# Giao trinh bai tap statistics 1

STATISTICS
FREQUENCY DISTRIBUTIONS & GRAPHS
Vuong Ba Thinh

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ACKNOWLEDMENT
 This slides are composed using the book:

Allan G. Bluman , Elementary Statistics: A Step by Step
Approach, eighth edition 2012.

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OUTLINE

 Organizing Data
 Histograms, Frequency Polygons, and Ogives
 Other Types of Graphs

 R functions
 Q&A

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Introduction
 Raw Data  Organizing Data  Presenting Data
 Example: a study on the ages of the top 50 wealthiest people

in the world  raw data

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Organizing Data
 How?

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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

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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

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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.

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Organizing Data (4)

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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

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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

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Organizing Data (7)

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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
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.
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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.

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Histograms, Frequency Polygons, & Ogives
 A picture is worth a thousand words

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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

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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:

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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:

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Relative Frequency Graphs

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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.

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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

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Other Types of Graphs (3)
 A time series graph represents data that occur over a

specific period of time.
 EX: Workplace Homicides

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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

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