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Business Statistics Chapter 2
- 1. © 2003 Prentice-Hall,Inc. Chapter 2 Presenting Data in Tables and Charts Business Statistics (9th Edition)
- 2. © 2003 Prentice-Hall,Inc. Chapter Topics Guidelines to Analyze data Organizing Numerical Data The Ordered Array Tabulating and Graphing Univariate Numerical Data Frequency Distributions: Tables, Histograms, Polygons Describing Distribution: Shape, Center and Spread Cumulative Distributions: Tables, the Ogive Graphing Bivariate Numerical Data
- 3. © 2003 Prentice-Hall,Inc. Chapter Topics Displaying Categorical Data Tabulating and Graphing Univariate Categorical Data The Summary Table Bar and Pie Charts Tabulating and Graphing Bivariate Categorical Data Contingency Tables Side by Side Bar Charts Graphical Excellence and Common Errors in Presenting Data (continued)
- 4. © 2003 Prentice-Hall,Inc. Guidelines to Analyze data First learn something about the context: What was measured? What are the units? How was the measurement carried out? Where the data measured for a particular purpose? Then make a picture. It is sometimes said that there are three rules for starting a data analysis: Plot the data, plot the data, and plot the data. Look for an overall pattern and for deviations from that pattern. Such deviations are called outliers.
- 5. © 2003 Prentice-Hall,Inc. Organizing Numerical Data Numerical Data Ordered Array Frequency Distributions Cumulative Distributions Histograms Ogive Tables 41, 24, 32, 26, 27, 27, 30, 24, 38, 21 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
- 6. © 2003 Prentice-Hall,Inc. Data in RawRaw Form (as Collected): 24, 26, 24, 21, 27, 27, 30, 41, 32, 38 Data in Ordered ArrayOrdered Array from Smallest to LargestSmallest to Largest: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 Organizing Numerical Data (continued)
- 7. © 2003 Prentice-Hall,Inc. Tabulating and Graphing Numerical Data Ogive 0 20 40 60 80 100 120 10 20 30 40 50 60 0 1 2 3 4 5 6 7 10 20 30 40 50 60 Numerical Data Ordered Array Histograms Ogive Tables 41, 24, 32, 26, 27, 27, 30, 24, 38, 21 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 Frequency Distributions Cumulative Distributions
- 8. © 2003 Prentice-Hall,Inc. Tabulating Numerical Data: Frequency Distributions 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) (To make it simple we will always use 10 as Class Interval or for this course) Determine Class Boundaries (Limits):10, 20, 30, 40, 50, 60 Compute Class Midpoints: 15, 25, 35, 45, 55 Count Observations & Assign to Classes
- 9. © 2003 Prentice-Hall,Inc. Frequency Distributions, Relative Frequency Distributions and Percentage Distributions Class Frequency 10 but under 20 3 .15 15 20 but under 30 6 .30 30 30 but under 40 5 .25 25 40 but under 50 4 .20 20 50 but under 60 2 .10 10 Total 20 1 100 Relative Frequency Percentage Data in Ordered Array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
- 10. © 2003 Prentice-Hall,Inc. Graphing Numerical Data: The Histogram Histogram 0 3 6 5 4 2 0 0 1 2 3 4 5 6 7 5 15 25 35 45 55 More 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 No Gaps Between Bars Class Midpoints Class Boundaries
- 11. © 2003 Prentice-Hall,Inc. Bar Chart How tall are the tallest soldiers in this group? 1. How many in this group are between 65 and 67 inches tall? 2. If we selected a soldier at random from this group, would you estimate that he or she is more likely to be taller than 65 inches or shorter than 65 inches? (Hint: No calculation is needed. Judge from the way the display looks.)
