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Презентация на тему Organizing data graphical and nabular descriptive techniques

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Learning ObjectivesOverall: To give students a basic understanding of best way of presentation of dataSpecific: Students will be able to Understand Types of data Draw TablesDraw GraphsMake Frequency distribution………….
2.Organizing Data Graphical and Tabular Descriptive TechniquesNumerical/Quantitative Data Qualitative/Categorical DataGraphical Presentation of Learning ObjectivesOverall: To give students a basic understanding of best way of 2.Descriptive statistics involves arranging, summarizing, and presenting a set of data in DATA MININGMost companies routinely collect data – at the cash register for DATA MINING is a collection of methods for obtaining useful knowledge by 1. Marketing and sales: companies have lots of information about past contacts Finance: Mining of financial data can be useful in forming and evaluating Statistical methods, such as hypothesis testing, are helpful as part of data 3. Product design: What particular combinations of features are customers ordering 4. Production 	Imagine a factory running 24/7 with thousands of partially completed 5. Fraud detections:Fraud can affect many areas of business, including YOU once received a telephone call from your credit card company asking Data mining is a large task that involves combining resources from many Statistics: All of the basic activities of statistics are involved: a design Some specialized statistical methods are particularly useful, including classification analysis (also called Computer science: Efficient algorithms (computer instructions) are needed for collecting, maintaining, organizing, Optimization:These methods help you achieve a goal, which might be very specific Alternatively, the goal might be more vague such as obtaining a better  WHAT IS PROBABILITY?Probability is a what if tool for understanding risk and You might learn, for example, that an international project has only an Here are additional examples of situations where finding the appropriate answer requires 3. What are the chances that a foreign country (where you have Probability is the inverse of statistics. Whereas statistics helps you go from Probability also works together with statistics by providing a solid foundation for 2.Definitions…A variable [Typically called a “random” variable since we do not know 2.We Deal with “2” Types of DataNumerical/Quantitative Data [Real Numbers]:	* height	* weight	* 2.Quantitative/Numerical Data…Quantitative Data is further broken down intoContinuous Data – Data can 2.Qualitative/Categorical DataNominal Data [has no natural order to the values]. 	E.g. responses 2.Graphical & Tabular Techniques for Nominal Data…The only allowable calculation on nominal 2.Nominal Data (Tabular Summary) - 2.Nominal Data (Frequency)Bar Charts are often used to display frequencies…Is there a 2.Nominal Data (Relative Frequency)Pie Charts show relative frequencies… Frequency DistributionsDefinitionA frequency distribution for qualitative data lists all categories and the Example 2.2A sample of 30 employees from large companies was selected, and Example 2.2Construct a frequency distribution table for these data. Solution 2.2Table 2.2 Frequency Distribution of Stress on Job Relative Frequency and Percentage DistributionsCalculating Relative Frequency of a Category Relative Frequency and Percentage Distributions cont.Calculating PercentagePercentage = = (Relative frequency) · 100 Example 2.3Determine the relative frequency and percentage for the data in Table 2.4. Solution 2-2Table 2.3 Relative Frequency and Percentage Distributions of Stress on Job Graphical Presentation of Qualitative Data	DefinitionA graph made of bars whose heights represent Figure 2.2 Bar graph for the frequency distribution of Table 2.3 Graphical Presentation of Qualitative Data cont.	DefinitionA circle divided into portions that represent Table 2.4 Calculating Angle Sizes for the Pie Chart Figure 2.4 Pie chart for the percentage distribution of Table 2.5. ORGANIZING AND GRAPHING QUANTITATIVE DATAFrequency DistributionsConstructing Frequency Distribution TablesRelative and Percentage DistributionsGraphing Grouped DataHistogramsPolygons Frequency DistributionsTable 2.7 Weekly Earnings of 100 Employees of a CompanyVariable Third Frequency Distributions cont.Definition A frequency distribution for quantitative data lists all the Essential Question :How do we construct a frequency distribution table? Process of Constructing a Frequency Table STEP 1: Determine the range. R STEP 2. Determine the tentative number of classes (k)k = 1 + STEP 3. Find the class width by dividing the range by the STEP 4. Write the classes or categories starting with the lowest score. STEP 5. Determine the frequency for each class by referring to the When constructing frequency tables, the following guidelines should be followed.The classes must 3. All classes should have the same width, although it is sometimes Let’s Try!!! Time magazine collected information on all 464 people who died 19		18	 30 	 40 	 41 33 	73 	2523 	25 	 21 Determine the range.R = Highest Value – Lowest ValueR = 76 – 16 = 60 Determine the tentative number of classes (K).   K = 1 Find the class width (c).* Round – off the quotient if the decimal part exceeds 0. Write the classes starting with lowest score. Using Table:What is the lower class limit of the highest class? Upper Example Table 2.9 gives the total home runs hit by all players Table 2.9 Home Runs Hit by Major League Baseball Teams During the 2012 Season Solution 2-3Now we round this approximate width to a convenient number – say, 22. Solution 2-3The lower limit of the first class can be taken as Table 2.10 Frequency Distribution for the Data of Table 2.9 Relative Frequency and Percentage DistributionsRelative Frequency and Percentage Distributions Example 2-4Calculate the relative frequencies and percentages for Table 2.10 Solution 2-4Table 2.11 Relative Frequency and Percentage Distributions for Table 2.10 Graphing Grouped DataDefinitionA histogram is a graph in which classes are marked Figure 2.3 Frequency histogram for Table 2.10.124 - 145146 - 167168 - Figure 2.4 Relative frequency histogram for Table 2.10.124 - 145146 - 167168 Graphing Grouped Data cont.DefinitionA graph formed by joining the midpoints of the Figure 2.5 Frequency polygon for Table 2.10.124 - 145146 - 167168 - Figure 2.6 Frequency Distribution curve    Frequencyx Example 2-5The following data give the average travel time from home to Example 2-5  Construct a frequency distribution table. Calculate the relative frequencies Solution 2-5 Solution 2-5Table 2.12 Frequency, Relative Frequency, and Percentage Example 2-6   The administration in a large city wanted to Solution 2-6Table 2.13 Frequency Distribution of Vehicles Owned Figure 2.7 Bar graph for Table 2.13. OgiveThe ogive is a graph that represents the cumulative frequencies for the Ogive 2.Patterns of Scatter Diagrams…Linearity and Direction are two concepts we are interested
Слайды презентации

