Presenting Data in Tables and Charts

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Chapter 2

• Presenting Data in Tables and Charts

2
Note

• Sections 2.1 2.2 - examining data from 1
  numerical variable.
• Section 2.3 - examining data from 2 numerical
  variables.
• Section 2.4 - examining data from 1 categorical
  variable (read).
• Section 2.5 - examining data from 2 categorical
  variables.

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Section 2.1

• Organizing Numerical Data
• Examining One Numerical Variable.

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Ordered Array

• Array of data ordered from smallest to largest
  value
• Makes it easier to see the extreme values and
  where the majority of values are located.

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Using Excel

• Data Sort
• Select the heading of the column you want to sort
  by first. Choose ascending or descending.
• Select the heading of the column you wanted to
  sort by second. Choose ascending or descending.
  Etc.
• Choose appropriate button Header row or No
  header row.

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Stem Leaf Display

• Shows how the data varies over a range of
  observations
• Separates data according to leading digits
  (stems) and trailing digits (leaves).

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Stem Leaf Display Stem Unit of 1
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Stem Leaf Display x
The 10 in the top right cell shows that the
number rounds to 80 but is in the 70s
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Using PHStat to create a Stem Leaf Display

• PHStat Descriptive Statistics Stem-and-Leaf
  Display
• Enter range of values
• If selection contains a heading, leave selected
  First cell contains a label.
• Select Stem Unit
• Enter Title

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Section 2.2

• Tables And Charts For Numerical Data
• Examining One Numerical Variable

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The Frequency Distribution

• Data is arranged into class groupings.
• Creating class groupings
• Number of classes
• Depends on number of observations
• Typically 5 lt class groupings lt 15
• Intervals should be the same width. Use the
  following
• Width of interval Range / Number of class
  groupings
• Avoid overlapping classes

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Frequency Distribution (continued)

• Consists of the number of occurrences of a value
  fitting within the range of each interval.
• Advantage - Data characteristics can be
  approximated.
• Disadvantage - Individual values are lost due to
  the grouping.

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Ex. Given the following data
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Frequency Distribution
Right boundary is not included.
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Using PHStat to create a Frequency Distribution

• PHStat Descriptive Statistics Frequency
  Distribution
• Enter the variable cell range
• Enter the bin cell range
• If you selected the heading when selecting the
  data, leave selected First cell in each range
  contains label.
• Leave selected Single Group Variable
• Enter title of your choice.

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Bin (Used for PHStat only)

• Contains the values that approximate the maximum
  value of each class.
• For example
• If your intervals are,
• -20.0 to -10.0
• -10.0 to 0.0
• 0 to 10.0
• 10.0 to 20.0
• Your bin values could be
• -10.1
• -0.1
• 9.9
• 19.9

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Bin Values
Intervals
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If your data were recorded with 2 places after
the decimal, your bin values would be

• -10.01
• -.01
• 9.99
• 19.99

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Example

• See the file Sec2.2.xls

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Relative Frequency Distribution

• First create a Frequency Distribution.
• The values in the Relative Frequency Distribution
  are formed by dividing the frequency of each
  value within each class by the total number of
  values.
• The Relative Frequency Distribution contains the
  proportion of times a value occurs within each
  class.

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Relative Frequency Distribution
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Percentage Distribution

• First create a Relative Frequency Distribution
• The values in the Percentage Distribution are
  formed by multiplying each proportion in the Rel.
  Freq. Dist. by 100.

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Percentage Distribution
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Benefit of a Relative Frequency Distribution or
Percentage Distribution

• Essential when comparing two sets of data
  consisting of a different number of values.

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For example
Study 2
Study 1
5 occurs 1/5 times. 1/5 0.2 Or 20 of the
time
5 occurs 7/12 times. 7/12 0.583 Or 58.3 of
the time
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Cumulative Percentage Distribution

• Demonstrates the growth over the classes.

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Cumulative Percentage Distribution
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Cumulative Percentage Distribution

• Top of Pg. 56. SOLUTION From Table 2.5 ...
• Error

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Using PHStat to create a Percentage or Cumulative
Percentage Distribution

• These are automatically generated when you create
  a Frequency distribution.

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Class Midpoint

• Point halfway between the boundaries of each
  class.

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Histogram

• Using a picture to demonstrate data.
• Describes the numerical data that has been
  grouped into a frequency, relative frequency, or
  percentage distribution.
• The random variable of interest is displayed
  along the horizontal axis (x-axis).
• The number, proportion or percentage of values
  per class are plotted along the vertical axis
  (y-axis)

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Histogram
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Polygon (same info as Histogram)

• Using a picture to demonstrate data.
• Describes the numerical data that has been
  grouped into a frequency, relative frequency, or
  percentage distribution.
• The random variable of interest is displayed
  along the horizontal axis (x-axis).
• The number, proportion or percentage of values
  per class are plotted along the vertical axis
  (y-axis)

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Polygon
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Using PHStat to create a Histogram Polygon

• PHStat Descriptive Statistics Histogram
  Polygons
• Enter the Variable Cell Range
• Enter the Bin Cell Range
• Enter the Midpoints Cell Range
• If the first row contains headings, leave
  selected First cell in each range contains
  label.
• Select Multiple Groups - Unstacked.
• Enter title of your choice
• Leave check boxes on default selection.

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Section 2.3

• Graphing Bivariate Numerical Data
• Examining 2 numerical variables.

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Scatter Diagram

• Used to demonstrate the relationship between to
  numerical variables.
• One numerical variable is plotted on the x-axis.
• The other numerical variable is plotted on the
  y-axis.
• The result is a point on the x-y plane.

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Example

• Cholesterol Level
• Meat Consumption in Ounces / Day

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Scatter Diagram of previous data
Cholesterol Level
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Section 2.4

• Tables and charts for categorical data
• Covered in CSC 199
• Read

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Section 2.5

• Tabulating and Graphing Bivariate Categorical
  Data
• Use a Contingency Table or a Side-By-Side
  Chart.

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Contingency Table

• Also called, Cross-Classification Table
• Used to study the values from two categorical
  variables.

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ExampleA sample of 20 graduates was taken and
each individual was asked1. What was your
major?2. What is your salary level?lt
30,00030,000 - 50,000gt 50,000
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Each value is divided by the total (12)
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28.57 of all polled make 30,000 or
under. 42.86 of all polled majored in
math. 21.43 of all polled majored in math and
make 50,000 or more.
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Each value is divided by the total of its row.
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Of those who majored in math, 50.00 make
50,000 or more. Of those who majored in
philosophy, 66.67 make 30,000 or less.
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Each value is divided by the total of its column
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Of those who make 30,000 or less, 50.00
majored in philosophy Of those who make between
30,000 and 50,000, 20.00 majored in
philosophy.
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Side-By-Side Chart

• Visual display of bivariate categorical data.
• Used to detect relationships in the data.

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Consider the following data
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Side-By-Side Chart of the previous data
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See the following

• Excel Handbook for Chapter 2
• Pg. 93 - 104