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Statistics for Managers Using Microsoft® Excel 4th Edition Chapter 2 Presenting Data in Tables and Charts
Statistics for Managers Using Microsoft Excel, 4e © 2004 PrenticeHall, Inc.
Chap 2-1
Chapter Goals After completing this chapter, you should be able to:
Create an ordered array and a stem-and-leaf display
Construct and interpret a frequency distribution, polygon, and ogive
Construct a histogram
Create and interpret bar charts, pie charts, and scatter diagrams
Present and interpret category data in bar charts and pie charts
Describe appropriate and inappropriate ways to display data graphically
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-2
Organizing and Presenting Data Graphically
Data in raw form are usually not easy to use for decision making
Some type of organization is needed
Table Graph
Techniques reviewed here:
Ordered Array Stem-and-Leaf Display Frequency Distributions and Histograms Bar charts and pie charts Contingency tables
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-3
Tables and Charts for Numerical Data Numerical Data
Frequency Distributions and Cumulative Distributions
Ordered Array
Stem-and-Leaf Display
Histogram
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Polygon
Ogive
Chap 2-4
The Ordered Array A sorted list of data: Shows range (min to max) Provides some signals about variability within the range May help identify outliers (unusual observations) If the data set is large, the ordered array is less useful
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-5
The Ordered Array (continued)
Data in raw form (as collected): 24, 26, 24, 21, 27, 27, 30, 41, 32, 38
Data in ordered array from smallest to largest: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-6
Stem-and-Leaf Diagram
A simple way to see distribution details in a data set METHOD: Separate the sorted data series into leading digits (the stem) and the trailing digits (the leaves)
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-7
Example Data in ordered array: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Here, use the 10’s digit for the stem unit: Stem Leaf
21 is shown as
2
1
38 is shown as
3
8
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-8
Example (continued)
Data in ordered array: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Completed stem-and-leaf diagram: Stem
Leaves
2
1 4 4 6 7 7
3
0 2 8
4
1
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-9
Using other stem units
Using the 100’s digit as the stem:
Round off the 10’s digit to form the leaves Stem
Leaf
613 would become
6
1
776 would become
7
8
12
2
... 1224 becomes
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-10
Using other stem units (continued)
Using the 100’s digit as the stem:
The completed stem-and-leaf display: Data: 613, 632, 658, 717, 722, 750, 776, 827, 841, 859, 863, 891, 894, 906, 928, 933, 955, 982, 1034, 1047,1056, 1140, 1169, 1224
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Stem 6
Leaves 136
7
2258
8
346699
9
13368
10
356
11
47
12
2 Chap 2-11
Tabulating Numerical Data: Frequency Distributions What is a Frequency Distribution?
A frequency distribution is a list or a table …
containing class groupings (categories or ranges within which the data falls) ...
and the corresponding frequencies with which data falls within each grouping or category
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-12
Why Use Frequency Distributions?
A frequency distribution is a way to summarize data
The distribution condenses the raw data into a more useful form...
and allows for a quick visual interpretation of the data
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-13
Class Intervals and Class Boundaries
Each class grouping has the same width Determine the width of each interval by range Width of int erval ≅ number of desired class groupings
Use at least 5 but no more than 15 groupings Class boundaries never overlap Round up the interval width to get desirable endpoints
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-14
Frequency Distribution Example Example: A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature 24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-15
Frequency Distribution Example (continued)
Sort raw data in ascending order: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Find range: 58 - 12 = 46
Select number of classes: 5 (usually between 5 and 15) Compute class interval (width): 10 (46/5 then round up) Determine class boundaries (limits): 10, 20, 30, 40, 50, 60 Compute class midpoints: 15, 25, 35, 45, 55
Count observations & assign to classes
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-16
Frequency Distribution Example (continued)
Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Frequency
Relative Frequency
Percentage
10 but less than 20 20 but less than 30 30 but less than 40
3 6 5
.15 .30 .25
15 30 25
40 but less than 50 50 but less than 60
4 2
.20 .10
20 10
Class
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-17
Graphing Numerical Data: The Histogram
A graph of the data in a frequency distribution is called a histogram
The class boundaries (or class midpoints) are shown on the horizontal axis
the vertical axis is either frequency, relative frequency, or percentage
Bars of the appropriate heights are used to represent the number of observations within each class
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-18
Histogram Example Class Midpoint Frequency
10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60
(No gaps between bars)
15 25 35 45 55
3 6 5 4 2
Histogram : Daily High Tem perature 7
6
6 Frequency
Class
5
5
4
4 3
3 2
2 1
0
0
0
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
5
15
25
35
45
Class Midpoints
55
More Chap 2-19
Histograms in Excel
1 Select Tools/Data Analysis
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-20
Histograms in Excel (continued)
2 Choose Histogram
( 3
Input data range and bin range (bin range is a cell range containing the upper class boundaries for each class grouping)
Select Chart Output and click “OK” Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-21