Слайд 2 Learning Objectives
Overall: To give students a basic understanding

Learning ObjectivesOverall: To give students a basic understanding of best way

of best way of presentation of data
Specific: Students will

be able to
Understand Types of data
Draw Tables
Draw Graphs
Make Frequency distribution………….

Слайд 3 2.
Descriptive statistics involves arranging, summarizing, and presenting a

2.Descriptive statistics involves arranging, summarizing, and presenting a set of data

set of data in such a way that useful

information is produced.






Descriptive statistics make use of graphical techniques and numerical techniques (such as averages) to summarize and present the data.

Data

Statistics

Information


Слайд 4 DATA MINING
Most companies routinely collect data – at

DATA MININGMost companies routinely collect data – at the cash register

the cash register for each purchase, on the factory

floor from each step of production, or on the Internet from each visit to its website – resulting in huge databases containing potentially useful information about how to increase sales, how to improve production, or how to turn mouse clicks into purchases.

Слайд 5 DATA MINING is a collection of methods for

DATA MINING is a collection of methods for obtaining useful knowledge

obtaining useful knowledge by analyzing large amounts of data,

often by searching for hidden patterns. Once a business has collected information for some purpose, it would be wasteful to leave it unexplored when it might be useful in many other ways. The goal of data mining is to obtain value from these vast stores of data, in order to improve the company with higher sales, lower costs, and better products. Here are just a few of the many areas of business in which data mining can be helpful:


Слайд 6 1. Marketing and sales: companies have lots of

1. Marketing and sales: companies have lots of information about past

information about past contacts with potential customers and their

results. These data can be mined for guidance on how (and when) to better reach customers in the future. One example is the difficult decision of when a store should reduce prices: reduce too soon and you lose money (on items that might have been sold for more); reduce too late and you may be stuck (with items no longer in season).

Слайд 7 Finance: Mining of financial data can be useful

Finance: Mining of financial data can be useful in forming and

in forming and evaluating investment strategies and in hedging

(or reducing) risk. In the stock markets alone, there are many companies: about 3,298 listed on the New York Stock Exchange and about 2,942 companies listed on the NASDAQ Stock Market. Historical information on price and volume (number of shares traded) is easily available to anyone interested in exploring investment strategies.


