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Copyright ©2011 Pearson Education 1-11-11-1
Introduction
Copyright ©2011 Pearson Education 1-21-21-2
Learning Objectives
In this chapter you learn:
How business uses statistics
The basic vocabulary of statistics
How to use Microsoft Excel with this book
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Why Learn Statistics
Make better sense of the world
Internet articles / reports
Magazine articles
Newspaper articles
Television & radio reports
Make better business decisions
Business memos
Business research
Technical journals
Technical reports
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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
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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
Collecting, summarizing, presenting and analyzing data
Inferential Statistics
Using data collected from a small group to draw conclusions about a larger group
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These Two Branches Are Used In The Important Activities
To summarize business data Descriptive methods used to create charts & tables
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 Inferential methods used to develop, quantify, and
improve the accuracy of predictive models To improve business processes
Involves managerial approaches like Six Sigma
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Descriptive Statistics
Collect data e.g., Survey
Present data e.g., Tables and graphs
Characterize data e.g., The sample mean
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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.
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Basic Vocabulary of Statistics
VARIABLESVariables are a characteristics of an item or individual and are what you analyze when you use a statistical method.
DATAData are the different values associated with a variable.
OPERATIONAL DEFINITIONSData values are meaningless unless their variables have operational definitions, universally accepted meanings that are clear to all associated with an analysis.
Copyright ©2011 Pearson Education 1-101-101-10
Basic Vocabulary of Statistics
POPULATIONA population consists of all the items or individuals about which you want to draw a conclusion. The population is the “large group”
SAMPLEA sample is the portion of a population selected for analysis. The sample is the “small group”
PARAMETERA parameter is a numerical measure that describes a characteristic of a population.
STATISTICA statistic is a numerical measure that describes a characteristic of a sample.
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Population vs. Sample
Population Sample
Measures used to describe the population are called parameters
Measures used to describe the sample are called statistics
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Chapter Summary
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
In this chapter, we have
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A Step by Step Process For Examining & Concluding From Data Is Helpful
In this book we will use DCOVA
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
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Types of Variables
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. Discrete variables arise from a counting process Continuous variables arise from a measuring process
DCOVA
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Types of Variables
Variables
Categorical Numerical
Discrete Continuous
Examples:
Marital Status Political Party Eye Color (Defined categories) Examples:
Number of Children Defects per hour (Counted items)
Examples:
Weight Voltage (Measured characteristics)
DCOVA
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Sources of Data
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.
DCOVA
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Sources of data fall into four categories
Data distributed by an organization or an individual
A designed experiment
A survey
An observational study
DCOVA
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Organizing Numerical Data: Frequency Distribution Example
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):
Class 1: 10 to less than 20 Class 2: 20 to less than 30 Class 3: 30 to less than 40 Class 4: 40 to less than 50 Class 5: 50 to less than 60
Compute class midpoints: 15, 25, 35, 45, 55 Count observations & assign to classes
DCOVA
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Organizing Numerical Data: Frequency Distribution Example
Class Midpoints Frequency
10 but less than 20 15 320 but less than 30 25 630 but less than 40 35 5 40 but less than 50 45 450 but less than 60 55 2 Total 20
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
DCOVA
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Organizing Numerical Data: Relative & Percent Frequency Distribution Example
Class Frequency
10 but less than 20 3 .15 1520 but less than 30 6 .30 3030 but less than 40 5 .25 25 40 but less than 50 4 .20 2050 but less than 60 2 .10 10 Total 20 1.00 100
RelativeFrequency Percentage
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
DCOVA
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Organizing Numerical Data: Cumulative Frequency Distribution Example
Class
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%
Total 20 100 20 100%
Percentage Cumulative Percentage
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
FrequencyCumulative Frequency
DCOVA
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Why Use a Frequency Distribution?
It condenses the raw data into a more useful form
It allows for a quick visual interpretation of the data
It enables the determination of the major characteristics of the data set including where the data are concentrated / clustered
DCOVA
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Frequency Distributions:Some Tips
Different class boundaries may provide different pictures for the same data (especially for smaller data sets)
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
When comparing two or more groups with different sample sizes, you must use either a relative frequency or a percentage distribution
DCOVA
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Visualizing Categorical Data: The Bar Chart
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
0% 5% 10% 15% 20% 25% 30% 35% 40% 45%
ATM
Automated or live telephone
Drive-through service at branch
In person at branch
Internet
DCOVA
Banking Preference? %
ATM 16%
Automated or live telephone
2%
Drive-through service at branch
17%
In person at branch 41%
Internet 24%
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Visualizing Categorical Data: The Pie Chart
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
16%
2%
17%
41%
24%
ATM
Automated or livetelephone
Drive-through service atbranch
In person at branch
Internet
DCOVA
Banking Preference? %
ATM 16%
Automated or live telephone
2%
Drive-through service at branch
17%
In person at branch 41%
Internet 24%
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Visualizing Numerical Data: The Histogram
A vertical bar chart of the data in a frequency distribution is called a histogram.
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.
The height of the bars represent the frequency, relative frequency, or percentage.
DCOVA
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Visualizing Numerical Data: The Histogram
Class Frequency
10 but less than 20 3 .15 1520 but less than 30 6 .30 3030 but less than 40 5 .25 25 40 but less than 50 4 .20 2050 but less than 60 2 .10 10 Total 20 1.00 100
RelativeFrequency Percentage
0
2
4
6
8
5 15 25 35 45 55 More
Fre
qu
en
cy
Histogram: Age Of Students
(In a percentage histogram the vertical axis would be defined to show the percentage of observations per class)
DCOVA
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Visualizing Numerical Data: The Polygon
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.
The cumulative percentage polygon, or ogive, displays the variable of interest along the X axis, and the cumulative percentages along the Y axis.
Useful when there are two or more groups to compare.
DCOVA
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01234567
5 15 25 35 45 55 65
Fre
que
ncy
Frequency Polygon: Age Of Students
Visualizing Numerical Data: The Frequency Polygon
Class Midpoints
Class
10 but less than 20 15 320 but less than 30 25 630 but less than 40 35 540 but less than 50 45 450 but less than 60 55 2
FrequencyClass
Midpoint
(In a percentage polygon the vertical axis would be defined to show the percentage of observations per class)
DCOVA
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Visualizing Numerical Data: The Ogive (Cumulative % Polygon)
Class
10 but less than 20 10 1520 but less than 30 20 4530 but less than 40 30 7040 but less than 50 40 9050 but less than 60 50 100
% lessthan lowerboundary
Lower class
boundary
020406080
100
10 20 30 40 50 60
Cum
ulat
ive
Perc
enta
ge
Ogive: Age Of Students
Lower Class Boundary
(In an ogive the percentage of the observations less than each lower class boundary are plotted versus the lower class boundaries.
DCOVA
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Visualizing Two Numerical Variables: The Scatter Plot
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
DCOVA
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Scatter Plot Example
Volume per day
Cost per day
23 125
26 140
29 146
33 160
38 167
42 170
50 188
55 195
60 200
Cost per Day vs. Production Volume
0
50
100
150
200
250
20 30 40 50 60 70
Volume per Day
Cost
per
Day
DCOVA