Questions for Grouping Data into Classes
1. How wide should each interval be? (How many classes should be used?)
2. How should the endpoints of the intervals be determined?
Often answered by trial and error, subject to user judgment The goal is to create a distribution that is neither too "jagged" nor too "blocky” Goal is to appropriately show the pattern of variation in the data
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-22
How Many Class Intervals? Many (Narrow class intervals)
3 2.5 2 1.5 1 0.5 More
60
56
52
48
44
40
36
32
28
24
20
16
8
0 4
may yield a very jagged distribution with gaps from empty classes Can give a poor indication of how frequency varies across classes
12
3.5
Frequency
Temperature
Few (Wide class intervals)
may compress variation too much and yield a blocky distribution can obscure important patterns of variation.
12 10 Frequency
8 6 4 2 0 0
30
60
More
Temperature
(X axis labels are upper class endpoints)
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-23
Graphing Numerical Data: The Frequency Polygon Class Midpoint Frequency
Class 10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60
15 25 35 45 55
3 6 5 4 2
Frequency Polygon: Daily High Temperature 7 6
(In a percentage polygon the vertical axis would be defined to show the percentage of observations per class)
Frequency
5 4 3 2 1 0
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
5
15
25
35
Class Midpoints
45
55
More Chap 2-24
Tabulating Numerical Data: Cumulative Frequency Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
Frequency Percentage
Cumulative Cumulative Frequency Percentage
10 but less than 20
3
15
3
15
20 but less than 30
6
30
9
45
30 but less than 40
5
25
14
70
40 but less than 50
4
20
18
90
50 but less than 60
2
10
20
100
20
100
Total
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-25
Graphing Cumulative Frequencies: The Ogive (Cumulative % Polygon)
Less than 10 10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60
10 20 30 40 50 60
0 15 45 70 90 100
Ogive: Daily High Temperature Cumulative Percentage
Class
Lower Cumulative class boundary Percentage
100 80 60 40 20 0 10
20
30
40
50
60
Class Boundaries (Not Midpoints) Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-26
Scatter Diagrams
Scatter Diagrams are used for bivariate numerical data
Bivariate data consists of paired observations taken from two numerical variables
The Scatter Diagram: one variable is measured on the vertical axis and the other variable is measured on the horizontal axis
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-27
Scatter Diagram Example Cost per Day vs. Production Volume
Cost per day
23
125
250
26
140
200
29
146
33
160
38
167
42
170
50
188
55
195
60
200
Cost per Day
Volume per day
150 100 50 0 0
10
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
20
30
40
50
60
70
Volume per Day
Chap 2-28
Scatter Diagrams in Excel 1 Select the chart wizard
2 Select XY(Scatter) option, then click “Next”
3 When prompted, enter the data range, desired legend, and desired destination to complete the scatter diagram Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-29
Tables and Charts for Categorical Data Categorical Data
Graphing Data
Tabulating Data Summary Table
Bar Charts
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Pie Charts
Pareto Diagram
Chap 2-30
The Summary Table Summarize data by category Example: Current Investment Portfolio Investment Amount Percentage Type (in thousands $) (%)
(Variables are Categorical)
Stocks Bonds CD Savings
46.5 32.0 15.5 16.0
42.27 29.09 14.09 14.55
Total
110.0
100.0
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-31
Bar and Pie Charts
Bar charts and Pie charts are often used for qualitative (category) data
Height of bar or size of pie slice shows the frequency or percentage for each category
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-32
Bar Chart Example Current Investment Portfolio Investment Type
Amount
(in thousands $)
Percentage (%)
Stocks Bonds CD Savings
46.5 32.0 15.5 16.0
42.27 29.09 14.09 14.55
Total
110.0
100.0
Investor's Portfolio Savings CD Bonds Stocks 0
10
20
30
40
50
