Transcript Table 2.7 (p. 35)

Chapter 2
Organization and
description of data
Box on Page 24
Describing a Data Set of Measurements
Types of data
1. Qualitative or categorical data
2. 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
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 slide.
Figure 2.1 (p. 26)
Pie chart of student opinion on change in dormitory regulations.
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:
Example (cont.):
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.
Figure 2.4 (p. 29)
Graphic display of the frequency distribution of data in Table 3.
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:
Figure 2.5 (p. 30)
Dot diagram for the heart transplant data.
• The second method is frequency distribution on intervals;
used when the data consist of a large number of
measurements.
Box on Page 30
Constructing a Frequency Distribution for a Continuous Variable
Table 2.4 (p. 32)
The Data of Forty Cash Register Receipts (in Dollars) at a University Bookstore
Table 2.5 (p. 33)
Frequency Distribution for Bookstore Sales Data
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.
Figure 2.7 (p. 34)
Histogram of the bookstore sales data of Tables 4 and 5. Sample size = 40.
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.)
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:
Table 2.6 (p. 35)
Examination Scores of 50 Students
Table 2.7 (p. 35)
Stem-and-Leaf Display for the Examination Scores