(Chapt. 3: The Histogram)

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(Chapt. 3 The Histogram)
Unit 2 Displaying Data
Graphical displays for analysis presentation of
data. The Current Population Survey collects
data on many variables. A VARIABLE is a
characteristic which may differ from person to
person in a study.
A.05
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Some Survey Questions
Question asked Corresponding Variable in a
survey . Variable . type
. How old are you? How many people in your
family? Are you currently married? How many
rooms in your house? How tall are you? What
is your major? Where were you born? How
much do you like chocolate? very much / somewhat
/ so-so / not much / not at all
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Variable types
Variables and data can be qualitative - the
answer to the question is not a
number quantitative - the answer to the question
is a number qualitative data can be - discrete
- takes on particular values only - continuous -
can be measured in arbitrarily small
amounts Another classification system
nominal - categorical ordinal - values fall in
ordered categories, may be numerical
interval - can be ordered AND we can indicate an
exact distance between values
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• Qualitative includes ________ and ________ data
  types.
• Quantitative includes ________ and ________ data
  types.

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Pie chart Bar chart

• CORPORATION MARKET SHARE ()
• Coca-Cola Co. 38.6
• Pepsico Inc. 27.4
• Dr Pepper Co. 7.1
• Seven-Up Co. 6.3
• RJR Nabisco 4.6
• Royal Crown Cola Co. 3.5
• Others 12.5

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Bar Chart for Cola Data
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Soft Drinks Revisited
N a DP Pe Co Oth 7U RC
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The Pareto Diagram

• The (frequency) Pareto Diagram is a bar chart
  which displays the causes of various defects, in
  order, from most to least frequent so that you
  can focus attention on the most important
  problems.

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National Demonstration Project

• Park Nicollet Pareto diagram with listing of
  Possible Causes for Patient Dissatisfaction

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Hot Dogs

• ( Consumer Reports )

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Steps in ConstructingA Stem-and-Leaf Diagram

• (1) Scan the data for approximate range.
  Choose a suitable pair of adjacent
  digits (eg. tens and ones).
• (2) Allocate a separate line in the display for
  each possible string of leading digits (STEM).
• (3) Split each data value between the selected
  two digits.
• (4) Write down the trailing digit(s) (LEAF) for
  each data value on the line corresponding to its
  leading digits. Sort the leaves. Provide a
  relevant key.

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Stem - -Leaf diagram

• Data from 25 subjects in a survey
• case age sex marital status children
  husb.educ.level wife educ.level
• --------- ----- ----- -------------------
  ------------ ---------------------
  ---------------------
• 1 70 M married 3 h.s. grad h.s. grad
• 2 28 F separated 3 h.s. grad college grad
• 3 47 M married 1 h.s. grad h.s. grad
• 4 48 M married 3 college grad college grad
• 5 23 M married 0 college grad h.s. grad
• 6 69 F divorced 3 - - grad 8th grade
• 7 31 F married 1 some grad work Master's
  degree
• 8 70 F single 0 - - h.s. grad
• 9 80 F widowed 0 - - less than 8th grade
• 10 37 F married 3 h.s. grad some h.s.
• 11 65 F single 0 - - some h.s.
• 12 71 F widowed 2 - - some h.s.
• 13 41 F married 3 h.s. grad h.s. grad
• 14 70 M married 5 some h.s. less than 8th grade

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(No Transcript)
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Stem--Leaf of Ages

• STEM AND LEAF PLOT OF AGE, N 25
• MINIMUM IS 21.0
• LOWER HINGE IS 31.0
• MEDIAN IS 47.0
• UPPER HINGE IS 65.0
• MAXIMUM IS 80.0
• 2 1 3 3 4 8
• 3H 1 1 4 7
• 4M 1 3 7 7 8 8
• 5 0 6
• 6H 3 5 9
• 7 0 0 0 1
• 8 0

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Age Data - Histogram
(FPP) In a histogram, the areas of the blocks
represent percentages. In a histogram, the area
of each block represents the percentage of
observations in the corresponding interval.
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0.25
6
0.20
5
4
0.15
3
0.10
2
0.05
1
20
50
80
110
AGE
7
0.25
6
0.20
5
4
0.15
3
0.10
2
0.05
1
20
50
80
110
AGE
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What to Look for in a Histogram

• 1. Look at the shape. Is it symmetric? skewed?
• 2. Detect outliers, if any.
• 3. Where is the average?

