Chap02 presenting data in chart & tables
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This document provides an overview of techniques for presenting numerical data in tables and charts. It discusses ordered arrays, stem-and-leaf displays, frequency distributions, histograms, polygons, ogives, bar charts, pie charts, and scatter diagrams. The chapter goals are to teach how to create and interpret these various data presentation methods using Microsoft Excel. Examples are provided for frequency distributions, histograms, polygons, and ogives to illustrate how to construct and make sense of these graphical representations of quantitative data.
Chap02 presenting data in chart & tables
- 1. Statistics for Managers Using Microsoft® Excel 4th Edition Chapter 2 Presenting Data in Tables and Charts Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 2-1
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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
- 11. Using other stem units (continued) Using the 100’s digit as the stem: The completed stem-and-leaf display: Data: Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Leaves 136 7 2258 8 346699 9 13368 10 356 11 47 12 613, 632, 658, 717, 722, 750, 776, 827, 841, 859, 863, 891, 894, 906, 928, 933, 955, 982, 1034, 1047,1056, 1140, 1169, 1224 Stem 6 2 Chap 2-11
- 12. 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
- 13. 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
- 14. 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
- 15. 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
- 16. 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
- 17. 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
- 18. 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
- 19. 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
- 20. Histograms in Excel 1 Select Tools/Data Analysis Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 2-20
- 21. 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
- 22. 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
- 23. 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
- 24. 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
- 25. 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
- 26. 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
- 27. 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
- 28. 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
- 29. 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
- 30. 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
- 31. 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
- 32. 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
- 33. 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
- 34. 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
- 35. 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
- 36. Pareto Diagram Example Current Investment Portfolio 100% 40% 90% 80% 35% 70% 30% 60% 25% 50% 20% 40% 15% 30% 10% 20% 5% 10% 0% cumulative % invested (line graph) % invested in each category (bar graph) 45% 0% Stocks Bonds Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Savings CD Chap 2-36
- 37. 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
- 38. 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
- 39. 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 Nor t h 30 20 10 0 1st Qt r 2nd Qt r Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. 3rd Qt r 4t h Qt r Chap 2-39
- 40. 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
- 41. 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
- 42. 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
- 43. 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
- 44. Compressing Vertical Axis Bad Presentation 200 $ Good Presentation Quarterly Sales 50 100 25 0 $ Quarterly Sales 0 Q1 Q2 Q3 Q4 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Q1 Q2 Q3 Q4 Chap 2-44
- 45. No Zero Point On Vertical Axis Bad Presentation $Good Presentations Monthly Sales 45 45 $ Monthly Sales 39 36 42 0 39 36 42 J or J F M A M 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
- 46. 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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