Outline: Graphical Methods

1
Outline Graphical Methods

• Graphical versus Numerical Methods
• Frequency distributions (tables)
• Histogram
• Stem-and-leaf plot
• Box plot
• Pie chart
• Scatter plot

2
Graphical vs. Numerical Methods

• Graphical methods
• Intuitive, easy to understand
• Difficult to construct manually
• Useful to find overall patterns
• Numerical methods
• Require some knowledge
• Provide more objective ways of describing data

3
Frequency Table

• Class and frequency
• Mutually exclusive and exhaustive
• Class limits should not overlap
• Class should not be omitted
• Class limits (boundaries)
• Class width
• Should be uniform (equal width)
• Class midpoint

4
Steps

• Determine the number of classes
• Find minimum and maximum values
• Select the number of classes
• Find the limits and boundaries
• Tally the data to get frequencies
• Relative frequency freq/N
• Cumulative frequency

5
Example

• Cereal Calories, question 15 on page 59
• Range 190 ( 270 - 80)
• 5 classes 50 class width
• Class midpoint 125, 175

class Freq.
Percent Cum. -----------------------------
------------------------------
lt100 8 17.39
17.39 100-150 14
30.43 47.82 150-200
13 28.26 76.08
200-250 9 19.57 95.65
250-300 2 4.35
100.00 ------------------------------------------
----------------- Total
46 100.00
6
Bar Chart
7
Histogram

• Continuous vertical bars for density

8
Histogram Polygon, Oglive

• Frequency polygon connects midpoints of classes
• Ogive is the cumulative frequency graph
• Histogram shapes, Figure 2-8 on page 56

9
Stem-and-leaf plot

• Provide much useful information
• Sort data in the ascending order
• Determine leading digits
• Record data by putting their trailing digit
• Question 15 on page 79
• Stem-and-leaf plot for tax
• 1 2788
• 2 001489
• 3 1367
• 4 148
• 5 0
• 6 0
• 7 6

10
Box plot

• Minimum, maximum
• 25th and 75th percentile (1th and 3th quartile)
• Mean, medium

11
Pie chart

• Degree(frequency/N)360

12
Scatter Plot (Q14 on page 89)

• To examine the relationship between two variables
• Positive, negative, linear, exponential,

13
Misleading Graphs

• Page 70-73
• Irrelevant scales
• Not report units and labels.
• Irrelevant type of graphs
• Irrelevant perspective

14
Perspectives