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Basic Shapes of Histograms
Normal, Triangular, Symmetric
Uniform, Rectangular
Skewed to left
Skewed to right
Bimodal
J-shaped
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Back-to-Back Displays
Weights of 50 college students (in pounds)

• Student 1 2 3 4 5 6 7 8 9 10
• Male/Female F M F M M F F M M F
• Weight 98 150 108 158 162 112 118 167
  170 120
• Student 11 12 13 14 15 16 17 18 19 20
• Male/Female M M M F F M F M M F
• Weight 177 186 191 128 135 195 137 205 190 120
• Student 21 22 23 24 25 26 27 28 29 30
• Male/Female M M F M F F M M M M
• Weight 188 176 118 168 115 115 162 157 154 148
• Student 31 32 33 34 35 36 37 38 39 40
• Male/Female F M M F M F M F M M
• Weight 101 143 145 108 155 110 154 116 161 165
• Student 41 42 43 44 45 46 47 48 49 50
• Male/Female F M F M M F F M M M
• Weight 142 184 120 170 195 132 129 215 176 183

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Back-to-Back Displays - 2
Stem--Leaf Diagram
09 8 10 1 8 8 11 0 2 5 5 6 8 8 12 0 0 0 8
9 13 2 5 7 14 2 3 5 8 15 0 4 4 5 7 8 16 1
2 2 5 7 8 17 0 0 6 6 7 18 3 4 6 8 19 0 1 5
5 20 5 21 5
FEMALE MALE

• 8 09
• 8 8 1 10
• 8 8 6 5 5 2 0 11
• 9 8 0 0 0 12
• 7 5 2 13
• 14 2 3 5 8
• 15 0 4 4 5 7 8
• 16 1 2 2 5 7 8
• 17 0 0 6 6 7
• 18 3 4 6 8
• 19 0 1 5 5
• 20 5
• 21 5

Back-to-Back Stem--Leaf Diagram
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Back-to-BackDisplays - 3
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Time Series Plots
Time in seconds
160
140
120
100
80
60
40
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Day 5 10 15 20 25 30 35
40 45 50 55
Average Time for Receptionist to Answer
Telephones Between 900 and 1000 a.m. (Park
Nicollet Project)
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Control Charts
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Newspaper Graphics Examples
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The Pareto Diagram

• The (frequency) Pareto Diagram is a bar chart
  which displays the causes of various defects, in
  order, from most to least frequent so that you
  can focus attention on the most important
  problems.

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Pareto Diagram

• Wooden glass doors are produced on a six day work
  week. At final checkout before shipping, the
  doors are inspected and each is classified as
  conforming or nonconforming. Nonconforming doors
  are further classified into one of the following
  categories, according to their defect.
• The data here give the number of defective doors
  by day and by classification.
• A Pareto chart can be made to show which type of
  defect is most prevalent.

Day Day inspected Window Window
misaligned Discolor Discolor Handle Handle
hole missing Hinges Hinges wrong Rough
Rough wood Glass Broken glass Warped
Warped
Variables are Day Window Discolor Handle
Hinges Rough Glass Warped
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Pareto Charts

• Day Window Discolor Handle Hinges
  Rough Glass Warped
• 1 1 3 2 7 1 4
• 2 2 2 3 3
• 3 2 1 4 4 1
• 4 2 3 3 1 1 1 1
• 5 1 2
• 6 2 2 4 1 1
• 8 1 1
• 9 1
• 10 2
• 11 5
• 12 1 1 4 4 1
• 13 1
• 15 2
• 16 2
• 17 2
• 18 1
• 19 6
• 20 3 2

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Frequency Pareto Chart
50
40
30
Count
20
10
Hinge Color Wood Hole Warp Glass Window
Problem
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Pareto Charts - 2
A Pareto Diagram can be made to display the costs
of various defects, in order, so that you can
focus attention on the most important
problems. The following costs can be assumed for
each of the defect types.
Day Day Inspected Window Window
misaligned 10.00 Discolor Discolor
5.00 Handle Handle hole missing
3.00 Hinges Hinges wrong 6.00 Rough
Rough wood 5.00 Glass Broken glass
8.00 Warped Warped 45.00

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Cost Pareto Chart
600
500
400
300
cost ()
200
100
Warp Hinge Color Wood Glass Hole Window
Problem