STATISTICS

FREQUENCY DISTRIBUTIONS & GRAPHS

Vuong Ba Thinh

1

Statistics

ACKNOWLEDMENT

This slides are composed using the book:

Allan G. Bluman , Elementary Statistics: A Step by Step

Approach, eighth edition 2012.

2

Statistics

OUTLINE

Organizing Data

Histograms, Frequency Polygons, and Ogives

Other Types of Graphs

R functions

Q&A

3

Statistics

Introduction

Raw Data Organizing Data Presenting Data

Example: a study on the ages of the top 50 wealthiest people

in the world raw data

4

Statistics

Organizing Data

How?

5

Statistics

Organizing Data (1)

Frequency Distribution

A frequency distribution consists of classes and their corresponding

frequencies

Each raw data value is placed into a quantitative or qualitative

category called a class

The frequency of a class then is the number of data values contained

in a specific class

6

Statistics

Organizing Data (2)

A frequency distribution is the organization of raw data

in table form, using classes and frequencies

Two types of frequency distributions: frequency distribution,

grouped frequency distribution

7

Statistics

Organizing Data (3)

Categorical Frequency Distributions

nominal or ordinal-level data

EX: Twenty-five army inductees were given a blood test to

determine their blood type. The data set is

Construct a frequency distribution for the data.

8

Statistics

Organizing Data (4)

9

Statistics

Organizing Data (5)

Grouped Frequency Distributions

grouped frequency distribution: When the range of the

data is large, the data must be grouped into classes that are

more than one unit in width

EX: a distribution of the number of hours that boat batteries

lasted is the following

10

Statistics

Organizing Data (6)

To construct a frequency distribution, follow these rules:

There should be between 5 and 20 classes

It is preferable but not absolutely necessary that the class width be an

odd number

The classes must be mutually exclusive

The classes must be continuous

The classes must be exhaustive

The classes must be equal in width

11

Statistics

Organizing Data (7)

12

Statistics

Applying the Concepts

The data represent the ages of our Presidents at the time they

were first inaugurated.

1. Were the data obtained from a population or a sample? Explain

your answer.

2. What was the age of the oldest President?

3. What was the age of the youngest President?

4. Construct a frequency distribution for the data.

13

Statistics

Applying the Concepts (2)

5. Are there any peaks in the distribution?

6. ldentify any possible outliers.

7. Write a brief summary of the nature of the data as shown in

the frequency distribution.

14

Statistics

Histograms, Frequency Polygons, & Ogives

A picture is worth a thousand words

15

Statistics

Histograms

The histogram is a graph that displays the data by using

contiguous vertical bars (unless the frequency of a class is 0)

of various heights to represent the frequencies of the classes.

EX: Construct a histogram to represent the data shown for

the record high temperatures for each of the 50 states

16

Statistics

Frequency Polygons

The frequency polygon is a graph that displays the data by

using lines that connect points plotted for the frequencies at

the midpoints of the classes. The frequencies are represented

by the heights of the points.

EX:

17

Statistics

Ogives

The ogive is a graph that represents the cumulative

frequencies for the classes in a frequency distribution.

Cumulative frequency graphs are used to visually represent

how many values are below a certain upper class boundary.

EX:

18

Statistics

19

Statistics

Relative Frequency Graphs

20

Statistics

Other Types of Graphs

Bar graph, Pareto chart, time series graph, and pie graph.

A bar graph represents the data by using vertical or

horizontal bars whose heights or lengths represent the

frequencies of the data.

21

Statistics

Other Types of Graphs (2)

A Pareto chart is used to represent a frequency distribution

for a categorical variable, and the frequencies are displayed

by the heights of vertical bars, which are arranged in order

from highest to lowest.

EX: Number of Homeless

22

Statistics

Other Types of Graphs (3)

A time series graph represents data that occur over a

specific period of time.

EX: Workplace Homicides

23

Statistics

Other Types of Graphs (4)

A pie graph is a circle that is divided into sections

according to the percentage of frequencies in each category

of the distribution.

