Descriptive Statistics, Part Two

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Descriptive Statistics, Part Two

• Farrokh Alemi, Ph.D.
• Kashif Haqqi, M.D.

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Table of Content

• Objectives
• Frequency distribution
• Categorical
• Ungrouped
• Grouped

• Histogram
• Cumulative frequency
• Pie chart
• Bar chart

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Objectives

• Given a set of nominal or ordinal data, interpret
  its frequency distribution, pie chart, and bar
  chart.
• Given a set of numerical data, interpret its
  frequency distribution, cumulative frequency
  distribution, and histogram.
• Given a set of numerical data, interpret the
  meaning of its range, variance, standard
  deviation, and coefficient of variation.

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Organizing Data

• Data when collected in original form is called
  raw data.
• For example

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Frequency Distribution

• The researches organizes the raw data by using
  frequency distribution.
• The frequency is the number of values in a
  specific class of data.
• A frequency distribution is the organizing of raw
  data in table form, using classes and frequencies.

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Frequency Distribution Cont.

• For the first data set, a frequency distribution
  is shown as follow

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Types of Frequency Distribution

• There are three basic types of frequency
  distribution
• Categorical
• Ungrouped
• Grouped

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Categorical Frequency Distribution

• The categorical frequency distribution is used
  for data that can be placed in specific
  categories, such as nominal or ordinal data.
• For example, data such as political affiliations,
  religion affiliations, or major field of study
  would use categorical frequency distribution.

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Example

• The blood type of different students

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Example Cont.
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Ungrouped Frequency Distribution

• When the range of data is small, the data must be
  grouped into classes that are not more than one
  unit in width.

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Example

• The range in the example is Rhighest value
  lowest value 11 4 7
• Since the range is small classes consisting of
  single data value can be used.

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Example Cont.
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Grouped Frequency Distribution

• When the range of the data is large, the data
  must be grouped into classes that are more than
  one unit in width.

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Example
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Example Cont.

• In this distribution, the values 1 and 3 of the
  first class are called class limits.
• 1 is the lower class limit and 3 is the upper
  class limit.

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Histogram

• The histogram is a graph that displays the data
  by using vertical bars of various heights to
  represent the frequencies.

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Histogram in Excel (Steps)

• Open the tools menu, choose the data analysis
  command and chose histogram from the analysis
  tools list box.
• Input range enter the reference for the range of
  cells containing the data.
• Bin range enter the reference of cells
  containing the values that separate the
  intervals, including the labels. (They must be in
  ascending order).

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Steps Continued

• Labels check this box to indicate that labels
  have been included in the references for the
  input range and bin range.
• Out put range enter the reference for the cell
  you want out put to appear.
• Chart output check this option to obtain a
  histogram chart in addition to the frequency
  distribution table on the worksheet.

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Create a histogram for the following data5, 6,
4, 7, 5, 9, 11, 12, 4, 5, 6, 7, 9, 19

• Do this in Excel

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Cumulative Frequency

• The cumulative frequency is the sum of the
  frequencies accumulated up to the upper boundary
  of a class in the distribution.
• They are used to visually represent how many
  values are below a certain upper class boundary.

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Example of Cumulative Frequency Distribution
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Pie Chart

• A pie chart is a circle that is divided into
  sections according to the percentage of
  frequencies in each category of the distribution.

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Example
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Example Cont.
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Bar Chart

• A bar chart is a broader concept than histogram.
• A bar chart may be used to display concepts other
  than frequency of an observations. For example,
  a bar chart may display the average exam results.
• Histogram is a bar chart of frequency
  distribution.

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