Amount in $1000's Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-33
Pie Chart Example Current Investment Portfolio Investment Type
Amount
(in thousands $)
Percentage (%)
Stocks Bonds CD Savings
46.5 32.0 15.5 16.0
42.27 29.09 14.09 14.55
Total
110.0
100.0
Savings 15% CD 14%
Bonds 29% Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Stocks 42%
Percentages are rounded to the nearest percent Chap 2-34
Pareto Diagram
Used to portray categorical data
A bar chart, where categories are shown in descending order of frequency
A cumulative polygon is often shown in the same graph
Used to separate the “vital few” from the “trivial many”
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-35
Pareto Diagram Example 45%
100%
40%
90%
80%
35%
70% 30% 60% 25% 50% 20% 40% 15% 30% 10%
20%
5%
10%
0%
0% Stocks
Bonds
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Savings
cumulative % invested (line graph)
% invested in each category (bar graph)
Current Investment Portfolio
CD
Chap 2-36
Tabulating and Graphing Multivariate Categorical Data
Contingency Table for Investment Choices ($1000’s)
Investment Category
Investor A
Investor B
Investor C
Total
Stocks
46.5
55
27.5
129
Bonds CD Savings
32.0 15.5 16.0
44 20 28
19.0 13.5 7.0
95 49 51
Total
110.0
147
67.0
324
(Individual values could also be expressed as percentages of the overall total, percentages of the row totals, or percentages of the column totals) Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-37
Tabulating and Graphing Multivariate Categorical Data (continued)
Side by side bar charts Comparing Investors S avings CD B onds S toc k s 0
10
20
Inves tor A Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
30 Inves tor B
40
50
60
Inves tor C Chap 2-38
Side-by-Side Chart Example
Sales by quarter for three sales territories: East West North
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr 20.4 27.4 59 20.4 30.6 38.6 34.6 31.6 45.9 46.9 45 43.9
60 50 40
East West North
30 20 10 0
1st Qtr
2nd Qtr
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
3rd Qtr
4th Qtr Chap 2-39
Principles of Graphical Excellence
Present data in a way that provides substance, statistics and design Communicate complex ideas with clarity, precision and efficiency Give the largest number of ideas in the most efficient manner Excellence almost always involves several dimensions Tell the truth about the data
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-40
Errors in Presenting Data
Using “chart junk”
Failing to provide a relative basis in comparing data between groups
Compressing or distorting the vertical axis
Providing no zero point on the vertical axis
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-41
Chart Junk Bad Presentation
Good Presentation
Minimum Wage 1960: $1.00 1970: $1.60 1980: $3.10
$
Minimum Wage
4 2 0 1960
1970
1980
1990
1990: $3.80 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-42
No Relative Basis
listen
Bad Presentation Freq. 300 200 100 0
A’s received by students.
Good Presentation % 30%
A’s received by students.
20% 10% FR SO
JR SR
0%
FR SO JR SR
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-43
Compressing Vertical Axis Bad Presentation 200
$
Good Presentation
Quarterly Sales 50
100
25
0
0 Q1 Q2
Q3 Q4
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
$
Quarterly Sales
Q1
Q2
Q3 Q4
Chap 2-44
No Zero Point On Vertical Axis Bad Presentation
$Good Presentations Monthly Sales
45
45
$
Monthly Sales
39 36
42
0
39 36
42
or
J F M A M J
J
F
J
F
M
A
M
J
$
60 40
Graphing the first six months of sales
20 0
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
M
A
M
J
Chap 2-45
Chapter Summary
Data in raw form are usually not easy to use for decision making -- Some type of organization is needed: ♦ Table ♦ Graph
Techniques reviewed in this chapter:
Ordered array and stem-and-leaf display Frequency distributions and histograms Percentage polygons and ogives Scatter diagrams for bivariate data Bar charts, pie charts, and Pareto diagrams Contingency tables and side-by-side bar charts
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-46
Statistics for Managers Using Microsoft Excel, 4e © 2004 PrenticeHall, Inc.
