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Summary Managerial Statistics
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CHAPTER 1. WHAT IS STATISTICSDescriptive statistics deals with methods of organizing, summarizing, and presenting data in a convenient
and informative way.
Two forms:
1) Graphical techniques – to make it easy to read.
2) Numerical techniques – summarize data (e.g. mean and average).
Inferential statistics is a body of methods used to draw conclusions or inferences about characteristics of
populations based on sample data.
1.1 KEY STATISTICAL CONCEPTS
Statistical inference (a conclusion reached on the basis of evidence and reasoning) problems involve
three key concepts: the population, the sample, and the statistical inference:
1) The population
- A population is the group of all items of interest to a statistics practitioner.
- In the language of statistics, population does not necessarily refer to a group of people. It may,
for example, refer to the population of ball bearings produced at a large plant.
- A descriptive measure of a population is called a parameter. In most applications of inferential
statistics the parameter represents the information we need (example, the proportion of the 5
million Florida voters who voted for Bush).
o Mean (µ)
o Standard deviation (σ)
2) The sample
- A sample is a set of data drawn from the studied population.
- A descriptive measure of a sample is called a statistic.
- A descriptive measure of a sample is called a statistic. We use statistics to make inferences
about parameters.
o Mean (ẋ)
o Standard deviation (S)
3) The statistical inference
- Statistical inference is the process of making an estimate, prediction, or decision about a
population based on sample data.
- However, such conclusions and estimates are not always going to be correct. For this reason,
we build into the statistical inference a measure of reliability.
- There are two such measures: the confidence level and the significance level.
o The confidence level is the proportion of times that an estimating procedure will be
correct.
o The significance level measures how frequently the conclusion will be wrong.
1.2 STATISTICAL APPLICATIONS IN BUSINESS
To provide sufficient background to understand the statistical application we introduce applications in
accounting, economics, finance, human resources management, marketing, and operations management.
We will provide readers with some background to these applications by describing their functions in two
ways.
1.3 LARGE REAL DATA
,Graphical depiction (video)
design
Population Sample
Describe (describtive)
Parameter Statistic
Inference
(true) (error)
(never changes) (changes)
,CHAPTER 2. GRAPHICAL DESCRIPTIVE TECHNIQUES I
In Chapter 1, we pointed out that statistics is divided into two basic areas: descriptive statistics and
inferential statistics. The purpose of this chapter, together with the next, is to present the principal methods
that fall under the heading of descriptive statistics. In this chapter, we introduce graphical and tabular
statistical methods that allow managers to summarize data visually to produce useful information that is
often used in decision making. Another class of descriptive techniques, numerical methods, is introduced in
Chapter 4.
Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that
useful information is produced. Its methods make use of graphical techniques and numerical descriptive
measures (such as averages) to summarize and present the data, allowing managers to make decisions
based on the information generated.
The two most important factors that determine the appropriate method to use are (1) the type of data and
(2) the information that is needed. Both are discussed next.
2.1 TYPES OF DATA AND INFORMATION
There are different types of data and information. To help explain this important principle, we need to define
some terms.
A variable is some characteristic of a population or sample.
- For example, the mark on a statistics exam is a characteristic of statistics exams that is
certainly of interest to readers of this book.
- We usually represent the name of the variable using uppercase letters such as X, Y, and Z.
The values of the variable are the possible observations of the variable.
- The values of statistics exam marks are the integers between 0 and 100 (assuming the exam
is marked out of 100).
Data are the observed values of a variable.
- For example, suppose that we observe the following midterm test marks of 10 students:
67 74 71 83 93 55 48 82 68 62
- These are the data from which we will extract the information we seek.
- Incidentally, data is plural for datum. The mark of one student is a datum.
- There are 3 types of data:
o Interval data are real numbers, such as heights, weights, incomes, and distances. We
also refer to this type of data as quantitative or numerical.
Values are real numbers
All calculations are valid
Data may be treated as ordinal or nominal
o Nominal data: categories are different but they have no order . For example,
responses to questions about marital status produce nominal data. The values of this
variable are single, married, divorced, and widowed. Notice that the values are not
numbers but instead are words that describe the categories. We often record nominal
data by arbitrarily assigning a number to each category. Nominal data are also called
qualitative or categorical.
single = 1, married = 2, divorced = 3, widowed = 4
Values are the arbitrary numbers that represent categories.
Only calculations based on the frequencies or percentages of occurrence are
valid.
Data may not be treated as ordinal or interval.
o Ordinal data (We can order the traits but we cannot say how much more one category
is than another) appear to be nominal, but the difference is that the order of their
values has meaning. The difference between nominal and ordinal types of data is that
the order of the values of the latter indicate a higher rating. Consequently, when
assigning codes to the values, we should maintain the order of the values. For
example, we can record the students’ evaluations as
, Poor = 1, Fair = 2, Good = 3, Very good = 4, Excellent = 5
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.
Calculations for Types of Data
Interval Data - All calculations are permitted on interval data. We often describe a set of interval data
by calculating the average.
Nominal Data - Because the codes of nominal data are completely arbitrary, we cannot perform any
calculations on these codes.
Ordinal Data - The most important aspect of ordinal data is the order of the values. As a result, the only
permissible calculations are those involving a ranking process. For example, we can place all the data in
order and select the code that lies in the middle. As we discuss in Chapter 4, this descriptive measurement
is called the median.
Hierarchy of Data
1. Interval data – because all computations are allowed.
2. Ordinal data – permissible calculations are ones that rank the data
3. Nominal data – because no calculations other than determining frequencies are permitted.
At the top of the list, we place the interval data type because virtually all computations are allowed. The
nominal data type is at the bottom because no calculations other than determining frequencies are
permitted. (We are permitted to perform calculations using the frequencies of codes, but this differs from
performing calculations on the codes themselves.) In between interval and nominal data lies the ordinal
data type. Permissible calculations are ones that rank the data.
Important to note:
- When we convert higher-level data as lower-level we lose information. For example, a mark of
83 on an accounting course exam gives far more information about the performance of that
student than does a letter grade of A, which might be the letter grade for marks between 80
and 90.
- It is also important to note that we cannot treat lower-level data types as higher-level types.
The variables whose observations constitute our data will be given the same name as the type of data.
Thus, for example, interval data are the observations of an interval variable
2.2 DESCRIBING A SET OF NOMINAL DATA
Two graphical techniques can be used to display the results shown in the table. A bar chart is often used to
display frequencies; a pie chart graphically shows relative frequencies.
Factors That Identify When to Use Frequency and Relative Frequency
Tables, Bar and Pie Charts:
1. Objective: Describe a single set of data.
2. Data type: Nominal or ordinal
There are no specific graphical techniques for ordinal data. Consequently, when we wish to describe a set
of ordinal data, we will treat the data as if they were nominal and use the techniques described in this
section. The only criterion is that the bars in bar charts should be arranged in ascending (or descending)
ordinal values; in pie charts, the wedges are typically arranged clockwise in ascending or descending order.
2.3 DESCRIBING THE RELATIONSHIP BETWEEN TWO NOMINAL VARIABLES AND COMPARING
TWO OR MORE NOMINAL DATA SETS
In Section 2.2, we presented graphical and tabular techniques used to summarize a set of nominal data.
Techniques applied to single sets of data are called univariate. There are many situations where we wish
to depict the relationship between variables; in such cases, bivariate methods are required. A cross-
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