Organization and description of data

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Chapter 2

• Organization and description of data

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Box on Page 24Describing a Data Set of
Measurements
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Types of data

• Qualitative or categorical data
• Numerical or measurement data
• We will use the term numerical-valued variable or
  just variable to refer to a characteristic that
  is measured on a numerical scale.
• Two type of variables
• Discrete
• Continuous

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Categorical data
Each observation is recorded as a member of one
of several categories. Data are organized in the
form of a frequency table that shows the
frequencies of the individual categories. Further
proportions of observations in each category are
calculated
An example in the next.
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Figure 2.1 (p. 26)Pie chart of student opinion
on change in dormitory regulations.
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Discrete data
The underlying scale is discrete and the distinct
values observed are not too numerous. As in case
of categorical data describe the data by
relative frequencies. Example
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Example (cont.)
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Figure 2.4 (p. 29)Graphic display of the
frequency distribution of data in Table 3.
Line Diagrams and Histograms
The distinct values of the variable are located
on the horizontal axis. Draw a vertical rectangle
(line) at each value and make the height equal to
the relative frequency.
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Figure 2.5 (p. 30)Dot diagram for the heart
transplant data.
Data on a continuous variable

• For small data set a dot diagram can be used
  individual measurements are plotted above a line
  as prominent dots.
• Example

• The second method is frequency distribution on
  intervals used when the data consist of a large
  number of measurements.

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Box on Page 30Constructing a Frequency
Distribution for a Continuous Variable
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Table 2.4 (p. 32)The Data of Forty Cash
Register Receipts (in Dollars) at a University
Bookstore
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Table 2.5 (p. 33)Frequency Distribution for
Bookstore Sales Data
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Presenting a frequency distribution as a
histogram

• Mark the class intervals on a horizontal axis
• On each interval draw a vertical rectangle
  whose area represents the relative frequency
• Height of the rectangle Relative frequency /
  width of interval
• The total are of a histogram is 1.

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Figure 2.7 (p. 34)Histogram of the bookstore
sales data of Tables 4 and 5. Sample size 40.
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Figure 2.8 (p. 35)Population tree (histograms)
of the male and female age distributions in the
US in 2001. (Source US Bureau of the Census.)
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Table 2.6 (p. 35)Examination Scores of 50
Students
A stem-and-leaf display provides a more efficient
variant of the histogram for displaying data
especially when the observations are two-digit
numbers. Example
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Table 2.7 (p. 35)Stem-and-Leaf Display for the
Examination Scores