- 12. © 2003 Prentice-Hall,Inc. Tabulating Numerical Data: Cumulative Frequency Lower Cumulative Cumulative Limit Frequency % Frequency 10 0 0 20 3 15 30 9 45 40 14 70 50 18 90 60 20 100 Data in Ordered Array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Always Starts at Zero Always Ends at at 100%
- 13. © 2003 Prentice-Hall,Inc. Graphing Numerical Data: The Ogive (Cumulative % Polygon) Ogive 0 20 40 60 80 100 10 20 30 40 50 60 Class Boundaries (Not Midpoints) Data in Ordered Array : 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
- 14. © 2003 Prentice-Hall,Inc. Graphing Bivariate Numerical Data (Scatter Plot) Mutual Funds Scatter Plot 0 10 20 30 40 0 10 20 30 40 Net Asset Values TotalYearto DateReturn(%)
- 15. © 2003 Prentice-Hall,Inc. Tabulating and Graphing Univariate Categorical Data Categorical Data Tabulating Data The Summary Table Graphing Data Pie Charts Pareto DiagramBar Charts
- 16. © 2003 Prentice-Hall,Inc. Univariate and Bivariate Analysis by Tables and Charts of Car Data Variables: •Miles per Gallon •Type of Drive •Weight
- 17. © 2003 Prentice-Hall,Inc. Variables We will be looking at 3 variables relating to cars We Will use Histograms Ogives Scatter Plots (Bivariate Data)
- 18. © 2003 Prentice-Hall,Inc. The following Data Relates to Front and Rear Wheel Drive Cars Drive Type and Miles per Gallon (Rear) Cumulative Frequency 12 to under 14 13 2 8.0% 12 0 0.00% 14 to under 16 15 4 16.0% 14 0 0.00% 16 to under 18 17 3 12.0% 16 4 17.39% 18 to under 20 19 8 32.0% 18 7 30.43% 20 to under 22 21 4 16.0% 20 15 65.22% 22 to under 24 23 2 8.0% 22 19 82.61% 24 to under 26 25 2 8.0% 24 21 91.30% 26 to under 28 27 0 0.0% 26 23 100.00% 28 to under 30 29 0 0.0% 28 23 100.00% 30 to under 32 31 0 0.0% 30 23 100.00% 32 to under 34 33 0 0.0% 32 23 100.00% Total 25 100.0% Cumulative % Frequency Distribution Percentage Distribution Lower Limit Cumulative Frequency Lo wer Upper Limit Mid points Drive Type and Miles per Gallon (Front) Cumulative Frequency 12 to under 14 13 0 0.00% 12 0 0.00% 14 to under 16 15 3 3.70% 14 0 0.00% 16 to under 18 17 1 1.23% 16 3 3.70% 18 to under 20 19 12 14.81% 18 4 4.94% 20 to under 22 21 19 23.46% 20 16 19.75% 22 to under 24 23 22 27.16% 22 35 43.21% 24 to under 26 25 11 13.58% 24 57 70.37% 26 to under 28 27 6 7.41% 26 68 83.95% 28 to under 30 29 4 4.94% 28 74 91.36% 30 to under 32 31 3 3.70% 30 78 96.30% 32 to under 34 33 0 0.00% 32 81 100.00% Cumulative % Frequency Distribution Percentage Distribution Lower Limit Cumulative Frequency Lower limit Upper Limit Mid points
- 19. © 2003 Prentice-Hall,Inc. 0% 20% 40% 60% 80% 100% 120% 12 14 16 18 20 22 24 26 28 30 32 Lower Limits: Miles per Gallon Percentage Ogive: Front Wheel Drive What percentage of the Front wheel Drive Cars do: - •More than 19 miles per gallon •Less than 27 Miles per gallon Estimate the miles per gallon for: - •50 Percentile of Front Wheel Drive Cars: •25 Percentile of Front Wheel Drive Cars
- 20. © 2003 Prentice-Hall,Inc. 0% 20% 40% 60% 80% 100% 120% 12 14 16 18 20 22 24 26 28 30 Lower limit: Miles per Gallon Percentage Ogive: Rear Wheel Drive What percentage of the Rear wheel Drive Cars do: - •More than 19 miles per gallon •Less than 27 Miles per gallon Estimate the miles per gallon for: - •50 Percentile of Rear Wheel Drive Cars: •Rear Percentile of Front Wheel Drive Cars
- 21. © 2003 Prentice-Hall,Inc. To Compare Distributions Compare Frequency and Percentage Polygons for Front and Rear Drive Cars Compare Ogives for Front and Rear Drive Cars
- 22. © 2003 Prentice-Hall,Inc. 0% 20% 40% 60% 80% 100% 120% 12 14 16 18 20 22 24 26 28 30 32 Lower Limit Miles per Gallon Front Rear Cumulative Percentage Polygon: Drive Type and Miles per Gallon Answer the following True or False. This graph shows: • Overall the miles per gallon for Front Wheel is better than Rear Wheel Drive Cars • 80% of Front Wheel Drive Cars do less than 21 Miles per gallon
- 23. © 2003 Prentice-Hall,Inc. Car Weight (lbs) V’s Miles per Gallon 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 0 5 10 15 20 25 30 35 Miles per Gallon Weight (lbs) Answer the Following True or False. This graph shows: • Overall the Weight of the car is associated with the Miles per gallon • The Heavier the car the greater the miles per gallon
- 24. © 2003 Prentice-Hall,Inc. Displaying Categorical Data Three Rules of Data Analysis: - Make a picture – It will reveal things you can not see on a table and will help you think clearly Make a picture – Well designed display will show the important features and patterns in your data i.e. missing wrong data or unexpected patterns Make Picture –It is the best way to tell others what about your data.
