive statistics are procedures used to organize and summarize data.
Chapter Summary
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B Inferential statistics involve taking a sample from a population and making estimates about a population based on the sample results.
1. A population is an entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.
2. A sample is a part of the population.
Chapter Summary
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III There are two types of variables.
A. A qualitative variable is categorical or nonnumeric.
1. Usually we are interested in the number or percent of the observations in each category.
2. Qualitative data are usually summarized in graphs and bar charts.
Chapter Summary
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B. There are two types of quantitative variables and they are usually reported numerically.
1. Discrete variables can assume only certain values, and there are usually gaps between values.
2. A continuous variable can assume any value within a specified range.
Chapter Summary
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IV There are four levels of measurement.
A. With the nominal level, the data are sorted into categories with no particular order to the categories.
B. The ordinal level of measurement presumes that one classification is ranked higher than another.
C. The interval level of measurement has the ranking characteristic of the ordinal level of measurement plus the characteristic that the distance between values is a constant size.
Chapter Summary
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D. The ratio level of measurement has all the characteristics of the interval level, plus there is a meaningful zero point and the ratio of two values is meaningful.
Chapter Summary
