Frequency Distributions

1
Frequency Distributions

• Organizing data in some comprehensible form so as
  to recognize trends and communicate meaningful
  information to others

2
Concepts

• What is a frequency distribution?
• What purpose does it serve?
• How would you organize the following data?

3
Frequency Distributions Tables
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Some tips about Frequency Dist Tables
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Frequency Distribution Histogram

• How would you represent this distribution
  graphically?

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Figure 2-2a (p. 44)An example of a frequency
distribution histogram. The same set of data is
presented in a frequency distribution table and
in a histogram.
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Figure 2-3 (p. 45) A frequency distribution
histogram showing the heights for a sample of n
20 adults.
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Figure 2-4 (p. 45) A frequency distribution in
which each individual is represented by a block
placed directly above the individuals score.
For example, three people had scores of X 2.
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Figure 2-5 (p. 46) An example of a frequency
distribution polygon. The same set of data is
presented in a frequency distribution table and
in a polygon. Note that these data are shown in
a histogram in Figure 2.2(a).
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Figure 2-12 (p. 51) Answers to Learning Check
Exercise 1.
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Frequency Distribution Histogram

• What if a set of data covers a wide range of
  values? What would be a practical way to
  organize such data?

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Rules for creating grouped freq dist tables
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Table 2.2 (p. 41) A grouped frequency
distribution table showing the data from Example
2.3. The original scores range from a high of X
94 to a low of X 53. This range has been
divided into 9 intervals with each interval
exactly 5 points wide. The frequency column (f)
lists the number of individuals with scores in
each of the class intervals.
14
Figure 2-15 (p. 56) A grouped frequency
distribution histogram and a stem and leaf
display showing the distribution of scores from
Table 2.3. The stem and leaf display is placed
on its side to demonstrate that the display gives
the same information provided in the histogram.
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Figure 2-6 (p. 46) An example of a frequency
distribution polygon for grouped data. The same
set of data is presented in a grouped frequency
distribution table and in a polygon. Note that
these data are shown in a histogram in Figure
2.2(b).
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Figure 2-7 (p. 47)A bar graph showing the
distribution of personality types in a sample of
college students. Because personality type is a
discrete variable measured on a nominal scale,
the graph is drawn with space between the bars.
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Figure 2-8 (p. 48)A frequency distribution
showing the relative frequency for two types of
fish. Notice that the exact number of fish is not
reported the graph simply says that there are
twice as many bluegill as there are bass.
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Cumulative Frequency, Percentiles and Percentile
Rank
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Smooth curves

• If data were collected for the entire population,
  or if samples were repeatedly drawn from a
  population over and over again and scores were
  recorded, the curve of the polygon will become
  smooth.
• This curve is called a bell-curve.
• Such a curve is assumed to be normal (i.e.,
  symmetrical distribution of scores).
• In a skewed distribution, the scores tend to
  pile up toward one end of the scale and taper off
  gradually at the other end.

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Figure 2-9 (p. 48)The population distribution
of IQ scores an example of a normal distribution.
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Figure 2-11 (p. 50) Examples of different
shapes for distributions.
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Figure 2-1 (p. 35)Hypothetical data showing the
number of humorous sentences and the number of
nonhumorous sentences recalled by participants in
a memory experiment.
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Stem-and-leaf display
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Table 2.3 (p. 56) A set of N 24 scores
presented as raw data and organized in a stem and
leaf display.
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Table 2.4 (p. 57) A stem and leaf display with
each stem split into two parts. Note that each
stem value is listed twice The first occurrence
is associated with the lower leaf values (0-4),
and the second occurrence is associated with the
upper leaf values (5-9). The data shown in this
display are taken from Table 2.3.
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Examples of interpolation
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Rules for Interpolating
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Visual Aid for Interpolation Example
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Figure 2-14 (p. 55) The graphic representation
of the process of interpolation. The same
interval is shown on two separate scales,
temperature and time. Only the endpoints of the
scales are known at 800, the temperature is
60, and at 1200, the temperature is 68.
Interpolation allows you to estimate values
within the interval by assuming that fractional
portions of one scale correspond to the same
fractional portions of the other. For example, it
is assumed that halfway through the temperature
scale corresponds to halfway through the time
scale.