Basic Business Statistics 9 th Edition Chapter 2

Basic Business Statistics (9 th Edition) Chapter 2 Presenting Data in Tables and Charts © 2004 Prentice-Hall, Inc. Chap 2 -1

Chapter Topics n Organizing Numerical Data n n Tabulating and Graphing Univariate Numerical Data n n n The Ordered Array and Stem-Leaf Display Frequency Distributions: Tables, Histograms, Polygons Cumulative Distributions: Tables, the Ogive Graphing Bivariate Numerical Data © 2004 Prentice-Hall, Inc. 2

Chapter Topics n n n (continued) Tabulating and Graphing Univariate Categorical Data n The Summary Table n Bar and Pie Charts, the Pareto Diagram Tabulating and Graphing Bivariate Categorical Data n Contingency Tables n Side by Side Bar Charts Graphical Excellence and Common Errors in Presenting Data © 2004 Prentice-Hall, Inc. 3

Organizing Numerical Data Ordered Array 21, 24, 26, 27, 30, 32, 38, 41 Stem and Leaf Display Frequency Distributions and Cumulative Distributions 2 144677 3 028 4 1 Histograms Tables © 2004 Prentice-Hall, Inc. 41, 24, 32, 26, 27, 30, 24, 38, 21 Ogive Polygons 4

Organizing Numerical Data (continued) n n n Data in Raw Form (as Collected): 24, 26, 24, 21, 27, 30, 41, 32, 38 Data in Ordered Array from Smallest to Largest: Largest 21, 24, 26, 27, 30, 32, 38, 41 Stem-and-Leaf Display: 2 144677 3 028 4 1 © 2004 Prentice-Hall, Inc. 5

Tabulating and Graphing Numerical Data Ordered Array 21, 24, 26, 27, 30, 32, 38, 41 Stem and Leaf Display Frequency Distributions and Cumulative Distributions 2 144677 3 028 4 1 Histograms Tables © 2004 Prentice-Hall, Inc. 41, 24, 32, 26, 27, 30, 24, 38, 21 Ogive Polygons 6

Tabulating Numerical Data: Frequency Distributions n Sort Raw Data in Ascending Order 12, 13, 17, 21, 24, 26, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 n Find Range: 58 - 12 = 46 n Select Number of Classes: 5 (usually between 5 and 15) n Compute Class Interval (Width): 10 (46/5 then round up) n Determine Class Boundaries (Limits): 10, 20, 30, 40, 50, 60 n Compute Class Midpoints: n Count Observations & Assign to Classes © 2004 Prentice-Hall, Inc. 15, 25, 35, 45, 55 7

Frequency Distributions, Relative Frequency Distributions and Percentage Distributions Data in Ordered Array: 12, 13, 17, 21, 24, 26, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Class 10 but under 20 20 but under 30 30 but under 40 40 but under 50 50 but under 60 Total © 2004 Prentice-Hall, Inc. Relative Frequency Percentage 3 6 5 4 2 20 . 15. 30. 25. 20. 10 1 15 30 25 20 10 100 8

Graphing Numerical Data: The Histogram Data in Ordered Array: 12, 13, 17, 21, 24, 26, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 No Gaps Between Bars Class Boundaries © 2004 Prentice-Hall, Inc. Class Midpoints 9

Graphing Numerical Data: The Frequency Polygon Data in Ordered Array: 12, 13, 17, 21, 24, 26, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 © 2004 Prentice-Hall, Inc. Class Midpoints 10

Tabulating Numerical Data: Cumulative Frequency Data in Ordered Array: 12, 13, 17, 21, 24, 26, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Lower Limit 10 20 30 40 50 60 © 2004 Prentice-Hall, Inc. Cumulative Frequency 0 3 9 14 18 20 Cumulative % Frequency 0 15 45 70 90 100 11

Graphing Numerical Data: The Ogive (Cumulative % Polygon) Data in Ordered Array : 12, 13, 17, 21, 24, 26, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Class Boundaries (Not Midpoints) © 2004 Prentice-Hall, Inc. 12

