Transcript Doing Statistics for Business

Doing Statistics for Business
Data, Inference, and Decision Making
Marilyn K. Pelosi
Theresa M. Sandifer
Chapter 2
The Language of
Statistics
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Chapter 2 Objectives
 Difference Between the Population & a
Sample of the Population
 Difference Between a Parameter & a
Statistic
 Factors that Influence Sample Size: Some
Sampling & Sample Size Considerations
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Chapter 2 Objectives (con’t)
 Selecting the Sample
 Types of Data
 The Difference Between Descriptive &
Inferential Statistics
 Ethical Issues in Data Analysis
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Chapter 2 Objectives (con’t)
 Communicating the Results
 Basic Summation Notation
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The Population is everything you wish to
study.
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A Variable is used to represent a characteristic
of each member of the population.
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The In-line Skate Company
Identifying Possible Variables to Study
There have been a number of failures on the braking device of a
new model of roller blades that your company manufactures.
What is the population of interest?
Name two variables or characteristics that you might wish to study.
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Figure 2.1 The Population and a Sample
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A Census is a study of the entire population.
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Sampling Error is the difference between
a characteristic of the entire population and a
sample of that population.
The amount of Variation refers to how
different the members of the population are
from each other with regard to the variable
being studied.
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Discovery Exercise 2.1
Introduction to Sampling &
Variability
Suppose that each set of data in this exercise represents an entire
population. Since we don’t yet have a way to quantify the amount of
variability in a population, the data sets are labeled as having a small
amount of variability or a large amount of variability. The first data set
shows the number of people in 50 families living in a small college
town in New England. The second set of data shows the number of
people in 50 families living in a large city in the South.
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DISCOVERY EXERCISE 2.1
New England Families: Large Amount of Variability
Average number of people in 50 families: 4.32
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DISCOVERY EXERCISE 2.1
Southern Families: Small Amount of Variability
Average number of people in 50 families: 4.44
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A Parameter is a number which describes a
characteristic of the population.
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A Statistic is a number that describes a
characteristic of a sample.
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The Size of the Population is the number of
members of the population. It will be referred
to as N.
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Fig 2.2 Bigger & Bigger Samples
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The Size of the Sample will be referred to as
n.
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A Biased Sample is a sample which does not
fairly represent the population.
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Stress Relief
Identifying Possible Biases in a Sample
You are studying the methods that students at your school use to relieve
stress. You decide to use your statistics class as your sample.
Why might this be a biased sample?
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A Simple Random Sample is a sample that
has been selected in such a way that all
members of the population have an equal
chance of being picked.
In addition, every sample of size n has the same
chance of becoming our sample.
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A Sampling Frame is a list of all members of
the population.
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A Table of Random Numbers is a table that
consists of numbers randomly generated and
listed in the order in which they were generated.
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Row
#
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Column #
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094632795
033413186
297556368
472960570
256883707
711501513
653475420
658953044
785645638
716249997
537971597
289063704
738968017
574817322
378236162
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562758635
485441982
414437050
817883255
467694224
410398128
460744361
296126017
976076280
193707682
182794408
328703833
075254187
843373358
380141891
Figure 2.3 Portion of a Table of Random Numbers
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The Glue Company
Selecting A Simple Random Sample
Select a sample of 5 tubes of glue for the glue company. You can
assume that each tube of glue has a 5-digit ID number, which the
company uses to track its inventory.
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Discovery Exercise 2.2
Introduction to Sampling
Suppose the data shown below represent an entire population. They show
the number of people in 50 families living in a small college town in New
England. (If you did Discovery Exercise 2.1 then you will recognize this
as the same data set.) Now a 2-digit ID number has also been included.
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Discovery Exercise 2.2
New England Families: Large Amount of Variability
Average number of people in 50 families: 4.32
ID: 01
0 ID: 02
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ID: 03
5 ID: 04
7 ID: 05
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ID: 06
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ID: 08
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ID: 11
4 ID: 12
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9 ID: 14
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ID: 16
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ID: 21
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ID: 23
3 ID: 24
1 ID: 25
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ID: 26
1 ID: 27
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ID: 28
5 ID: 29
0 ID: 30
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ID: 31
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ID: 33
8 ID: 34
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ID: 46
1 ID: 47
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8 ID: 49
0 ID: 50
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Qualitative Data describe a particular
characteristic of a sample item. They are
most often non-numerical in nature.
