Creating and Using Frequency Distributions

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Chapter 2

• Creating and Using Frequency Distributions

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Going Forward

• Your goals in this chapter are to learn
• What frequency is and how a frequency
  distribution is created
• When to graph frequency distributions using a bar
  graph, histogram, or polygon
• What normal, skewed, and bimodal distributions
  are
• What relative frequency and percentile are and
  how we use the area under the normal curve to
  compute them

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New Symbols and Terminology

• Raw scores are the scores we initially measure in
  a study
• The number of times a score occurs in a set of
  data is the scores frequency
• A frequency distribution organizes the scores
  based on each scores frequency

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New Symbols and Terminology

• The frequency of a score is symbolized by f
• N is the total number of scores in the data

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Understanding Frequency Distributions
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Frequency Distribution

• A frequency distribution table shows the number
  of times each score occurs in a set of data
• N is the total of all the individual frequencies
  in the f column of a frequency distribution table

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Raw Scores

• Use the following raw scores to construct a
  frequency distribution table.

14 14 13 15 11 15
13 10 12 13 14 13
14 15 17 14 14 15
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Frequency Distribution Table
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Graphing Frequency Distributions

• A frequency distribution graph always shows the
  scores on the X axis and their frequency on the Y
  axis
• The type of measurement scale (nominal, ordinal,
  interval, or ratio) determines whether we use
• A bar graph
• A histogram
• A polygon

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Frequency Bar Graph for Nominal and Ordinal Data
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Histogram for a Small Number of Different
Interval or Ratio Scores
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Frequency Polygon for Many Different Interval or
Ratio Scores
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Types of Frequency Distributions
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The Normal Distribution

• A bell-shaped curve
• Called a normal curve or a normal distribution
• Symmetrical
• The far left and right portions containing the
  relatively low-frequency, extreme high or low
  scores are called the tails of the distribution

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An Ideal Normal Distribution
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Skewed Distributions

• A skewed distribution is not symmetrical as it
  has only one pronounced tail
• A distribution may be either negatively skewed or
  positively skewed
• The direction in which the distinctive tail
  slopes indicates whether the skew is positive or
  negative

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Negatively Skewed Distribution

• A negatively
• skewed distribution contains extreme
• low scores having low frequency, but
• does not contain low-frequency, extreme high
  scores.

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Positively Skewed Distribution

• A positively
• skewed distribution
• contains extreme
• high scores having low frequency, but
• does not contain low-frequency, extreme low
  scores.

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Bimodal Distribution

• A bimodal
• distribution is a
• symmetrical
• distribution
• containing two
• distinct humps.

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Frequency Distribution Shape

• The shape of the frequency distribution is an
  important characteristic of the data
• The shape also determines which statistical
  procedures we should use

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Relative Frequency and the Normal Curve
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Relative Frequency

• Relative frequency is the proportion of the time
  a score occurs in a sample
• The formula for computing a scores relative
  frequency is
• Relative frequency

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Finding Relative Frequency Using the Normal Curve
The proportion of the total area under the normal
curve occupied by a group of scores corresponds
to the relative frequency of those scores.
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Understanding Percentile and Cumulative Frequency
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Percentile

• A percentile is the percent of all scores in the
  data located below a score
• One way to determine a scores percentile is to
  find the area under the normal curve to the left
  of the score

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Cumulative Frequency

• The cumulative frequency is the number of scores
  in the data that are at or below a particular
  score.

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Percentiles
Normal distribution showing the area under the
curve to the left of selected scores.
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Example

• Using the following data set, find the relative
  frequency and cumulative frequency of the score
  12.

14 14 13 15 11 15
13 10 12 13 14 13
14 15 17 14 14 15
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Example

• The frequency table for this set of data.

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ExampleRelative Frequency

• The frequency for the score of 12 is 1 and N 18
• Therefore, the relative frequency of 12 is

Relative Frequency
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ExampleCumulative Frequency

• There is one score at 12 and two scores below 12
  (one score of 11 and one score of 10)
• Therefore, the cumulative frequency of 12 is 3