Graphing Bivariate Numerical Data (Scatter Plot) © 2004 Prentice-Hall, Inc. 13

Tabulating and Graphing Univariate Categorical Data Tabulating Data The Summary Table Graphing Data Pie Charts Bar Charts © 2004 Prentice-Hall, Inc. Pareto Diagram 14

Summary Table (for an Investor’s Portfolio) Investment Category Amount Percentage (in thousands $) Stocks Bonds CD Savings Total 46. 5 32 15. 5 16 110 42. 27 29. 09 14. 55 100 Variables are Categorical © 2004 Prentice-Hall, Inc. 15

Graphing Univariate Categorical Data Tabulating Data The Summary Table Graphing Data Pie Charts Bar Charts © 2004 Prentice-Hall, Inc. Pareto Diagram 16

Bar Chart (for an Investor’s Portfolio) © 2004 Prentice-Hall, Inc. 17

Pie Chart (for an Investor’s Portfolio) Amount Invested in K$ Savings 15% Stocks 42% CD 14% Bonds 29% © 2004 Prentice-Hall, Inc. Percentages are rounded to the nearest percent 18

Pareto Diagram Axis for bar chart shows % invested in each category Axis for line graph shows cumulative % invested © 2004 Prentice-Hall, Inc. 19

Tabulating and Graphing Bivariate Categorical Data n Contingency Tables: Investment in Thousands of Dollars Investment Category Investor A Stocks Bonds CD Savings 46. 5 32 15. 5 16 55 44 20 28 27. 5 19 13. 5 7 129 95 49 51 Total 110 147 67 324 © 2004 Prentice-Hall, Inc. Investor B Investor C Total 20

Tabulating and Graphing Bivariate Categorical Data n Side by Side Charts © 2004 Prentice-Hall, Inc. 21

Principles of Graphical Excellence n Well-Designed Presentation of Data that Provides: n n n n Substance Statistics Design Communicate Complex Ideas with Clarity, Precision and Efficiency Gives the Largest Number of Ideas in the Most Efficient Manner Almost Always Involves Several Dimensions Telling the Truth about the Data © 2004 Prentice-Hall, Inc. 22

Errors in Presenting Data n n Using ‘Chart Junk’ No Relative Basis in Comparing Data between Groups n Compressing the Vertical Axis n No Zero Point on the Vertical Axis © 2004 Prentice-Hall, Inc. 23

‘Chart Junk’ Bad Presentation Good Presentation Minimum Wage 1960: $1. 00 1970: $1. 60 Minimum Wage 4 $ 2 1980: $3. 10 0 1990: $3. 80 © 2004 Prentice-Hall, Inc. 1960 1970 1980 1990 24

No Relative Basis Bad Presentation Good Presentation A’s received by students Freq. 300 200 30 % 10 0 FR SO JR SR A’s received by students FR SO JR SR FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior © 2004 Prentice-Hall, Inc. 25

Compressing Vertical Axis Bad Presentation 200 $ Good Presentation Quarterly Sales 50 100 25 0 0 Q 1 Q 2 © 2004 Prentice-Hall, Inc. Q 3 Q 4 $ Quarterly Sales Q 1 Q 2 Q 3 Q 4 26

No Zero Point on Vertical Axis Bad Presentation 45 $ Monthly Sales 42 39 45 42 39 Good Presentation $ Monthly Sales 36 36 J F M A M J 0 J F M A M J Graphing the first six months of sales © 2004 Prentice-Hall, Inc. 27

Chapter Summary n Organized Numerical Data n n Tabulated and Graphed Univariate Numerical Data n n n The Ordered Array and Stem-Leaf Display Frequency Distributions: Tables, Histograms, Polygons Cumulative Distributions: Tables, the Ogive Graphed Bivariate Numerical Data © 2004 Prentice-Hall, Inc. 28

Chapter Summary n Tabulated and Graphed Univariate Categorical Data n n n The Summary Table Bar and Pie Charts, the Pareto Diagram Tabulated and Graphed Bivariate Categorical Data n n n (continued) Contingency Tables Side by Side Charts Discussed Graphical Excellence and Common Errors in Presenting Data © 2004 Prentice-Hall, Inc. 29