Слайд 8 Statistical methods, such as hypothesis testing, are helpful

Statistical methods, such as hypothesis testing, are helpful as part of

as part of data mining distinguish random from systematic

behavior because stock that performed well last year will not necessarily perform well next year. Imagine that you toss 100 coins six times each and then carefully choose the one that came up “heads” all six times – this coin is not as special as it might seem!

Слайд 9 3. Product design: What particular combinations of

3. Product design: What particular combinations of features are customers

features are customers ordering in larger-than-expected quantities? The answers

could help you create products to appeal to a group of potential customers who would not take the trouble to place special orders.


Слайд 10 4. Production
Imagine a factory running 24/7 with

4. Production 	Imagine a factory running 24/7 with thousands of partially

thousands of partially completed units, each with its bar

code, being carefully tracked by the computer system, with efficiency and quality being recorder as well. This is a tremendous source of information that can tell you about the kinds of situations that cause trouble (such as finding a machine that needs adjustment by noticing clusters of units that don’t work) or the kinds of situations that lead to extra-fast production of the highest quality.

Слайд 11 5. Fraud detections:
Fraud can affect many

5. Fraud detections:Fraud can affect many areas of business, including

areas of business, including consumer finance, insurance, and networks

(including telephone and the Internet). One of the best methods of protection involves mining data to distinguish between ordinary and fraudulent patterns of usage, then using the results to classify new transactions, and looking carefully at suspicious new occurrences to decide where or not fraud is actually involved.


Слайд 12 YOU once received a telephone call from your

YOU once received a telephone call from your credit card company

credit card company asking you to verify recent transactions

– identified by its statistical analysis – that departed from your typical pattern of spending. One fraud risk identification system that helps detect fraudulent use of credit card is Falcon Fraud Manager from Fair Isaac, which uses the flexible “neural network” data-mining technique

Слайд 13
Data mining is a large task that involves

Data mining is a large task that involves combining resources from

combining resources from many fields. Here is how statistics,

computer science, and optimization are used in data mining.


Слайд 14 Statistics: All of the basic activities of statistics

Statistics: All of the basic activities of statistics are involved: a

are involved: a design for collecting the data, exploring

for patterns, a modeling framework, estimation of features, and hypothesis testing to assess significance of patterns as a “reality check” on the results. Nearly every method in the rest of this lectures has the potential to be useful in data mining, depending on the database and the needs of the company.


Слайд 15 Some specialized statistical methods are particularly useful, including

Some specialized statistical methods are particularly useful, including classification analysis (also

classification analysis (also called discriminant analysis) to assign a

new case to a category (such as “likely purchaser” or “fraudulent”), cluster analysis to identify homogeneous group of individuals, and prediction analysis (also called regression analysis).

Слайд 16 Computer science: Efficient algorithms (computer instructions) are needed

Computer science: Efficient algorithms (computer instructions) are needed for collecting, maintaining,

for collecting, maintaining, organizing, and analyzing data. Creative methods

involving artificial intelligence are useful, including machine learning techniques for prediction analysis such as neural networks and boosting, to learn from the data by identifying useful patterns automatically. Some of these methods from computer science are closely related to statistical prediction analysis.


Слайд 17 Optimization:
These methods help you achieve a goal, which

Optimization:These methods help you achieve a goal, which might be very

might be very specific such as maximizing profits, lowering

production cost, finding new customers, developing profitable new product models, or increasing sales volume.

Слайд 18 Alternatively, the goal might be more vague such

Alternatively, the goal might be more vague such as obtaining a

as obtaining a better understanding of the different types

of customers you serve, characterizing the differences in production quality that occur under different circumstances, or identifying relationships that occur more or less consistently throughout the data. Optimization is often accomplished by adjusting the parameters of a model until the objective is achieved.

Слайд 19  WHAT IS PROBABILITY?
Probability is a what if tool

 WHAT IS PROBABILITY?Probability is a what if tool for understanding risk

for understanding risk and uncertainty. Probability shows you the

likelihood, or chances, for each of the various potential future events, based on a set of assumptions about how the world works. For example, you might assume that you know basically how the world works (i.e., all of the details of process that will produce success or failure or payoffs in between). Probabilities of various outcomes would then be computed for each of several strategies to indicate how successful each strategy would be.