Chap 2-1
Chapter Goals After completing this chapter, you should be able to:
Create an ordered array and a stem-and-leaf display
Construct and interpret a frequency distribution, polygon, and ogive
Construct a histogram
Create and interpret bar charts, pie charts, and scatter diagrams
Present and interpret category data in bar charts and pie charts
Describe appropriate and inappropriate ways to display data graphically
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-2
Organizing and Presenting Data Graphically
Data in raw form are usually not easy to use for decision making
Some type of organization is needed
Table Graph
Techniques reviewed here:
Ordered Array Stem-and-Leaf Display Frequency Distributions and Histograms Bar charts and pie charts Contingency tables
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-3
Tables and Charts for Numerical Data Numerical Data
Frequency Distributions and Cumulative Distributions
Ordered Array
Stem-and-Leaf Display
Histogram
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Polygon
Ogive
Chap 2-4
The Ordered Array A sorted list of data: Shows range (min to max) Provides some signals about variability within the range May help identify outliers (unusual observations) If the data set is large, the ordered array is less useful
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-5
The Ordered Array (continued)
Data in raw form (as collected): 24, 26, 24, 21, 27, 27, 30, 41, 32, 38
Data in ordered array from smallest to largest: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-6
Stem-and-Leaf Diagram
A simple way to see distribution details in a data set METHOD: Separate the sorted data series into leading digits (the stem) and the trailing digits (the leaves)
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-7
Example Data in ordered array: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Here, use the 10’s digit for the stem unit: Stem Leaf
21 is shown as
2
1
38 is shown as
3
8
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-8
Example (continued)
Data in ordered array: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Completed stem-and-leaf diagram: Stem
Leaves
2
1 4 4 6 7 7
3
0 2 8
4
1
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-9
Using other stem units
Using the 100’s digit as the stem:
Round off the 10’s digit to form the leaves Stem
Leaf
613 would become
6
1
776 would become
7
8
12
2
... 1224 becomes
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-10
Using other stem units (continued)
Using the 100’s digit as the stem:
The completed stem-and-leaf display: Data: 613, 632, 658, 717, 722, 750, 776, 827, 841, 859, 863, 891, 894, 906, 928, 933, 955, 982, 1034, 1047,1056, 1140, 1169, 1224
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Stem 6
Leaves 136
7
2258
8
346699
9
13368
10
356
11
47
12
2 Chap 2-11
Tabulating Numerical Data: Frequency Distributions What is a Frequency Distribution?
A frequency distribution is a list or a table …
containing class groupings (categories or ranges within which the data falls) ...
and the corresponding frequencies with which data falls within each grouping or category
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-12
Why Use Frequency Distributions?
A frequency distribution is a way to summarize data
The distribution condenses the raw data into a more useful form...
and allows for a quick visual interpretation of the data
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-13
Class Intervals and Class Boundaries
Each class grouping has the same width Determine the width of each interval by range Width of int erval ≅ number of desired class groupings
Use at least 5 but no more than 15 groupings Class boundaries never overlap Round up the interval width to get desirable endpoints
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-14
Frequency Distribution Example Example: A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature 24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-15
Frequency Distribution Example (continued)
Sort raw data in ascending order: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Find range: 58 - 12 = 46
Select number of classes: 5 (usually between 5 and 15) Compute class interval (width): 10 (46/5 then round up) Determine class boundaries (limits): 10, 20, 30, 40, 50, 60 Compute class midpoints: 15, 25, 35, 45, 55
Count observations & assign to classes
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-16
Frequency Distribution Example (continued)
Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Frequency
Relative Frequency
Percentage
10 but less than 20 20 but less than 30 30 but less than 40
3 6 5
.15 .30 .25
15 30 25
40 but less than 50 50 but less than 60
4 2
.20 .10
20 10
Class
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-17
Graphing Numerical Data: The Histogram
A graph of the data in a frequency distribution is called a histogram
The class boundaries (or class midpoints) are shown on the horizontal axis
the vertical axis is either frequency, relative frequency, or percentage
Bars of the appropriate heights are used to represent the number of observations within each class
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-18
Histogram Example Class Midpoint Frequency
10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60
(No gaps between bars)
15 25 35 45 55
3 6 5 4 2
Histogram : Daily High Tem perature 7
6
6 Frequency
Class
5
5
4
4 3
3 2
2 1
0
0
0
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
5
15
25
35
45
Class Midpoints
55
More Chap 2-19
Histograms in Excel
1 Select Tools/Data Analysis
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-20
Histograms in Excel (continued)
2 Choose Histogram
( 3
Input data range and bin range (bin range is a cell range containing the upper class boundaries for each class grouping)
Select Chart Output and click “OK” Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-21
