Charts and Graphs

1
Charts and Graphs

• Chapter 2
• MSIS 111 Prof. Nick Dedeke

2
Objectives

• Understanding data presentation
• Discrete versus continuous data Differentiate
  between grouped and ungrouped data
• Construct frequency distributions
• Construct histogram, frequency polygon and other
  charts

3
Types of Variables

• Discrete variables have parameters that are whole
  numbers only, e.g. 3 cars, 5 cars, 6 cars , 7
  cars, 9 cars, 11 cars
• Continuous variables have parameters that allow
  both whole numbers and decimal numbers, e.g.
  1.2, 1.4, 4.2

4
Exercise Using Frequency Distribution for
Discrete Data

• What is the average of these dimension data (all
  observations number of houses)?1,1,1,1,1,1,1,12
  ,2,2,2,2,2,2,24,4,5,5,6,6,8,89,9,9,
  10,10,10,10,10,1011,11,11

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Data Presentation

• One of the characteristics of good statistics is
  the fact that everyone uses the same approach to
  organize data.
• The approaches used are called tools of
  descriptive statistics

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Xi Frequency (Fi) Relative Frequency (fi)
1 inches 8 8/36
2 inches 8 8/36
4 inches 2 2/36
5 inches 2 2/36
6 inches 2 2/36
8 inches 2 2/36
9 inches 3 3/36
10 inches 6 6/36
11 inches 3 3/36
? 36 1
7
Problem Frequency Distribution for Continuous
Data

• What is the average of these continuous data (all
  observations in inches)?1.6,1.5,1.2,1.4,1.6,1.2,
  1.6,1.62.1,2.7,2.3,2.5,2.8,2.9,2.8,2.94.2,4.6,5.
  2,5.4,6.1,6.5,,7.6,8.3,8.69.6,9.1,9.6,10.0,10.5,1
  0.6,10.8,10.3,10.4,11.8,11.8,11.8, 12.3,12.4,12.5

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Exercise Frequency Distribution for Continuous
Data

• Range Largest Smallest number
  12.5 1.2 11.3Set number of classes to use
  to group data 6 classesClass width 11.3/6
  1.88 or 2Class width of 2 means that one builds
  classes where the difference between the highest
  and lowest number in each class is 2

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Class Width
650
750
700
Lowercutpoint
Uppercutpoint
Midpoint
10
Exercise Frequency Distribution for Grouped Data
Class interval Frequency (Fi) Relative Frequency (fi)
1 3) inches 16 16/40
3 5) inches 2 2/40
5 7) inches 4 4/40
7 9) inches 3 3/40
9 11) inches 9 9/40
11 13) inches 6 6/40
? 40 1
11
Types of ChartsPie Charts
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Types of Charts Oglive
13
Types of Charts Histograms
14
Graph Box-plots
IQR

• Vertical line in box represents median
• Left end of box depicts the 25th percentile (1st
  quartile)
• Right end of box depicts the 75th percentile (2nd
  quartile)
• Horizontal line from each end of box are drawn to
  the most extreme data points (only those no
  farther than 1.5 Inter quartile range (IQR))

1Q 2Q 3Q 4Q
75th percentile
25th percentile
50th percentile
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Graph Box-plots vs. Histograms

• Vertical line in box represents median
• Left end of box depicts the 25th percentile (1st
  quartile)
• Right end of box depicts the 75th percentile (2nd
  quartile)
• Horizontal line from each end of box are drawn to
  the most extreme data points ( no farther than
  1.5 Inter quartile range (IQR)

1Q 2Q 3Q 4Q
25th percentile
75th percentile
50th percentile
Frequency
1Q 2Q 3Q 4Q
X
Median
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Simulations

• Box plots vs. histograms
• Hints
• Match extreme values
• Match the length of the inter quartile range or
  the middle 50 of the data to histogram
• Use the pattern of the data to visualize the
  position of the median
• Median moves forward
• Median moves backwards