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(Chapt. 3: The Histogram)

Unit 2Displaying 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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Question asked Corresponding Variablein 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

Some Survey Questions

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

Coca Cola Co

Dr Pepper Co

Others

Pepsico Inc

RJR Nabisco

Royal Crown

Seven Up Co

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Bar Chart for Cola Data

0.0

0.1

0.2

0.3

0.4

NAME

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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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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. gradcollege grad

3 47 M married 1 h.s. grad h.s. grad

4 48 M married 3 college gradcollege 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 workMaster'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. gradsome 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

15 56 F married 1 grad 8th gradegrad 8th grade

16 34 F married 4 some h.s.grad 8th grade

17 48 F married 6 h.s. gradsome h.s.

18 43 F divorced 3 - -college grad

19 50 F married 1 h.s. gradsome h.s.

20 24 F married 2 college gradcollege grad

21 23 M married 1 college gradcollege grad

22 47 F married 4 PhD degreePhD degree

23 63 M single 0 h.s. grad- -

24 31 F married 4 college grad h.s. grad

25 21 F separated 3 some h.s.some h.s.

Stem - & -Leaf diagram

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Stem-&-Leaf of Ages

STEM AND LEAF PLOT OF AGE, N = 25

MINIMUM IS: 21.0LOWER HINGE IS: 31.0MEDIAN IS: 47.0UPPER HINGE IS: 65.0MAXIMUM IS: 80.0 2 1 3 3 4 8

3H 1 1 4 74M 1 3 7 7 8 85 0 66H 3 5 97 0 0 0 18 0

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Age Data - Histogram

0.05

0.10

0.15

0.20

0.25

123

456

7

20 50 80 110

AGE

0.05

0.10

0.15

0.20

0.25

123

456

7

20 50 80 110

AGE

(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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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

Student 1 2 3 4 5 6 7 8 9 10

Male/Female F M F M M F F M MF

Weight 98 150108 158 162 112 118 167 170 120

Student 11 12 13 14 15 16 17 18 1920

Male/Female M M M F F M F M MF

Weight 177 186 191 128 135 195 137 205 190120

Student 21 22 23 24 25 26 27 28 2930

Male/Female M M F M F F M M MM

Weight 188 176 118 168 115 115 162 157 154148

Student 31 32 33 34 35 36 37 38 3940

Male/Female F M M F M F M F MM

Weight 101 143 145 108 155 110 154 116 161165

Student 41 42 43 44 45 46 47 48 4950

Male/Female F M F M M F F M MM

Weight 142 184 120 170 195 132 129 215 176183

Weights of 50 college students (in pounds)

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Back-to-Back Displays - 2

09 810 1 8 811 0 2 5 5 6 8 812 0 0 0 8 913 2 5 714 2 3 5 815 0 4 4 5 7 816 1 2 2 5 7 817 0 0 6 6 718 3 4 6 819 0 1 5 520 521 5

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 5 815 0 4 4 5 7 816 1 2 2 5 7 817 0 0 6 6 718 3 4 6 819 0 1 5 520 521 5

Back-to-BackStem-&-LeafDiagram

Stem-&-Leaf Diagram

FEMALE MALE

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Back-to-BackDisplays - 3

80 100 120 160 200 220 pounds

weights of male and female college students

10

20

30

40

%

per

interval

female

male

35 25 15 5 0 5 15 25 35

MALES FEMALES

commonverticalscale

% per interval

same scale on horizontal axis

Back-to-back histogram for weights of maleand female college students

90

110

130

220

200

180

160

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Time Series Plots

Day 5 10 15 20 25 30 35 40 45 50 55

Time in seconds

160

80

120

60

40

20

140

100

Average Time for Receptionist to Answer TelephonesBetween 9:00 and 10:00 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 DiagramWooden 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 Warped1 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

22 2 1

23 3

24 1 2 1

25 2 2 3 2 1 2

26 1 2 3 4

27 2 3 1

29 1

30 2

31 5

Total 6 24 24 47 24 12 14

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Frequency Pareto Chart

40

50

30

20

10

Count

Problem

Hinge Color Wood Hole Warp Glass Window

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Pareto Charts - 2

•

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

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.

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Cost Pareto Chart

400

500

300

200

100

cost ($)

Warp Hinge Color Wood Glass Hole Window

600

Problem