Questions for Grouping Data into Classes
1. How wide should each interval be? (How many classes should be used?)
2. How should the endpoints of the intervals be determined?
Often answered by trial and error, subject to user judgment The goal is to create a distribution that is neither too "jagged" nor too "blocky” Goal is to appropriately show the pattern of variation in the data
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-22
How Many Class Intervals? Many (Narrow class intervals)
3 2.5 2 1.5 1 0.5 More
60
56
52
48
44
40
36
32
28
24
20
16
8
0 4
may yield a very jagged distribution with gaps from empty classes Can give a poor indication of how frequency varies across classes
12
3.5
Frequency
Temperature
Few (Wide class intervals)
may compress variation too much and yield a blocky distribution can obscure important patterns of variation.
12 10 Frequency
8 6 4 2 0 0
30
60
More
Temperature
(X axis labels are upper class endpoints)
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-23
Graphing Numerical Data: The Frequency Polygon Class Midpoint Frequency
Class 10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60
15 25 35 45 55
3 6 5 4 2
Frequency Polygon: Daily High Temperature 7 6
(In a percentage polygon the vertical axis would be defined to show the percentage of observations per class)
Frequency
5 4 3 2 1 0
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
5
15
25
35
Class Midpoints
45
55
More Chap 2-24
Tabulating Numerical Data: Cumulative Frequency Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
Frequency Percentage
Cumulative Cumulative Frequency Percentage
10 but less than 20
3
15
3
15
20 but less than 30
6
30
9
45
30 but less than 40
5
25
14
70
40 but less than 50
4
20
18
90
50 but less than 60
2
10
20
100
20
100
Total
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-25
Graphing Cumulative Frequencies: The Ogive (Cumulative % Polygon)
Less than 10 10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60
10 20 30 40 50 60
0 15 45 70 90 100
Ogive: Daily High Temperature Cumulative Percentage
Class
Lower Cumulative class boundary Percentage
100 80 60 40 20 0 10
20
30
40
50
60
Class Boundaries (Not Midpoints) Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-26
Scatter Diagrams
Scatter Diagrams are used for bivariate numerical data
Bivariate data consists of paired observations taken from two numerical variables
The Scatter Diagram: one variable is measured on the vertical axis and the other variable is measured on the horizontal axis
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-27
Scatter Diagram Example Cost per Day vs. Production Volume
Cost per day
23
125
250
26
140
200
29
146
33
160
38
167
42
170
50
188
55
195
60
200
Cost per Day
Volume per day
150 100 50 0 0
10
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
20
30
40
50
60
70
Volume per Day
Chap 2-28
Scatter Diagrams in Excel 1 Select the chart wizard
2 Select XY(Scatter) option, then click “Next”
3 When prompted, enter the data range, desired legend, and desired destination to complete the scatter diagram Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-29
Tables and Charts for Categorical Data Categorical Data
Graphing Data
Tabulating Data Summary Table
Bar Charts
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Pie Charts
Pareto Diagram
Chap 2-30
The Summary Table Summarize data by category Example: Current Investment Portfolio Investment Amount Percentage Type (in thousands $) (%)
(Variables are Categorical)
Stocks Bonds CD Savings
46.5 32.0 15.5 16.0
42.27 29.09 14.09 14.55
Total
110.0
100.0
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-31
Bar and Pie Charts
Bar charts and Pie charts are often used for qualitative (category) data
Height of bar or size of pie slice shows the frequency or percentage for each category
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-32
Bar Chart Example Current Investment Portfolio Investment Type
Amount
(in thousands $)
Percentage (%)
Stocks Bonds CD Savings
46.5 32.0 15.5 16.0
42.27 29.09 14.09 14.55
Total
110.0
100.0
Investor's Portfolio Savings CD Bonds Stocks 0
10
20
30
40
50