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Dress Down Day
Possible Qualitative Variables
The company considering the dress down day tries this policy out
with a sample of employees. After the policy has been in effect for some
time, the company decides to measure the change in productivity for the
employees. It appears that for some employees productivity has
increased, while for others it has decreased. What qualitative data might
have been collected to help the company understand the differences
observed?
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Data that are created by assigning numbers to
different categories when the numbers have no
real meaning are called Nominal Data.
Data that are created by assigning numbers to
categories where the order of assignment has
meaning are called Ordinal Data.
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Discrete Data are data that can take on only
certain values. These values are often integers
or whole numbers.
Continuous Data are data that can take on any
one of an infinite number of possible values over
an interval on the number line. These values are
most often the result of measurement.
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Tools of Descriptive Statistics allow you to
summarize the data.
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An Inference is a deduction of a conclusion.
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Fig 2.4 Pie Chart
Fig 2.4 Bar Chart
PIE CHART
A
20%
E
25%
BAR CHART
30
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10%
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Inferential Statistics
Probability
Figure 2.5 Relationship between
probability and inferential statistics
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The Techniques of Inferential Statistics allow
us to draw inferences or conclusions about the
population from the sample.
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We will use Probability theory to calculate the
likelihood of observing or selecting a particular
sample from a population.
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Sigma Notation is shorthand notation used to
write formulas. It is so named because it uses
the Greek capital letter sigma, written as .
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The Mail-Order Company
Using Sigma Notation
A mail-order company wants some information on the daily demand
for a product that has been heavily advertised. The company looks at the
orders for an 8-day period and obtains the following data:
Demand
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Use the sigma notation to write down the expression which means to add
up all the data values.
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The Mail-Order Company
Using Sigma Notation to Sum Differences
A mail-order company wants some information on the daily demand
for a product that has been heavily advertised. The company looks at the
orders for an 8-day period and obtains the following data:
Demand
31
28
29
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30
31
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30
Use the sigma notation to write down the expression that means to add
up all the differences between the data values and the number 30.
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Selecting a Sample in Excel
1. From the Tools menu, select Data Analysis.
2. Scroll down the Analysis Tools list and select Sampling.
You must tell Excel three things to obtain the sample: (!)
the location of the population, (2) the type of sampling
method and the number of samples, and (3) where you
want the sample placed.
3. Position the cursor in the box labeled Input Range and
then highlight the range in the worksheet that contains the
data. Since the first row of the population is a title, ID
Codes, check the box marked Labels.
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Selecting a Sample in Excel (con’t)
4. In the section labeled Sampling Method, click the radio
button for the Random sampling methods and type “5” in
the text box for Number of Samples:.
5. In the section labeled Output Options, you can specify
that the sample be located in a section of the current
worksheet, a new worksheet in the same workbook, or a
new workbook.
6. Click OK; the random sample of 5 ID codes will appear in
the location you specified.
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Figure 2.7
Data Analysis Dialogue Box
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Figure 2.8
Sampling Dialogue Box
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Figure 2.9
Completed Sampling Dialogue Box
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Figure 2.10
Random Sample of 5 ID Codes
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Chapter 2 Summary
In this chapter you have learned:
 The basic language of statistics.
 A Population is the complete group you wish to
study.
 A Variable is a characteristic of each member of
the population.
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Chapter 2 Summary (con’t)
 There are two types of variables:
Quantitative
Qualitative
 A Sample is a piece of the population.
 Sampling Error is the difference between the
behavior of the entire population and a sample of
that population.
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Chapter 2 Summary (con’t)
 It is important that a sample is a fair representation
of the entire population or an Unbiased Sample.
 A Simple Random Sample is a sample that has
been selected in such a way that all members of
the population have an equal chance of being
picked.
 You can select a select a Simple Random Sample
by using a Table of Random Numbers or Excel.
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Chapter 2 Summary (con’t)
 Sigma Notation is the shorthand notation used to
write equations throughout the remainder of the
book.
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