Introductionto Statistics

Chapter 1

Learning Objectives Learning Objectives• Define statistics• Become aware of a wide range of

applications of statistics in business• Differentiate between descriptive and

inferential statistics• Classify numbers by level of data and

understand why doing so is important

What is Statistics?What is Statistics?

• Science of gathering, analyzing, interpreting, and presenting data

• Branch of mathematics• Course of study• Facts• Measurement taken on a sample• Type of distribution being used to

analyze data

Population Versus SamplePopulation Versus Sample

• Population — the whole– a collection of persons, objects, or items

under study• Census — gathering data from the

entire population• Sample — a portion of the whole

– a subset of the population

PopulationPopulation

Population and Census DataPopulation and Census Data

Identifier Color MPG

RD1 Red 12

RD2 Red 10RD3 Red 13

RD4 Red 10RD5 Red 13BL1 Blue 27BL2 Blue 24

GR1 Green

35GR2 Gree

n35

GY1 Gray 15GY2 Gray 18GY3 Gray 17

Sample and Sample DataSample and Sample Data

Identifier Color MPG

RD2 Red 10

RD5 Red 13

GR1 Green

35

GY2 Gray 18

Descriptive vs. Inferential StatisticsDescriptive vs. Inferential Statistics

• Descriptive Statistics — using data gathered on a group to describe or reach conclusions about that same group only

• Inferential Statistics — using sample data to reach conclusions about the population from which the sample was taken

Parameter vs. StatisticParameter vs. Statistic

• Parameter — descriptive measure of the population– Usually represented by Greek letters

• Statistic — descriptive measure of a sample– Usually represented by Roman letters

Symbols for Population ParametersSymbols for Population Parameters

denotes population parameter

2 denotes population variance

denotes population standard deviation

Symbols for Sample StatisticsSymbols for Sample Statistics

x denotes sample mean2S denotes sample variance

S denotes sample standard deviation

Process of Inferential StatisticsProcess of Inferential Statistics

Population

(parameter)

Sample

x

(statistic)

Calculate x

to estimate

Select a

random sample

Levels of Data MeasurementLevels of Data Measurement

• Nominal - Lowest level of measurement• Ordinal• Interval• Ratio - Highest level of measurement

Nominal Level DataNominal Level Data

• Numbers are used to classify or categorizeExample: Employment Classification

– 1 for Educator– 2 for Construction Worker– 3 for Manufacturing Worker

Example: Ethnicity– 1 for African-American– 2 for Anglo-American– 3 for Hispanic-American– 4 for Oriental-American

Ordinal Level DataOrdinal Level Data

• Numbers are used to indicate rank or order– Relative magnitude of numbers is meaningful– Differences between numbers are not comparable

Example: Taste test ranking of three brands of soft drink

Example: Position within an organization– 1 for President– 2 for Vice President– 3 for Plant Manager– 4 for Department Supervisor– 5 for Employee

Example of Ordinal MeasurementExample of Ordinal Measurement

f

i

n

is

h

1

2

3

4

5

6

Ordinal DataOrdinal Data

Faculty and staff should receive preferential treatment for parking space.

1 2 3 4 5

StronglyAgree

Agree StronglyDisagree

DisagreeNeutral

Interval Level DataInterval Level Data• Distances between consecutive integers

are equal– Relative magnitude of numbers is

meaningful– Differences between numbers are

comparable– Location of origin, zero, is not absolute

Examples: Fahrenheit Temperature, Calendar Time, Monetary Units

Ratio Level DataRatio Level Data• Highest level of measurement

– Relative magnitude of numbers is meaningful– Differences between numbers are

comparable– Location of origin, zero, is absolute (natural)

Examples: Height, Weight, and Volume

Usage Potential of VariousLevels of Data

Usage Potential of VariousLevels of Data

Nominal

Ordinal

Interval

Ratio

Data Level, Operations, and Statistical Methods

Data Level, Operations, and Statistical Methods

Data Level

Nominal

Ordinal

Interval

Ratio

Meaningful Operations

Classifying and Counting

All of above plus Ranking

All of above plus Addition, Subtraction, Multiplication, and Division

All of the above

StatisticalMethods

Nonparametric

Nonparametric

Parametric

Parametric

Qualitative vs Quantitative Data

Qualitative Data is data of the nominal or ordinal level that classifies by a label or category. The labels may be numeric or nonnumeric.

Quantitative Data is data of the interval or ratio level that measures on a naturally occurring numeric scale.

Discrete and Continuous Data

Discrete Data is numeric data in which the values can come only from a list of specific values. Discrete data results from a counting process.

Continuos Data is numeric data that can take on values at every point over a given interval. Continuous data result from a measuring process.

Summary of Data Classifications

Data

nal Ordinal

InterlRatio

Qualitative(Categorical)

Quantitative

Nonnumeric Numeric

Discrete

Numeric

Discrete or Continuous

Data

Nominal Ordinal Interval Ratio

QuantitativeQualitative

Numeric Numeric

Discrete

Nonnumeric

Discrete orContinuous