Слайд 20 You might learn, for example, that an international

You might learn, for example, that an international project has only

project has only an 8% chance of success (i.e.

the probability of success is 0.08), but if you assume that the government can keep inflation low, then the chance of success rises to 35% - still very risky, but a much better situation than the 8% chance. Probability will not tell you whether to invest in the project, but it will help you keep your eyes open to the realities of the situation.

Слайд 21 Here are additional examples of situations where finding

Here are additional examples of situations where finding the appropriate answer

the appropriate answer requires computing or estimating a probability

number:
Given the nature of an investment portfolio and a set of assumptions that describe how financial markets work, what are the chances that you will profit over a one-year horizon?
What are the chances of rain tomorrow? What are the chances that next winter will be cold enough so that your heating-oil business will make a profit?



Слайд 22 3. What are the chances that a foreign

3. What are the chances that a foreign country (where you

country (where you have a manufacturing plant) will become

involved in civil war over the next two years?
4. What are the chances that the college student you just interviewed for a job will become a valued employee over the coming months?

Слайд 23 Probability is the inverse of statistics. Whereas statistics

Probability is the inverse of statistics. Whereas statistics helps you go

helps you go from observed data to generalizations about

how the world works, probability goes the other direction: if you assume you know how the world works, then you can figure out what kinds of data you are likely to see and the likelihood for each.


Слайд 24 Probability also works together with statistics by providing

Probability also works together with statistics by providing a solid foundation

a solid foundation for statistical inference. When there is

uncertainty, you cannot know exactly what will happen, and there is some chance of error. Using probability, you will learn ways to control the error rate so that it is, say, less than 5% or less than 1% of the time.


Слайд 26 2.
Definitions…
A variable [Typically called a “random” variable since

2.Definitions…A variable [Typically called a “random” variable since we do not

we do not know it’s value until we observe

it] is some characteristic of a population or sample.
E.g. student grades, weight of a potato, # heads in 10 flips of a coin, etc.
Typically denoted with a capital letter: X, Y, Z…
The values of the variable are the range of possible values for a variable.
E.g. student marks (0..100)
Data are the observed values of a random variable.
E.g. student marks: {67, 74, 71, 83, 93, 55, 48}

Слайд 27 2.
We Deal with “2” Types of Data
Numerical/Quantitative Data

2.We Deal with “2” Types of DataNumerical/Quantitative Data [Real Numbers]:	* height	*

[Real Numbers]:
* height
* weight
* temperature
Qualitative/Categorical Data [Labels rather

than numbers]:
* favorite color
* Gender
* SES



Слайд 28 2.
Quantitative/Numerical Data…
Quantitative Data is further broken down into
Continuous

2.Quantitative/Numerical Data…Quantitative Data is further broken down intoContinuous Data – Data

Data – Data can be any real number within

a given range. Normally measurement data [weights, Age, Prices, etc]
Discrete Data – Data can only be very specific values which we can list. Normally count data [# of firecrackers in a package of 100 that fail to pop, # of accidents on the UTA campus each week, etc]


Слайд 29 2.
Qualitative/Categorical Data
Nominal Data [has no natural order to

2.Qualitative/Categorical DataNominal Data [has no natural order to the values]. 	E.g.

the values].
E.g. responses to questions about marital status:

Single = 1, Married = 2, Divorced = 3, Widowed = 4
Arithmetic operations don’t make any sense (e.g. does Widowed ÷ 2 = Married?!)
Ordinal Data [values have a natural order]:
E.g. College course rating system: poor = 1, fair = 2, good = 3, very good = 4, excellent = 5

Слайд 30 2.
Graphical & Tabular Techniques for Nominal Data…
The only

2.Graphical & Tabular Techniques for Nominal Data…The only allowable calculation on

allowable calculation on nominal data is to count the

frequency of each value of the variable.
We can summarize the data in a table that presents the categories and their counts called a frequency distribution.
A relative frequency distribution lists the categories and the proportion with which each occurs.
Since Nominal data has no order, if we arrange the outcomes from the most frequently occurring to the least frequently occurring, we call this a “pareto chart”


Слайд 31 2.
Nominal Data (Tabular Summary) -

2.Nominal Data (Tabular Summary) -

Слайд 32 2.
Nominal Data (Frequency)
Bar Charts are often used to

2.Nominal Data (Frequency)Bar Charts are often used to display frequencies…Is there

display frequencies…
Is there a better way to order these?