Amount in $1000's Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-33
Pie Chart Example Current Investment Portfolio Investment Type
Amount
(in thousands $)
Percentage (%)
Stocks Bonds CD Savings
46.5 32.0 15.5 16.0
42.27 29.09 14.09 14.55
Total
110.0
100.0
Savings 15% CD 14%
Bonds 29% Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Stocks 42%
Percentages are rounded to the nearest percent Chap 2-34
Pareto Diagram
Used to portray categorical data
A bar chart, where categories are shown in descending order of frequency
A cumulative polygon is often shown in the same graph
Used to separate the “vital few” from the “trivial many”
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-35
Pareto Diagram Example 45%
100%
40%
90%
80%
35%
70% 30% 60% 25% 50% 20% 40% 15% 30% 10%
20%
5%
10%
0%
0% Stocks
Bonds
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Savings
cumulative % invested (line graph)
% invested in each category (bar graph)
Current Investment Portfolio
CD
Chap 2-36
Tabulating and Graphing Multivariate Categorical Data
Contingency Table for Investment Choices ($1000’s)
Investment Category
Investor A
Investor B
Investor C
Total
Stocks
46.5
55
27.5
129
Bonds CD Savings
32.0 15.5 16.0
44 20 28
19.0 13.5 7.0
95 49 51
Total
110.0
147
67.0
324
(Individual values could also be expressed as percentages of the overall total, percentages of the row totals, or percentages of the column totals) Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-37
Tabulating and Graphing Multivariate Categorical Data (continued)
Side by side bar charts Comparing Investors S avings CD B onds S toc k s 0
10
20
Inves tor A Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
30 Inves tor B
40
50
60
Inves tor C Chap 2-38
Side-by-Side Chart Example
Sales by quarter for three sales territories: East West North
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr 20.4 27.4 59 20.4 30.6 38.6 34.6 31.6 45.9 46.9 45 43.9
60 50 40
East West North
30 20 10 0
1st Qtr
2nd Qtr
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
3rd Qtr
4th Qtr Chap 2-39
Principles of Graphical Excellence
Present data in a way that provides substance, statistics and design Communicate complex ideas with clarity, precision and efficiency Give the largest number of ideas in the most efficient manner Excellence almost always involves several dimensions Tell the truth about the data
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-40
Errors in Presenting Data
Using “chart junk”
Failing to provide a relative basis in comparing data between groups
Compressing or distorting the vertical axis
Providing no zero point on the vertical axis
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-41
Chart Junk Bad Presentation
Good Presentation
Minimum Wage 1960: $1.00 1970: $1.60 1980: $3.10
$
Minimum Wage
4 2 0 1960
1970
1980
1990
1990: $3.80 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-42
No Relative Basis
listen
Bad Presentation Freq. 300 200 100 0
A’s received by students.
Good Presentation % 30%
A’s received by students.
20% 10% FR SO
JR SR
0%
FR SO JR SR
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-43
Compressing Vertical Axis Bad Presentation 200
$
Good Presentation
Quarterly Sales 50
100
25
0
0 Q1 Q2
Q3 Q4
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
$
Quarterly Sales
Q1
Q2
Q3 Q4
Chap 2-44
No Zero Point On Vertical Axis Bad Presentation
$Good Presentations Monthly Sales
45
45
$
Monthly Sales
39 36
42
0
39 36
42
or
J F M A M J
J
F
J
F
M
A
M
J
$
60 40
Graphing the first six months of sales
20 0
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
M
A
M
J
Chap 2-45
Chapter Summary
Data in raw form are usually not easy to use for decision making -- Some type of organization is needed: ♦ Table ♦ Graph
Techniques reviewed in this chapter:
Ordered array and stem-and-leaf display Frequency distributions and histograms Percentage polygons and ogives Scatter diagrams for bivariate data Bar charts, pie charts, and Pareto diagrams Contingency tables and side-by-side bar charts
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 2-46
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