- 25. © 2003 Prentice-Hall,Inc. Frequency Tables 1. What is the most common hair color in this group of children? 2. What is the second most common color? 3. Are the categories given here well-defined? 4. If not, how would you improve them? 5. Does this distribution of hair colors resemble the distribution you see among people in Cambodia? 6. If not, how does it differ? Fair Red Medium Dark Black 27% 5.3% 39.7% 25.8 % 2.2%
- 26. © 2003 Prentice-Hall,Inc. 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% Red Medium Dark Black Bar Chart 1. What is the most common hair color in this group of children? 2. What is the second most common color? 3. Is there a greater difference between the relative frequencies of Red and Black, or between the relative frequencies of Medium and Dark?
- 27. © 2003 Prentice-Hall,Inc. Graphing Univariate Categorical Data 0 10 20 30 40 50 Stoc ks B onds S avings CD Categorical Data Tabulating Data The Summary Table Graphing Data Pie Charts Bar Charts
- 28. © 2003 Prentice-Hall,Inc. Tabulating and Graphing Bivariate Categorical Data Contingency Tables: Standard of Living A B C Total Rich 8 5 0 13 Medium 15 10 1 26 Poor 39 39 25 103 Poorest 37 41 50 128 Total 99 95 76 270 Standard of Living A B C Total Rich 8% 5% 0% 5% Medium 15% 11% 1% 10% Poor 39% 41% 33% 38% Poorest 37% 43% 66% 47% Total 100% 100% 100% 100% Cummune Cummune
- 29. © 2003 Prentice-Hall,Inc. Pie Chart (Analyzing Standard of Living in 4 Communes) Rich 5% Medium 10% Poor 38% Poorest 47% Rich Medium Poor Poorest Standard of Living
- 30. © 2003 Prentice-Hall,Inc. Bivariate Categorical Data (for Standard of Living by Commune) 0 10 2 0 3 0 4 0 5 0 6 0 Rich Medium Poor Poorest C B A Commun e Frequency
- 31. © 2003 Prentice-Hall,Inc. Stacked Bar Chart Bivariate Categorical Data 0% 20% 40% 60% 80% 100% A B C Poorest Poor Medium Rich Which commune has the largest percentage of the Poorest?
- 32. © 2003 Prentice-Hall,Inc. Principles of Graphical Excellence Well-Designed Presentation of Data that Provides: 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
- 33. © 2003 Prentice-Hall,Inc. Errors in Presenting Data Using ‘Chart Junk’ No Relative Basis in Comparing Data between Groups Compressing the Vertical Axis No Zero Point on the Vertical Axis
- 34. © 2003 Prentice-Hall,Inc. ‘Chart Junk’ Good Presentation 1960: $1.00 1970: $1.60 1980: $3.10 1990: $3.80 Minimum Wage Minimum Wage 0 2 4 1960 1970 1980 1990 $ Bad Presentation
- 35. © 2003 Prentice-Hall,Inc. No Relative Basis Good Presentation A’s received by students A’s received by students Bad Presentation 0 100 200 300 FR SO JR SR Freq. 0 10 20 30 FR SO JR SR % FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior
- 36. © 2003 Prentice-Hall,Inc. Compressing Vertical Axis Good Presentation Quarterly Sales Quarterly Sales Bad Presentation 0 25 50 Q1 Q2 Q3 Q4 $ 0 100 200 Q1 Q2 Q3 Q4 $
- 37. © 2003 Prentice-Hall,Inc. No Zero Point on Vertical Axis Good Presentation Monthly Sales Monthly Sales Bad Presentation 0 39 42 45 J F M A M J $ 36 39 42 45 J F M A M J $ Graphing the first six months of sales 36
- 38. © 2003 Prentice-Hall,Inc. Chapter Summary Organized Numerical Data The Ordered Array and Stem-Leaf Display Tabulated and Graphed Univariate Numerical Data Frequency Distributions: Tables, Histograms, Polygons Cumulative Distributions: Tables, the Ogive Graphed Bivariate Numerical Data
- 39. © 2003 Prentice-Hall,Inc. Chapter Summary Tabulated and Graphed Univariate Categorical Data The Summary Table Bar and Pie Charts, the Pareto Diagram Tabulated and Graphed Bivariate Categorical Data Contingency Tables Side by Side Charts Discussed Graphical Excellence and Common Errors in Presenting Data (continued)