Would Bar Chart
look different if we plotted “relative frequency” rather than “frequency”?


Слайд 33 2.
Nominal Data (Relative Frequency)
Pie Charts show relative frequencies…

2.Nominal Data (Relative Frequency)Pie Charts show relative frequencies…

Слайд 34 Frequency Distributions
Definition
A frequency distribution for qualitative data lists

Frequency DistributionsDefinitionA frequency distribution for qualitative data lists all categories and

all categories and the number of elements that belong

to each of the categories.

Слайд 35 Example 2.2
A sample of 30 employees from large

Example 2.2A sample of 30 employees from large companies was selected,

companies was selected, and these employees were asked how

stressful their jobs were. The responses of these employees are recorded next where very represents very stressful, somewhat means somewhat stressful, and none stands for not stressful at all.

Слайд 36 Example 2.2
Construct a frequency distribution table for these

Example 2.2Construct a frequency distribution table for these data.

data.


Слайд 37 Solution 2.2
Table 2.2 Frequency Distribution of Stress on

Solution 2.2Table 2.2 Frequency Distribution of Stress on Job

Слайд 38 Relative Frequency and Percentage Distributions
Calculating Relative Frequency of

Relative Frequency and Percentage DistributionsCalculating Relative Frequency of a Category

a Category


Слайд 39 Relative Frequency and Percentage Distributions cont.
Calculating Percentage

Percentage =

Relative Frequency and Percentage Distributions cont.Calculating PercentagePercentage = = (Relative frequency) · 100


= (Relative frequency) · 100


Слайд 40 Example 2.3
Determine the relative frequency and percentage for

Example 2.3Determine the relative frequency and percentage for the data in Table 2.4.

the data in Table 2.4.


Слайд 41 Solution 2-2
Table 2.3 Relative Frequency and Percentage Distributions

Solution 2-2Table 2.3 Relative Frequency and Percentage Distributions of Stress on Job

of Stress on Job


Слайд 42 Graphical Presentation of Qualitative Data
Definition
A graph made of

Graphical Presentation of Qualitative Data	DefinitionA graph made of bars whose heights

bars whose heights represent the frequencies of respective categories

is called a bar graph.

Слайд 43 Figure 2.2 Bar graph for the frequency distribution

Figure 2.2 Bar graph for the frequency distribution of Table 2.3

of Table 2.3


Слайд 44 Graphical Presentation of Qualitative Data cont.
Definition
A circle divided

Graphical Presentation of Qualitative Data cont.	DefinitionA circle divided into portions that

into portions that represent the relative frequencies or percentages

of a population or a sample belonging to different categories is called a pie chart.

Слайд 45 Table 2.4 Calculating Angle Sizes for the Pie

Table 2.4 Calculating Angle Sizes for the Pie Chart

Chart


Слайд 46 Figure 2.4 Pie chart for the percentage distribution

Figure 2.4 Pie chart for the percentage distribution of Table 2.5.

of Table 2.5.


Слайд 47 ORGANIZING AND GRAPHING QUANTITATIVE DATA
Frequency Distributions
Constructing Frequency Distribution

ORGANIZING AND GRAPHING QUANTITATIVE DATAFrequency DistributionsConstructing Frequency Distribution TablesRelative and Percentage DistributionsGraphing Grouped DataHistogramsPolygons

Tables
Relative and Percentage Distributions
Graphing Grouped Data
Histograms
Polygons


Слайд 48 Frequency Distributions




Table 2.7 Weekly Earnings of 100 Employees

Frequency DistributionsTable 2.7 Weekly Earnings of 100 Employees of a CompanyVariable

of a Company
Variable
Third class
Lower limit of the sixth

class


Upper limit of the sixth class

Frequency of the third class

Frequency column


Слайд 49 Frequency Distributions cont.
Definition
A frequency distribution for quantitative

Frequency Distributions cont.Definition A frequency distribution for quantitative data lists all

data lists all the classes and the number of

values that belong to each class. Data presented in the form of a frequency distribution are called grouped data.

