Download First week

Probability and Statistics
Frequency table and graphs
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Dr. Saeid Moloudzadeh
www.soran.edu.iq
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Contents
Descriptive Statistics
Axioms of Probability
Combinatorial Methods
Conditional Probability and
Independence
Distribution Functions and
Discrete Random Variables
Special Discrete Distributions
Continuous Random Variables
Special Continuous Distributions
Bivariate Distributions
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Probability and Statistics
Contents
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Descriptive Statistics
Axioms of Probability
Combinatorial Methods
Conditional Probability and Independence
Distribution Functions and Discrete Random Variables
Special Discrete Distributions
Continuous Random Variables
Special Continuous Distributions
Bivariate Distributions
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Chapter 0: Descriptive Statistics
0.1
0.2
0.3
0.4
Contents
Fundamental Concepts
Frequency table and graphs
Measures of center
Measures of variation
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Chapter 0: Descriptive Statistics
0.1
0.2
0.3
0.4
Contents
Fundamental Concepts
Frequency table and graphs
Measures of center
Measures of variation
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Section 2: Frequency table and graphs
0.2.1 Ordinary frequency table
The information in a discrete data set can be
summarized in a frequency table, or frequency
distribution that includes frequency, relative
frequencies, cumulative frequency and cumulative
relative frequency.
The number of observations that fall into particular
class of the quantitative variable is called the
frequency of that class. A table listing all classes and
their frequencies is called a frequency distribution.
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Section 2: Frequency table and graphs
In addition of the frequencies, we are often
interested in the percentage of a class. We find the
percentage by dividing the frequency of the class by
the total number of observations and multiplying
the result by 100. The percentage of the class,
expressed as a decimal, is usually referred to as the
relative frequency of the class.
A table listing all classes and their relative frequencies is
called a relative frequency distribution
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Section 2: Frequency table and graphs
A cumulative frequency (cumulative relative
frequency) is obtained by summing the
frequencies (relative frequencies) of all classes
up to the specific class.
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Section 2: Frequency table and graphs
Example 0.3: The following data represent the
number of days of sick leave taken by each of 50
workers of a given company over the last 6
weeks:
2, 2, 0, 0, 5, 8, 3, 4, 1, 0, 0, 7, 1, 7, 1, 5, 4, 0, 4, 0, 1, 8, 9, 7, 0,
1, 7, 2, 5, 5, 4, 3, 3, 0, 0, 2, 5, 1, 3, 0, 1, 0, 2, 4, 5, 0, 5, 7, 5, 1
Summarizing data in a frequency table.
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
0.2.2 Line Graphs, Bar Graphs and Frequency Polygons
Data from a frequency table can be graphically pictured
by a line graph, which plots the successive values on
the horizontal axis and indicates the corresponding
frequency by the height of a vertical line. A line graph
for the data of example 1-2-1 is shown in the
following figure.
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
Sometimes the frequencies are represented not
by lines but rather by bars having some
thickness. These graphs, called bar graphs, are
often utilized. Following figure presents a bar
graph for the data of the example 1-2-1.
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
Another type of graph used to represent a
frequency table is the frequency polygon,
which plots the frequencies of the different
data values and then connects the plotted
points with straight lines. Following figure
presents the frequency polygon of the data of
the example 1-2-1.
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
A polygon plot of these relative frequencies is
presented in the following figure. A plot of the
relative frequencies looks exactly like a plot of
the absolute frequencies, except that the labels
on the vertical axis are the old labels divided by
the total number of observations in the data set.
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
0.2.3 Frequency distribution for grouped data
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
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Section 2: Frequency table and graphs
0.2.4 frequency histogram
A bar graph plot of the data, with the bars placed
adjacent to each other, is called a histogram. The
vertical axis of a histogram can represent either
the class frequency or the relative class
frequency. In the former case, the histogram is
called a frequency histogram and in the latter a
relative frequency histogram. The following figure
presents a frequency histogram of the data of the
example 1-3-1.
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Section 2: Frequency table and graphs
To Construct a Histogram from a Data Set
1. Arrange the data in increasing order.
2. Choose class intervals so that all data points
are covered.
3. Construct a frequency table.
4. Draw adjacent bars having heights
determined by the frequencies in step 3.
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Section 2: Frequency table and graphs
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Frequency
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0
0-47.5
47.5-52.5
52.5-57.5
57.5-62.5
62.5-67.5
67.5-72.5
72.5-77.5
Weight
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