Business statistics

Business Statistics (BUSA 3101)
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help! Applications in Business and Economics
 Data
 Data Sources
 Descriptive Statistics
 Statistical Inference
 Computers and
Statistical Analysis

Accounting
 Auditing
 Costing
Finance
 Financial trends
 Forecasting
Management
 Describe employees
 Quality improvement
Marketing
 Consumer preferences
 Marketing mix effects

 Accounting
 Economics
Public accounting firms use statistical
sampling procedures when conducting
audits for their clients.
Economists use statistical information
in making forecasts about the future of
the economy or some aspect of it.

Applications in
Business and Economics
A variety of statistical quality
control charts are used to monitor
the output of a production process.
 Production
Electronic point-of-sale scanners at
retail checkout counters are used to
collect data for a variety of marketing
research applications.
 Marketing

Applications in
Business and Economics
Financial advisors use price-earnings ratios and
dividend yields to guide their investment
recommendations.
 Finance

 Obtain input to a research study
 Measure performance
 Assist in formulating decision alternatives
 Satisfy curiosity
 Knowledge for the sake of knowledge

 Data are the facts and figures collected,
summarized,
analyzed, and interpreted.
 The data collected in a particular study are referred
to as the data set.

 The elements are the entities on which data are
collected.
 A variable is a characteristic of interest for the elements.
 The set of measurements collected for a particular
element is called an observation.
 The total number of data values in a data set is the
number of elements multiplied by the number of
variables.
Elements, Variables, and Observations

Stock Annual Earn/
Exchange Sales($M) Share($)
Data, Data Sets,
Elements, Variables, and Observations
Company
Dataram
EnergySouth
Keystone
LandCare
Psychemedics
AMEX 73.10 0.86
OTC 74.00 1.67
NYSE 365.70 0.86
NYSE 111.40 0.33
AMEX 17.60 0.13
Variables
Element
Names
Data Set

The scale indicates the data summarization and
statistical analyses that are most appropriate.
The scale determines the amount of information
contained in the data.
Scales of measurement include:
Nominal
Ordinal
Interval
Ratio

 Nominal
A nonnumeric label or numeric code may be used.
Data are labels or names used to identify an
attribute of the element.

Example:
Students of a university are classified by the
school in which they are enrolled using a
nonnumeric label such as Business, Humanities,
Education, and so on.
Alternatively, a numeric code could be used for
the school variable (e.g. 1 denotes Business,
2 denotes Humanities, 3 denotes Education, and
so on).
Scales of Measurement
 Nominal

 Ordinal
A nonnumeric label or numeric code may be used.
The data have the properties of nominal data and
the order or rank of the data is meaningful.

 Ordinal
Example:
Students of a university are classified by their
class standing using a nonnumeric label such as
Freshman, Sophomore, Junior, or Senior.
Alternatively, a numeric code could be used for
the class standing variable (e.g. 1 denotes
Freshman, 2 denotes Sophomore, and so on).

 Interval
Interval data are always numeric.
The data have the properties of ordinal data, and
the interval between observations is expressed in
terms of a fixed unit of measure.

 Interval
Example:
Melissa has an SAT score of 1205, while Kevin
has an SAT score of 1090. Melissa scored 115
points more than Kevin.

 Ratio
The data have all the properties of interval data
and the ratio of two values is meaningful.
Variables such as distance, height, weight, and time
use the ratio scale.
This scale must contain a zero value that indicates
that nothing exists for the variable at the zero point.

 Ratio
Example:
Melissa’s college record shows 36 credit hours
earned, while Kevin’s record shows 72 credit
hours earned. Kevin has twice as many credit
hours earned as Melissa.

Data
Numerical
(Quantitative)
Categorical
(Qualitative)
Discrete Continuous

Data can be further classified as being qualitative
or quantitative.
The statistical analysis that is appropriate depends
on whether the data for the variable are qualitative
or quantitative.
In general, there are more alternatives for statistical
analysis when the data are quantitative.
Qualitative and Quantitative Data

Labels or names used to identify an attribute of each
element
Often referred to as categorical data
Use either the nominal or ordinal scale of
measurement
Can be either numeric or nonnumeric
Appropriate statistical analyses are rather limited

Quantitative Data
Quantitative data indicate how many or how much:
discrete, if measuring how many
continuous, if measuring how much
Quantitative data are always numeric.
Ordinary arithmetic operations are meaningful for
quantitative data.