Слайд 50 Essential Question :
How do we construct a frequency

Essential Question :How do we construct a frequency distribution table?

distribution table?


Слайд 51 Process of Constructing a Frequency Table
STEP 1:

Process of Constructing a Frequency Table STEP 1: Determine the range.

Determine the range.

R = Highest Value – Lowest

Value

Слайд 52 STEP 2. Determine the tentative number of classes

STEP 2. Determine the tentative number of classes (k)k = 1

(k)

k = 1 + 3.322 log N

Always round

– off

Note: The number of classes should be between 5 and 20. The actual number of classes may be affected by convenience or other subjective factors

Слайд 53 STEP 3. Find the class width by dividing

STEP 3. Find the class width by dividing the range by

the range by the number of classes.






(Always round –

off )



Слайд 54 STEP 4. Write the classes or categories starting

STEP 4. Write the classes or categories starting with the lowest

with the lowest score. Stop when the class already

includes the highest score.

Add the class width to the starting point to get the second lower class limit. Add the class width to the second lower class limit to get the third, and so on. List the lower class limits in a vertical column and enter the upper class limits, which can be easily identified at this stage.

Слайд 55 STEP 5. Determine the frequency for each class

STEP 5. Determine the frequency for each class by referring to

by referring to the tally columns and present the

results in a table.

Слайд 56 When constructing frequency tables, the following guidelines should

When constructing frequency tables, the following guidelines should be followed.The classes

be followed.
The classes must be mutually exclusive. That is,

each score must belong to exactly one class.
Include all classes, even if the frequency might be zero.

Слайд 57 3. All classes should have the same width,

3. All classes should have the same width, although it is

although it is sometimes impossible to avoid open –

ended intervals such as “65 years or older”.

4. The number of classes should be between 5 and 20.



Слайд 58 Let’s Try!!!
Time magazine collected information on all

Let’s Try!!! Time magazine collected information on all 464 people who

464 people who died from gunfire in the Philippines

during one week. Here are the ages of 50 men randomly selected from that population. Construct a frequency distribution table.

Слайд 59 19 18 30 40 41 33 73

19		18	 30 	 40 	 41 33 	73 	2523 	25

25
23 25 21 33 65 17 20 76
47 69

20 31 18 24 35 24
17 36 65 70 22 25 65 16
24 29 42 37 26 46 27 63
21 27 23 25 71 37 75 25
27 23

Слайд 60 Determine the range.
R = Highest Value – Lowest

Determine the range.R = Highest Value – Lowest ValueR = 76 – 16 = 60

Value
R = 76 – 16 = 60


Слайд 61 Determine the tentative number of classes (K).

Determine the tentative number of classes (K).  K = 1

K = 1 + 3. 322 log N

= 1 + 3.322 log 50
= 1 + 3.322 (1.69897) = 6.64
*Round – off the result to the next integer if the decimal part exceeds 0.
K = 7

Слайд 62 Find the class width (c).





* Round – off

Find the class width (c).* Round – off the quotient if the decimal part exceeds 0.

the quotient if the decimal part exceeds 0.



Слайд 63 Write the classes starting with lowest score.

Write the classes starting with lowest score.

Слайд 64 Using Table:
What is the lower class limit of

Using Table:What is the lower class limit of the highest class?

the highest class?
Upper class limit of the lowest

class?
Find the class mark of the class 43 – 51.
What is the frequency of the class 16 – 24?

Слайд 66 Example
Table 2.9 gives the total home runs

Example Table 2.9 gives the total home runs hit by all

hit by all players of each of the 30

Major League Baseball teams during the 2012 season. Construct a frequency distribution table.

Слайд 67 Table 2.9 Home Runs Hit by Major League

Table 2.9 Home Runs Hit by Major League Baseball Teams During the 2012 Season

Baseball Teams During the 2012 Season


Слайд 68 Solution 2-3
Now we round this approximate width to

Solution 2-3Now we round this approximate width to a convenient number – say, 22.

a convenient number – say, 22.


