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### chap02

Course: BUS 90, Spring 2009
School: San Jose State
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for Statistics 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 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...

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for Statistics 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 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 Chap 2-2 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 Chap 2-3 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Tables and Charts for Numerical Data Numerical Data Ordered Array Frequency Distributions and Cumulative Distributions Histogram Polygon Ogive Stem-and-Leaf Display Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 38 is shown as 2 3 1 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 3 4 1 4 4 6 7 7 0 2 8 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 1 8 2 613 would become 776 would become ... 1224 becomes 6 7 12 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 Stem 6 7 8 9 10 11 12 Leaves 136 2258 346699 13368 356 47 2 Chap 2-11 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 fall) ... and the corresponding frequencies with which data fall 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 Chap 2-14 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 Chap 2-16 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 Relative Frequency Class Frequency Percentage 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 3 6 5 4 2 .15 .30 .25 .20 .10 15 30 25 20 10 Chap 2-17 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 Chap 2-18 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Histogram Example 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 Class Midpoint Frequency 15 25 35 45 55 3 6 5 4 2 Histogram : Daily High Tem perature 7 6 Frequency 5 4 3 2 1 0 5 15 0 0 3 2 6 5 4 (No gaps between bars) Class Midpoints 25 35 45 55 More Chap 2-19 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 Chap 2-22 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. How Many Class Intervals? Many (Narrow class intervals) 3.5 3 2.5 Frequency 2 1.5 1 0.5 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 More may yield a very jagged distribution with gaps from empty classes Can give a poor indication of how frequency varies across classes Temperature Few (Wide class intervals) 12 10 Frequency 8 6 4 2 0 0 30 60 More Temperature may compress variation too much and yield a blocky distribution can obscure important patterns of variation. (X axis labels are upper class endpoints) Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Chap Numerical 2-23 Graphing Data: The Frequency Polygon 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 Class Midpoint Frequency 15 25 35 45 55 3 6 5 4 2 Frequency Polygon: Daily High Temperature 7 6 5 Frequency 4 3 2 1 0 5 15 25 35 45 55 More Chap 2-24 (In a percentage polygon the vertical axis would be defined to show the percentage of observations per class) Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Class Midpoints 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 Cumulative Cumulative Frequency Percentage 3 9 14 18 20 15 45 70 90 100 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 Total Frequency Percentage 3 6 5 4 2 20 15 30 25 20 10 100 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Chap 2-25 Graphing Cumulative Frequencies: The Ogive (Cumulative % Polygon) Lower Cumulative class boundary Percentage 10 20 30 40 50 60 0 15 45 70 90 100 Class 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 Ogive: Daily High Temperature Cumulative 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 Chap 2-27 Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Scatter Diagram Example Volume per day 23 26 29 33 38 42 50 55 60 Cost per day 125 140 146 160 167 170 188 195 200 Cost per Day vs. Production Volume 250 200 Cost per Day 150 100 50 0 0 10 20 30 40 50 60 70 Volume per Day Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 Tabulating Data Summary Table Bar Charts Graphing Data Pie Charts Pareto Diagram Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Chap 2-30 The Summary Table Summarize data by category Example: Current Investment Portfolio Investment Amount Percentage Type (in thousands \$) (%) Stocks Bonds CD Savings Total 46.5 32.0 15.5 16.0 110.0 42.27 29.09 14.09 14.55 100.0 Chap 2-31 (Variables are Categorical) Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 (in thousands \$) Amount Percentage (%) Stocks Bonds CD Savings Total 46.5 32.0 15.5 16.0 110.0 42.27 29.09 14.09 14.55 100.0 Savings CD Bonds Stocks 0 Investor's Portfolio 10 20 30 40 50 Chap 2-33 Amount in \$1000's Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Pie Chart Example Current Investment Portfolio Investment Type (in thousands \$) Amount Percentage (%) Stocks Bonds CD Savings Total 46.5 32.0 15.5 16.0 110.0 42.27 29.09 14.09 14.55 100.0 CD 14% Savings 15% Stocks 42% Bonds 29% Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. 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 Current Investment Portfolio 45% 100% 90% % invested in each category (bar graph) 40% 35% 80% 70% cumulative % invested (line graph) 30% 60% 25% 50% 20% 40% 15% 30% 10% 20% 5% 10% 0% Stocks Bonds Savings CD 0% Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Chap 2-36 Tabulating and Graphing Multivariate Categorical Data Contingency Table for Investment Choices (\$1000's) Investor A Investor B Investor C Total Investment Category Stocks Bonds CD Savings To...

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