Introduction to business statistics

Introduction

Copyright ©2011 Pearson Education

1-1

Learning Objectives
In this chapter you learn:


How business uses statistics



The basic vocabulary of statistics



How to use Microsoft Excel with this book


1-2

Why Learn Statistics
Make better sense of the world

Make better business decisions



Internet articles / reports



Business memos



Magazine articles



Business research



Newspaper articles



Technical journals



Television & radio reports



Technical reports


1-3

In Business, Statistics Has
Many Important Uses


To summarize business data



To draw conclusions from business data



To make reliable forecasts about business
activities



To improve business processes


1-4

Two Different Branches Of
Statistics Are Used In Business
Statistics
The branch of mathematics that transforms data into
useful information for decision makers.

Descriptive Statistics

Inferential Statistics

Collecting, summarizing, prese
nting and analyzing data

Using data collected from a
small group to draw conclusions
about a larger group


1-5

These Two Branches Are Used
In The Important Activities


To summarize business data




To draw conclusions from business data




Inferential methods used to reach conclusions about
a large group based on data from a smaller group

To make reliable forecasts about business
activities




Descriptive methods used to create charts & tables

Inferential methods used to develop, quantify, and
improve the accuracy of predictive models

To improve business processes


Involves managerial approaches like Six Sigma


1-6

Descriptive Statistics


Collect data




Present data




e.g., Survey

e.g., Tables and graphs

Characterize data


e.g., The sample mean


1-7

Inferential Statistics


Estimation




e.g., Estimate the population
mean weight using the sample
mean weight

Hypothesis testing


e.g., Test the claim that the
population mean weight is 120
pounds

Drawing conclusions about a large group of
individuals based on a smaller group.

1-8

Basic Vocabulary of Statistics
VARIABLES
Variables are a characteristics of an item or individual and are what you
analyze when you use a statistical method.
DATA
Data are the different values associated with a variable.
OPERATIONAL DEFINITIONS
Data values are meaningless unless their variables have operational
definitions, universally accepted meanings that are clear to all associated
with an analysis.


1-9

Basic Vocabulary of Statistics
POPULATION
A population consists of all the items or individuals about which
you want to draw a conclusion. The population is the “large
group”
SAMPLE
A sample is the portion of a population selected for analysis. The
sample is the “small group”
PARAMETER
A parameter is a numerical measure that describes a characteristic
of a population.
STATISTIC
A statistic is a numerical measure that describes a characteristic of
a sample.

1-10

Population vs. Sample
Population

Measures used to describe the
population are called parameters

Sample

Measures used to describe the
sample are called statistics
1-11

Chapter Summary
In this chapter, we have
 Introduced the basic vocabulary of statistics and the
role of statistics in turning data into information to
facilitate decision making

 Examined the use of statistics to:
 Summarize data
 Draw conclusions from data
 Make reliable forecasts

 Improve business processes

 Examined descriptive vs. inferential statistics

1-12

A Step by Step Process For Examining &
Concluding From Data Is Helpful
In this book we will use DCOVA








2-13

Define the variables for which you want to reach
conclusions
Collect the data from appropriate sources
Organize the data collected by developing tables
Visualize the data by developing charts
Analyze the data by examining the appropriate
tables and charts (and in later chapters by using
other statistical methods) to reach conclusions
Copyright ©2011 Pearson
Education

Types of Variables
DCOVA


Categorical (qualitative) variables have values that
can only be placed into categories, such as “yes” and
“no.”



Numerical (quantitative) variables have values that
represent quantities.



2-14

Discrete variables arise from a counting process
Continuous variables arise from a measuring process

Education

Types of Variables
DCOVA
Variables

Categorical

Numerical

Examples:




Marital Status
Political Party
Eye Color
(Defined categories)

Discrete
Examples:



2-15

Number of Children
Defects per hour
(Counted items)

Continuous
Examples:



Weight
Voltage
(Measured characteristics)
Education

Sources of Data
DCOVA
 Primary Sources: The data collector is the one using the data
for analysis
 Data from a political survey
 Data collected from an experiment
 Observed data

 Secondary Sources: The person performing data analysis is
not the data collector
 Analyzing census data
 Examining data from print journals or data published on the internet.

2-16

Education

Sources of data fall into four
categories

DCOVA





A designed experiment



A survey



2-17

Data distributed by an organization or an
individual

An observational study
Education

Organizing Numerical Data:
Frequency Distribution Example
DCOVA


Sort raw data in ascending order:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58






Find range: 58 - 12 = 46
Select number of classes: 5 (usually between 5 and 15)
Compute class interval (width): 10 (46/5 then round up)
Determine class boundaries (limits):









2-18

Class 1:
Class 2:
Class 3:
Class 4:
Class 5:

10 to less than 20
20 to less than 30
30 to less than 40
40 to less than 50
50 to less than 60

Compute class midpoints: 15, 25, 35, 45, 55
Count observations & assign to classes
Education

Organizing Numerical Data: Frequency
Distribution Example
DCOVA
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Class

