Chapter 1: Definitions

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Chapter 1 Definitions

• A collection of data values forms a data set.
  Each value in the data set is called a data
  value.
• A population consists of all subjects (human or
  otherwise) that are being studied.
• A sample is a group of subjects selected from a
  population.

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• A variable is a characteristic or attribute that
  can assume different values.
• Qualitative variables are variables that can be
  placed into distinct categories, according to
  some immeasurable characteristic or attribute.
• Give examples of qualitative variables
• Quantitative variables are numerical and can be
  ordered or ranked.
• Give examples of quantitative variables

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Chapter 2 Frequency Distributions and Graphs

• 21 Introduction
• 22 Organizing Data
• 23 Histograms
• 24 Pie Chart

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2.2 Organizing Data

• To describe situations, draw conclusions, or make
  inferences about events, the researcher must
  organize the data in some meaningful way. The
  most convenient method of organizing data is to
  construct a frequency distribution.
• After organizing the data, the researcher must
  present them so they can be understood by those
  who will benefit from reading the study. The most
  useful method of presenting the data is by
  constructing statistical charts and graphs.

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• A frequency distribution is the organization of
  raw data in table form, using classes and
  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.
• Two types of frequency distributions that are
  most often used are the categorical frequency
  distribution and the grouped frequency
  distribution.

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Categorical Frequency Distributions The
categorical frequency distribution is used for
data that can be placed in specific categories,
such as nominal- or ordinal-level data. Example1
(2.2 exercise 7) A survey was taken on how
much trust people place in the information they
read on the Internet. A trust in everything
they read, M trust in most of what they read,
H trust in about half of what they read, S
trust in a small portion of what they
read. Construct a categorical frequency
distribution for the data.
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• Grouped Frequency Distributions
• When the range of the data is large, the data
  must be grouped into classes that are more than
  one unit in width.
• Example2
• Class limits Class boundaries Frequency
  Cumulative frequency
• 2430 23.530.5 3 3
• 3137 30.537.5 1 4
• 3844 37.544.5 5 9
• 4551 44.551.5 9 18
• 5258 51.558.5 6 24
• 5965 58.565.5 1 25
• The basic rule of thumb is that the class limits
  should have the same decimal place value as the
  data, but the class boundaries should have one
  additional place value and end in a 5.

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• Constructing a Grouped Frequency Distribution
• Step 1 Determine the classes.
• Find the range of the data Range highest value
  - lowest value.
• Find the width by dividing the range by the
  desired number of classes and rounding up.
• Select a starting point (usually the lowest value
  or any convenient number less than the lowest
  value) add the width to get the lower limits.
• Find the upper class limits.( lower
  limitwidth-1)
• Find the boundaries.
• Step 2 Tally the data.
• Step 3 Find the numerical frequencies from the
  tallies.
• Step 4 Find the cumulative frequencies.

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Example 3 (2.2 exercise 11) The average
quantitative GRE scores for the top 30 graduate
schools of engineering are listed below.
Construct a frequency distribution with six
classes.
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Example4 (exercise13) The ages of the signers
of the Declaration of Independence are shown
below (age is approximate since only the birth
year appeared in the source, and one has been
omitted since his birth year is unknown).
Construct a frequency distribution for the data
using seven classes.