Chapter 4 Organization and Description of Data

1
Chapter 4 - Organization and Description of Data

• Qualitative vs. Quantitative data
• Discrete vs. Continuous Data
• Graphical Displays

2
Qualitative (Categorical) Data

• The raw (un-summarized) data are merely labels or
  categories

Quantitative (Numerical) Data
The raw (un-summarized) data are numerical
3
Qualitative Data Examples

• Class Standing (Fr, So, Ju, Sr)
• Section (1,2,3,4,5,6)
• Automobile Make (Ford, Chevrolet, Nissan)
• Questionnaire response (disagree, neutral, agree)

4
Quantitative Data Examples

• Voltage
• Height
• Weight
• SAT Score
• Number of students arriving late for class every
  week.
• Time to complete a task

5
Data may be further classified asDiscrete or
Continuous
Types of data
Quantitative (numerical)
Qualitative (Categorical)
Continuous
Discrete
Discrete
6
Discrete Data

• Only certain values are possible (there are gaps
  between the possible values)

Continuous Data
Theoretically, any value within an interval is
possible with a fine enough measuring device
7
Discrete Data Examples

• Number of students late for class every week
• Number of crimes reported a day to SB police
• Number of times the word number is used in a
  day
• (generally, discrete data are counts)

8
Continuous Data Examples

• Voltage
• Height
• Weight
• Time to complete a homework assignment

9
Discrete data -- Gaps between possible values
Continuous data -- Theoretically, no gaps between
possible values
10

• A Discrete Variable For example, the number of
  correct answers on a five-question,
  multiple-choice test is a discrete variable.
• 
  
  
• Continuous For example, the amount of water
  poured into a 50-mL glass container.

11
Who Cares?
Qualitative and quantitative data behave
differently and therefore are studied differently.
12
4.3 Displaying distributions Qualitative
variables

• Pie Charts
• Bar Graphs

13
PIE CHART

• A pie chart is especially useful in displaying a
  relative frequency (percentage) distribution
• EXAMPLE A sample of 200 college students were
  asked to indicate their favorite soft drink. The
  results of the survey are given on the next
  slide. Draw a pie chart for this information.

14
(No Transcript)
15
PIE CHART FOR THE TASTE TEST
Coca-Cola
Pepsi
Others
Seven up
Dr Pepper
16
Bar Chart
Source Dept. of Health Human Services.
17
BAR CHART FOR THE AIDS DATA
1 ATLANTA
2 AUSTIN
3 DALLAS
4 HOUSTON
5 NY, NY.
6 SAN. FRAN.
7 WASH D.C.
8 W. P. BEACH
18

• LDI 4.1 4.2 4.3 4.5

19
A Misleading Bar Graph
Problem The bar graph that follows presents the
total sales figures for three realtors. When the
bars are replaced with pictures, often related to
the topic of the graph, the graph is called a
pictogram.
Realtor 3
Realtor 2
Realtor 1
(a) How does the height of the home for Realtor
1 compare to that for Realtor 3? (b) How does
the area of the home for Realtor 1 compare to
that for Realtor 3?
20
4.4 Displaying Distributions Quantitative
Variables

• Frequency plots
• Stem and Leaf Plots
• Histograms
• Time plots
• Scatterplots

21
Frequency PlotsExample 4.6 . Ice-Cream-Cone
Prices

• In September 1985, the prices (in cents) of a
  single-scoop ice cream cone at 17 Los Angeles
  stores were as follows
• 25, 53, 70, 75, 90, 90, 91,
  95, 95,
• 95, 95, 96, 100, 105, 110, 115, 120.
• (a) What are the minimum value and the maximum
  value?
• (b) Draw the corresponding frequency plot.
• (c) Describe the distribution of ice cream cone
  prices.
• Frequency Plot
• 
  
  X
• 
  
  X
• 
  X
  X
• X X
  X X XX XX X
  X X X X
• 25 30 35 40 45 50 55 60 65
  70 75 80 85 90 95 100 105 110 115
  120
• Price

22
4.4.3 STEM-AND-LEAF

• The stem is the leading digit.
• The leaf is the trailing digit.
• The stem is placed to the left of a vertical line
  and the leaf to the right.