10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
Total
2-19

Midpoints

15
25
35
45
55

Frequency

3
6
5
4
2
20
Education

Organizing Numerical Data: Relative &
Percent Frequency Distribution Example
DCOVA
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Class

10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
Total
2-20

Frequency

3
6
5
4
2
20

Relative
Frequency

.15
.30
.25
.20
.10
1.00

Percentage

15
30
25
20
10
100
Education

Organizing Numerical Data: Cumulative
Frequency Distribution Example
DCOVA
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Class

Frequency Percentage

Cumulative Cumulative
Frequency Percentage

10 but less than 20

3

15%

3

15%

20 but less than 30

6

30%

9

45%

30 but less than 40

5

25%

14

70%

40 but less than 50

4

20%

18

90%

50 but less than 60

2

10%

20

100%

100

20

100%

Total
2-21

20

Education

Why Use a Frequency Distribution?
DCOVA




It allows for a quick visual interpretation of
the data



2-22

It condenses the raw data into a more
useful form

It enables the determination of the major
characteristics of the data set including
where the data are concentrated /
clustered
Education

Frequency Distributions:
Some Tips
DCOVA




Shifts in data concentration may show up when different
class boundaries are chosen



As the size of the data set increases, the impact of
alterations in the selection of class boundaries is greatly
reduced



2-23

Different class boundaries may provide different pictures for
the same data (especially for smaller data sets)

When comparing two or more groups with different sample
sizes, you must use either a relative frequency or a
percentage distribution
Education

Visualizing Categorical Data:
The Bar Chart


DCOVA

In a bar chart, a bar shows each category, the length of which
represents the amount, frequency or percentage of values falling into
a category which come from the summary table of the variable.
Banking Preference

Banking Preference?
ATM
Automated or live
telephone

%

Internet

16%
2%

Drive-through service at
branch

17%

In person at branch

41%

Internet

In person at branch
Drive-through service at branch

24%

Automated or live telephone
ATM
0%

2-24

5% 10% 15% 20% 25% 30% 35% 40% 45%
Education

Visualizing Categorical Data:
The Pie Chart
DCOVA


The pie chart is a circle broken up into slices that represent categories.
The size of each slice of the pie varies according to the percentage in
each category.
Banking Preference

Banking Preference?

%

ATM

16%
ATM

Automated or live
telephone

16%

24%
2%

2%

branch

17%

In person at branch

41%

Internet

24%

17%

Automated or live
telephone
branch
In person at branch
Internet

41%

2-25

Education

Visualizing Numerical Data:
The Histogram

DCOVA





In a histogram there are no gaps between adjacent bars.



The class boundaries (or class midpoints) are shown on the
horizontal axis.



The vertical axis is either frequency, relative frequency, or
percentage.



2-26

A vertical bar chart of the data in a frequency distribution is
called a histogram.

The height of the bars represent the frequency, relative
frequency, or percentage.
Education

The Histogram
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
Total

Frequency

3
6
5
4
2
20

(In a percentage
histogram the vertical
axis would be defined to
show the percentage of
observations per class)

Relative
Frequency

.15
.30
.25
.20
.10
1.00

Percentage
15
30
25
20
10
100

8
Histogram: Age Of Students

Frequency

Class

DCOVA

6
4

2
0
5

2-27

15 25 35 45 55 More

Education

The Polygon

DCOVA





The cumulative percentage polygon, or ogive, displays the
variable of interest along the X axis, and the cumulative
percentages along the Y axis.



2-28

A percentage polygon is formed by having the midpoint of
each class represent the data in that class and then connecting
the sequence of midpoints at their respective class
percentages.

Useful when there are two or more groups to compare.
Education

The Frequency Polygon
Class
Midpoint Frequency

Class

15
25
35
45
55

3
6
5
4
2

Frequency Polygon: Age Of Students

Frequency

10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60

(In a percentage
polygon the vertical axis
would be defined to
show the percentage of
observations per class)
2-29

DCOVA

7
6
5
4
3
2
1
0
5

15

25

35

45

55

65

Class Midpoints
Education

The Ogive (Cumulative % Polygon)
DCOVA
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60

10
20
30
40
50

(In an ogive the percentage
of the observations less
than each lower class
boundary are plotted versus
the lower class boundaries.

2-30

15
45
70
90
100

Ogive: Age Of Students
Cumulative Percentage

Class

Lower
% less
class
than lower
boundary boundary

100
80
60
40
20
0
10

20

30

40

50

60

Lower Class Boundary
Education

Visualizing Two Numerical
Variables: The Scatter Plot
DCOVA
 Scatter plots are used for numerical data consisting of paired
observations taken from two numerical variables
 One variable is measured on the vertical axis and the other
variable is measured on the horizontal axis
 Scatter plots are used to examine possible relationships
between two numerical variables

2-31

Education

Scatter Plot Example
Volume
per day

Cost per
day

23

125

146

33

160

250

140

29

Cost per Day vs. Production Volume

38

167

42

170

50

188

55

195

60

Cost per Day

26

2-32

DCOVA

200
150
100

200

50
0
20

30

40

50

60

70

Volume per Day

Education

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