Ch. 2: The Art of Presenting Data
Data in raw form are usually not easy to use for decision
making. Some type of organization is needed
• Table and Graph
•Techniques reviewed here:
– Quantitative Data:
• Ordered Array
• Stem-and-Leaf Display
• Frequency and Cumulative Distributions -- Histograms,
Polygons, and Ogives
– Qualitative (categorical) Data
• Bar charts and pie charts
• Contingency tables
The Art of Presentation, Con’t
• The Ordered Array – Sort data from min. to
max.
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Provides some signals about variability within the range
May help identify outliers (unusual observations)
If the data set is large, the ordered array is less useful.
Then, we need a simple way to see the distribution
details of the data set.
Stem-and-Leaf Diagram
•METHOD: Separate the sorted data series into leading digits
(the stem) and the trailing digits (the leaves)
•Example:
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What are the values of the 1st and the 8th observations?
What the Minimum, maximum values?
Are values concentrated?
What is the range?
•What if the data set is too large even for stem-and- leaf
display?
Frequency Distributions
What is a Frequency Distribution?
• A frequency distribution is a way to condense data
into a more useful form. It allows for for a quick
visual interpretation of the data.
• A frequency distribution is a a table or graph
containing nonoverlapping class groupings
(categories or ranges within which the data fall) and
the corresponding frequencies with which data fall
within each grouping or category
How to Built a Frequency Distribution, Table
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Sort raw data in ascending order
Find the range
Select number of desired classes
Create class grouping (intervals) of the same width
Determine the width of each interval by
range
Width of int erval 
number of desired class groupings
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Use at least 5 but no more than 15 groupings
Round up the interval width to get desirable boundaries
Compute class midpoints
Count observations and assign to classes
How to Built a Frequency Distribution,
Graphs
• A graph of the data in a frequency distribution is called a
histogram
• The class boundaries, Bins, (or class midpoints) are
shown on the horizontal axis
• the vertical axis is either frequency, relative frequency,
or percentage
• Bars of the appropriate heights are used to represent the
number of observations within each class
• A graph of the height of frequencies at midpoint values is
called Polygon– good for comparing two or more
distributions
• A graph of Cumulative Frequencies is called Ogive
Presentation of Qualitative Data
• One variable:
– Bar charts and Pie charts -- are often used for
qualitative (category) data. Height of bar or size of pie
slice shows the frequency or percentage for each
category
– Pareto Diagram – are used to portray categorical data –
See page 71.
• It is a bar chart, where categories are shown in descending order of
frequency
• A cumulative polygon is often shown in the same graph
• Used to separate the “vital few” from the “trivial many”
Presentation of Qualitative Data
• Two or More Variables:
Multivariate Categorical Data can be presented by a
Contingency Table.
– Individual values could be expressed as absolute
values, percentages of the overall total, percentages of
the row totals, or percentages of the column totals
Scatter Diagram
Scatter Diagrams are used for bivariate
numerical (quantitative) data
–Bivariate data consists 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
–This is a graph of the relationship between two
variables and does not necessarily means
causality