EX: blood types of the army inductees

24

Statistics

Misleading Graphs

25

Statistics

FREQUENCY DISTRIBUTIONS & GRAPHS

Vuong Ba Thinh

1

Statistics

ACKNOWLEDMENT

This slides are composed using the book:

Allan G. Bluman , Elementary Statistics: A Step by Step

Approach, eighth edition 2012.

2

Statistics

OUTLINE

Organizing Data

Histograms, Frequency Polygons, and Ogives

Other Types of Graphs

R functions

Q&A

3

Statistics

Introduction

Raw Data Organizing Data Presenting Data

Example: a study on the ages of the top 50 wealthiest people

in the world raw data

4

Statistics

Organizing Data

How?

5

Statistics

Organizing Data (1)

Frequency Distribution

A frequency distribution consists of classes and their corresponding

frequencies

Each raw data value is placed into a quantitative or qualitative

category called a class

The frequency of a class then is the number of data values contained

in a specific class

6

Statistics

Organizing Data (2)

A frequency distribution is the organization of raw data

in table form, using classes and frequencies

Two types of frequency distributions: frequency distribution,

grouped frequency distribution

7

Statistics

Organizing Data (3)

Categorical Frequency Distributions

nominal or ordinal-level data

EX: Twenty-five army inductees were given a blood test to

determine their blood type. The data set is

Construct a frequency distribution for the data.

8

Statistics

Organizing Data (4)

9

Statistics

Organizing Data (5)

Grouped Frequency Distributions

grouped frequency distribution: When the range of the

data is large, the data must be grouped into classes that are

more than one unit in width

EX: a distribution of the number of hours that boat batteries

lasted is the following

10

Statistics

Organizing Data (6)

To construct a frequency distribution, follow these rules:

There should be between 5 and 20 classes

It is preferable but not absolutely necessary that the class width be an

odd number

The classes must be mutually exclusive

The classes must be continuous

The classes must be exhaustive

The classes must be equal in width

11

Statistics

Organizing Data (7)

12

Statistics

Applying the Concepts

The data represent the ages of our Presidents at the time they

were first inaugurated.

1. Were the data obtained from a population or a sample? Explain

your answer.

2. What was the age of the oldest President?

3. What was the age of the youngest President?

4. Construct a frequency distribution for the data.

13

Statistics

Applying the Concepts (2)

5. Are there any peaks in the distribution?

6. ldentify any possible outliers.

7. Write a brief summary of the nature of the data as shown in

the frequency distribution.

14

Statistics

Histograms, Frequency Polygons, & Ogives

A picture is worth a thousand words

15

Statistics

Histograms

The histogram is a graph that displays the data by using

contiguous vertical bars (unless the frequency of a class is 0)

of various heights to represent the frequencies of the classes.

EX: Construct a histogram to represent the data shown for

the record high temperatures for each of the 50 states

16

Statistics

Frequency Polygons

The frequency polygon is a graph that displays the data by

using lines that connect points plotted for the frequencies at

the midpoints of the classes. The frequencies are represented

by the heights of the points.

EX:

17

Statistics

Ogives

The ogive is a graph that represents the cumulative

frequencies for the classes in a frequency distribution.

Cumulative frequency graphs are used to visually represent

how many values are below a certain upper class boundary.

EX:

18

Statistics

19

Statistics

Relative Frequency Graphs

20

Statistics

Other Types of Graphs

Bar graph, Pareto chart, time series graph, and pie graph.

A bar graph represents the data by using vertical or

horizontal bars whose heights or lengths represent the

frequencies of the data.

21

Statistics

Other Types of Graphs (2)

A Pareto chart is used to represent a frequency distribution

for a categorical variable, and the frequencies are displayed

by the heights of vertical bars, which are arranged in order

from highest to lowest.

EX: Number of Homeless

22

Statistics

Other Types of Graphs (3)

A time series graph represents data that occur over a

specific period of time.

EX: Workplace Homicides

23

Statistics

Other Types of Graphs (4)

A pie graph is a circle that is divided into sections

according to the percentage of frequencies in each category

of the distribution.

EX: blood types of the army inductees

24

Statistics

Misleading Graphs

25

Statistics

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