Слайд 69 Solution 2-3
The lower limit of the first class

Solution 2-3The lower limit of the first class can be taken

can be taken as 124 or any number less

than 124. Suppose we take 124 as the lower limit of the first class. Then our classes will be
124 – 145, 146 – 167, 168 – 189, 190 – 211, and 212 - 233


Слайд 70 Table 2.10 Frequency Distribution for the Data of

Table 2.10 Frequency Distribution for the Data of Table 2.9

Table 2.9


Слайд 71 Relative Frequency and Percentage Distributions
Relative Frequency and Percentage

Relative Frequency and Percentage DistributionsRelative Frequency and Percentage Distributions

Distributions


Слайд 72 Example 2-4
Calculate the relative frequencies and percentages for

Example 2-4Calculate the relative frequencies and percentages for Table 2.10

Table 2.10


Слайд 73 Solution 2-4
Table 2.11 Relative Frequency and Percentage Distributions

Solution 2-4Table 2.11 Relative Frequency and Percentage Distributions for Table 2.10

for Table 2.10


Слайд 74 Graphing Grouped Data
Definition
A histogram is a graph in

Graphing Grouped DataDefinitionA histogram is a graph in which classes are

which classes are marked on the horizontal axis and

the frequencies, relative frequencies, or percentages are marked on the vertical axis. The frequencies, relative frequencies, or percentages are represented by the heights of the bars. In a histogram, the bars are drawn adjacent to each other.

Слайд 75 Figure 2.3 Frequency histogram for Table 2.10.
124 -

Figure 2.3 Frequency histogram for Table 2.10.124 - 145146 - 167168

145
146 - 167
168 - 189
190 - 211
212 - 233
Total

home runs

15
12
9
6
3
0

Frequency


Слайд 76 Figure 2.4 Relative frequency histogram for Table 2.10.
124

Figure 2.4 Relative frequency histogram for Table 2.10.124 - 145146 -

- 145
146 - 167
168 - 189
190 - 211
212 -

233

Total home runs

.50
.40
.30
.20
.10
0

Relative Frequency


Слайд 77 Graphing Grouped Data cont.
Definition
A graph formed by joining

Graphing Grouped Data cont.DefinitionA graph formed by joining the midpoints of

the midpoints of the tops of successive bars in

a histogram with straight lines is called a polygon.

Слайд 78 Figure 2.5 Frequency polygon for Table 2.10.
124 -

Figure 2.5 Frequency polygon for Table 2.10.124 - 145146 - 167168

145
146 - 167
168 - 189
190 - 211
212 - 233
15
12
9
6
3
0
Frequency



Слайд 79 Figure 2.6 Frequency Distribution curve

Figure 2.6 Frequency Distribution curve  Frequencyx

Frequency
x


Слайд 80 Example 2-5
The following data give the average travel

Example 2-5The following data give the average travel time from home

time from home to work (in minutes) for 50

states. The data are based on a sample survey of 700,000 households conducted by the Census Bureau (USA TODAY, August 6, 2013).

Слайд 81 Example 2-5

Construct a frequency distribution table.

Example 2-5 Construct a frequency distribution table. Calculate the relative frequencies

Calculate the relative frequencies and percentages for all classes.



Слайд 82 Solution 2-5

Solution 2-5

Слайд 83 Solution 2-5
Table 2.12 Frequency, Relative Frequency, and Percentage

Solution 2-5Table 2.12 Frequency, Relative Frequency, and Percentage

Distributions of Average

Travel Time to Work

Слайд 84 Example 2-6
The administration in a

Example 2-6  The administration in a large city wanted to

large city wanted to know the distribution of vehicles

owned by households in that city. A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned:
5 1 1 2 0 1 1 2 1 1
1 3 3 0 2 5 1 2 3 4
2 1 2 2 1 2 2 1 1 1
4 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data, and draw a bar graph.

Слайд 85 Solution 2-6
Table 2.13 Frequency Distribution of Vehicles Owned

Solution 2-6Table 2.13 Frequency Distribution of Vehicles Owned

Слайд 86 Figure 2.7 Bar graph for Table 2.13.

Figure 2.7 Bar graph for Table 2.13.

Слайд 87 Ogive
The ogive is a graph that represents the

OgiveThe ogive is a graph that represents the cumulative frequencies for

cumulative frequencies for the classes in a frequency distribution
Step

1. Find the cumulative frequency for each class.
Step 2. Draw the x and y axes. Label the x-axis with the class boundaries.
Step 3. Plot the cumulative frequency at each upper class boundary.

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