23

• The Dean of the College of Business reports the
  following number of students in the 15 sections
  of basic statistics offered this semester
  (quarter). Construct a stem-and-leaf chart for
  the data.
• 27 36 29 21 24 26 32 30 36
  30 28 23 17 41 19.

Key 1 7 represents 17
24

• Example 4.7 Basic Stem-and-Leaf Plot for Age
• Problem
• Consider the ages of the 20 subjects from Data
  Set 1.
• 45, 41, 51, 46, 47, 42, 43,
  50, 39, 32,
• 41, 44, 47, 49, 45, 42, 41,
  40, 45, 37.

• 2 7 9
• 0 1 1 1 2 2 3 4 5 5 5 6 7 7
• 5 0 1

Key 32 represents 32
25
Histogram

• Frequency distribution grouping of data into
  categories showing the number of observations in
  each of the mutually exclusive classes.
• EXAMPLE Mr. Bagdonos is the city manager for the
  town of Geneva. He has been asked by the city
  council to study the water usage in the
  community. He selects a random sample of 30
  families and determines the number of gallons of
  water used by each family last year. The data is
  reported in thousands of gallons

26
EXAMPLE

• 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8,
  13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4,
  18.3, 29.8, 17.1, 18.9, 14.3, 26.1, 15.7, 14.0,
  17.8, 33.8, 23.2, 25.9, 27.1, 16.6. Organize the
  data into a frequency distribution.

• Consider the classes 8 up to 13 and 13 up to 18.
  The class marks will be 10.5 and 15.5. The class
  interval will be (13 - 8) 5.

27
HISTOGRAM FOR WATER USAGE (1,000 GALLONS)
28
Lower Class Limits

• are the smallest numbers that can actually
  belong to different classes

29
Upper Class Limits

• are the largest numbers that can actually
  belong to different classes

30
Class Midpoints
can be found by adding the lower class limit to
the upper class limit and

dividing the sum by two
31
Class Width

• is the difference between two consecutive lower
  class limits or two consecutive
  lower class
  boundaries

Editor Substitute Table 2-2
32
Constructing A Frequency Distribution

• 1. Decide on the number of classes
• (should be between 5 and 20).
• 2. Calculate (round up).

33
p. 259Example 4.9 .Histogram of Age

• CLASS TALLY OBSERVATIONS PERCENTA
  GE
• 30,35) / 1 1/20
  0.05 5
• 35,40) // 2 2/20
  0.10 10
• 40,45) //////// 8
  8/20 0.40 40
• 45,50) /////// 7
  7/20 0.35 35
• 50,55) // 2
  2/20 0.10 10

34
(No Transcript)
35
Note the visual impact of area ...
36
Example 4.10 .Histogram versus Bar Graph
GRAPH I
GRAPH II
GRAPH III
GRAPH IV
37
4.4.2 Shapes of Distributions
Bimodal Heights of a population with women and
men
Symmetric, bell-shaped, unimodal Sat scores of a
students at a University
38
Symmetric and Unimodal
39
Critical ThinkingInterpreting Histograms
One key characteristic of a normal distribution
is that it has a bell shape. The histogram
below illustrates this.
40
Skewed Right
41
Skewed Left
42
4.4.4 Displaying data over time Time Plots
Trends- increasing or decreasing, changes in
location of the center, changes in variation or
spread Seasonal variation or cycles- fairly
regular increasing or decreasing movements.
43
4.4.6 Displaying Relationship between two
quantitative variables Scatterplots

• Definitions
• Studies are often conducted to attempt to show
  that some explanatory variable causes the
  values of some response variable to occur.
• The response or dependent variable is the
  response of interest, the variable we want to
  predict, and is usually denoted by y.
• The explanatory or independent variable attempts
  to explain the response and is usually denoted by
  x.

44
(No Transcript)
45
4.3.3 Displaying Relationship between two
qualitative variables
46

• LDI 4.10 , 4.11, 4.12, 4.17, 4.18, 4.20, 4.23