Scales of Measurement
Qualitative Quantitative
Numerical NumericalNon-numerical
Data
Nominal Ordinal Nominal Ordinal Interval Ratio

Cross-Sectional Data
Cross-sectional data are collected at the same or
approximately the same point in time.
Example: data detailing the number of building
permits issued in June 2003 in each of the counties
of Ohio

Time Series Data
Time series data are collected over several time
periods.
Example: data detailing the number of building
permits issued in Lucas County, Ohio in each of
the last 36 months

Data
Sources
Primary Secondary
Experiment Published
(& On-Line)
Survey Observation

 Existing Sources
Within a firm – almost any department
Business database services – Dow Jones & Co.
Government agencies - U.S. Department of Labor
Industry associations – Travel Industry Association
of America
Special-interest organizations – Graduate Management
Admission Council
Internet – more and more firms

 Statistical Studies
In experimental studies the variables of interest
are first identified. Then one or more factors are
controlled so that data can be obtained about how
the factors influence the variables.
In observational (non-experimental) studies no
attempt is made to control or influence the
variables of interest.
a survey is a
good example

Time Requirement
Cost of Acquisition
Data Errors
• Searching for information can be time consuming.
• Information may no longer be useful by the time it
is available.
• Organizations often charge for information even
when it is not their primary business activity.
• Using any data that happens to be available or
that were acquired with little care can lead to poor
and misleading information.

 Collecting data
 e.g., Survey
 Presenting data
 e.g., Charts & tables
 Characterizing data
 e.g., Average
Data
Analysis
Decision-
Making
Why?

Statistical
Methods
Descriptive
Statistics
Inferential
Statistics

 Descriptive statistics are the tabular,
graphical, and numerical methods used to
summarize data.
Descriptive Statistics:
These are statistical
methods used to
describe data that
have been collected.

Example: Hudson Auto Repair
The manager of Hudson Auto
would like to have a better
understanding of the cost
of parts used in the engine
tune-ups performed in the
shop. She examines 50
customer invoices for tune-ups. The costs of parts,
rounded to the nearest dollar, are listed on the next
slide.

91 78 93 57 75 52 99 80 97 62
71 69 72 89 66 75 79 75 72 76
104 74 62 68 97 105 77 65 80 109
85 97 88 68 83 68 71 69 67 74
62 82 98 101 79 105 79 69 62 73
Example: Hudson Auto Repair
 Sample of Parts Cost for 50 Tune-ups

50-59
60-69
70-79
80-89
90-99
100-109
2
13
16
7
7
5
50
4
26
32
14
14
10
100
(2/50)100
Parts
Cost ($)
Parts
Frequency
Percent
Frequency

2
4
6
8
10
12
14
16
18
Parts
Cost ($)
Frequency
50-59 60-69 70-79 80-89 90-99 100-110
Tune-up Parts Cost

 Hudson’s average cost of parts, based on the 50
tune-ups studied, is $79 (found by summing the
50 cost values and then dividing by 50).
 The most common numerical descriptive statistic
is the average (or mean).

 Involves
 Estimation
 Hypothesis
testing
 Purpose
 Make decisions about
population
characteristics
Population?
Inferential Statistics: These are
statistical methods used to find out
something about population based
on a sample.

Statistical Inference
Population
Sample
Statistical inference
Census
Sample survey
- the set of all elements of interest in a
particular study
- a subset of the population
- the process of using data obtained
from a sample to make estimates
and test hypotheses about the
characteristics of a population
- collecting data for a population
- collecting data for a sample

1. Population
consists of all
tune-ups. Average
cost of parts is
unknown.
2. A sample of 50
engine tune-ups
is examined.
3. The sample data
provide a sample
average parts cost
of $79 per tune-up.
4. The sample average
is used to estimate the
population average.

 Statistical analysis typically involves working with
large amounts of data.
 Computer software is typically used to conduct the
analysis.
 Frequently the data that is to be analyzed resides in a
spreadsheet.
 Modern spreadsheet packages are capable of data
management, analysis, and presentation.
 MS Excel is the most widely available spreadsheet
software in business organizations.

Statistical Analysis Using Microsoft Excel
 3 tasks might be needed:
• Enter Data
• Enter Functions and Formulas
• Apply Tools
A
1
Parts
Cost
2 91
3 71
4 104
5 85
6 62
7 78
8 69
D E
Mean =AVERAGE(A2:A71)
Median =MEDIAN(A2:A71)
Mode =MODE(A2:A71)
Range =MAX(A2:A71)-MIN(A2:A71)

 Excel Worksheet (showing data)
Note: Rows 10-51 are not shown.
A B C D
1 Customer Invoice #
Parts
Cost ($)
Labor
Cost ($)
2 Sam Abrams 20994 91 185
3 Mary Gagnon 21003 71 205
4 Ted Dunn 21010 104 192
5 ABC Appliances 21094 85 178
6 Harry Morgan 21116 62 242
7 Sara Morehead 21155 78 148
8 Vista Travel, Inc. 21172 69 165
9 John Williams 21198 74 190

 Excel Formula Worksheet
Note: Columns A-B and rows 10-51 are not shown.
C D E F G
1
Parts
Cost ($)
Labor
Cost ($)
2 91 185 Average Parts Cost =AVERAGE(C2:C51)
3 71 205
4 104 192
5 85 178
6 62 242
7 78 148
8 69 165
9 74 190

 Excel Value Worksheet
Note: Columns A-B and rows 10-51 are not shown.
C D E F G
1
Parts
Cost ($)
Labor
Cost ($)
2 91 185 Average Parts Cost 79
3 71 205
4 104 192
5 85 178
6 62 242
7 78 148
8 69 165
9 74 190

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Business statistics

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