Chapter 2_Presentation of Data.ppt mean, median, mode, variance
- 1. Graphs, Charts, and Tables- Presenting Your Data Chapter 2 BUB3123N: BUSINESS STATISTICS
- 2. Learning Outcomes Outcome 1. Construct frequency distributions. Outcome 2. Construct and interpret a frequency histogram. Outcome 3. Develop and interpret joint frequency distributions. Outcome 4. Construct and interpret various types of bar charts. Outcome 5. Build a stem and leaf diagram. Outcome 6. Create a line chart and interpret the trend in the data. Outcome 7. Construct a scatter diagram and interpret it.
- 3. Tabular and Graphical Procedures Data Qualitative Data Quantitative Data Tabular Methods Tabular Methods Graphical Methods Graphical Methods •Frequency Distribution •Rel. Freq. Dist. •% Freq. Dist. •Bar Graph •Pie Chart •Stem-and-Leaf •Frequency Distribution •Rel. Freq. Dist. •Cum. Freq. Dist. •Cum. Rel. Freq. Distribution •Histogram •Line graph •Scatter diagram 3
- 4. Tabular and Graphical Presentations Tabular and Graphical Presentations • Summarizing Qualitative Data • Summarizing Quantitative Data 4
- 5. Summarizing Qualitative Data • Frequency distributions • Relative Frequency • Percent Frequency Distribution • Bar Graph • Pie Chart 5
- 6. Summarizing Qualitative Data • A frequency distribution: a tabular summary of data showing the frequency (or number) of items in each of several nonoverlapping classes. • The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data. Frequency Distribution 6
- 7. Example: Swiss Inn Guests staying at Swiss Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are Above average Below average Below average Below average Average Poor Poor Above average Above average Excellent Above average Above average Average Above average Above average Average Above average Average Above average Average At issue: How do we summarize the information in the above box? 7
- 8. Frequency Distribution Poor Below Average Average Above Average Excellent 2 3 5 9 1 Total 20 Rating Frequency (f) Frequency Distribution 8
- 9. Relative Frequency Distribution • The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class. • A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class. 9
- 10. • The percent frequency of a class is the relative frequency multiplied by 100. • A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class. Percent Frequency Distribution 10
- 11. Relative Frequency and Percent Frequency Distributions .10(100) 1/20 Rating Frequency(f) Relative Frequency Percent Frequency Poor 2 0.10 10 Below average 3 0.15 15 Average 5 0.25 25 Above average 9 0.45 45 Excellent 1 0.05 5 Total 20 1.00 100 11
- 12. Bar Charts • A graphical representation of a categorical data set in which a rectangle or bar is drawn over each category or class • The length or height of each bar represents the frequency or percentage of observations or some other measure associated with the category. • The bars may be vertical or horizontal.
- 13. Bar Chart Example (Vertical)
- 14. Bar Chart Example (Vertical) 2015 New Car Sales for the Top Ten Automobile Companies (USA)
- 15. Bar Chart Example (Vertical) Starting Salary Data
- 16. Bar Chart Example (Horizontal)
- 17. Pie Charts • A graph in the shape of a circle. • Use to show visually the parts of a total • The circle is divided into “slices” corresponding to the categories or classes to be displayed. • The size of each slice is proportional to the magnitude of the displayed variable associated with each category or class.
- 18. 1-18 Constructing Pie Chart 1. Collect data that represents categories and their corresponding values. Product A: 40 units Product B: 30 units Product C: 20 units Product D: 10 units 2. Calculate Percentages: Add up the total of all values. Divide each category's value by the total and multiply by 100 to get percentages Total units = 40 + 30 + 20 + 10 = 100 Product A = (40 / 100) * 100 = 40% Product B = (30 / 100) * 100 = 30% Product C = (20 / 100) * 100 = 20% Product D = (10 / 100) * 10 = 10%
- 19. 1-19 Constructing Pie Chart 3. Convert Percentages to Angles: •A pie chart is a circle of 360 degrees. •To find the angle for each category, multiply the percentage by 360. 4. Draw the Pie Chart: •Draw a circle. •Use a protractor to mark the angles for each category, starting from a fixed point (like the top of the circle). •Label each segment with the category name and percentage.
- 21. 2-21 Pie Chart Example Golfers’ Responses to What Technology is Most Important in Determining Driving Distance off the Tee.
- 22. Incorrect Use of a Pie Chart The Tax Dollars Allocated by the State of Idaho to Each of the Four Higher Education Facilities in the State
- 23. Why is This the Wrong Type of Chart?
- 24. Summarizing Quantitative Data • Stem-and-Leaf • Frequency Distribution • Relative Frequency Distribution • Cumulative Frequency Distribution • Histogram • Line graph • Scatter diagram 24
- 25. Stem-and-Leaf 5 2 7 6 2 2 2 2 7 7 7 8 8 8 9 9 9 7 2 2 2 2 4 4 4 5 5 5 7 7 7 9 9 9 8 0 0 2 2 2 8 9 9 3 3 7 7 7 8 9 10 1 5 5 5 9 •A stem-and-leaf display shows both the rank order and shape of the distribution of the data. Each line in the display is referred to as a stem. •Each digit on a stem is a leaf. First digit Last digit Key : means 91 25
- 26. A. Raw data B. Data array (from lowest to highest) 93 77 93 57 75 52 99 80 97 62 72 69 72 89 67 75 79 75 72 77 105 74 62 68 97 105 77 67 80 109 82 97 88 68 82 68 72 69 67 74 62 82 98 101 79 105 79 69 62 74 52 62 68 72 74 77 79 82 97 101 57 67 68 72 74 77 80 88 97 105 62 67 69 72 75 77 80 89 97 105 62 67 69 72 75 79 82 93 98 105 62 68 69 74 75 79 82 93 99 109 26
- 27. 52 62 68 72 74 77 79 82 97 101 57 67 68 72 74 77 80 88 97 105 62 67 69 72 75 77 80 89 97 105 62 67 69 72 75 79 82 93 98 105 62 68 69 74 75 79 82 93 99 109 x f 52 1 57 1 62 4 67 3 68 3 69 3 72 4 74 3 75 3 77 3 79 3 80 2 82 3 88 1 89 1 93 2 97 3 98 1 99 1 101 1 105 3 109 1 We said ungrouped because each value of x in the distribution stands alone Ungrouped Frequency Distribution 27
- 28. Grouped Frequency Distribution • Guidelines for Selecting Number of Classes Use between 5 and 15 classes. 2k > n, where k = number of classes, n = number of observation 2k > 50, k log 2 > log 50, k > 5.64 ≈ 6 • Guidelines for Selecting Width of Classes Use classes of equal width. . Approximate Class Width (i) ≥ ≥ Largest Data Value (H) Smallest Data Value (L) Number of Classes (k) 28
- 29. Grouped Frequency Distribution • Class interval is the difference between the upper and lower class boundaries of any class. E.g. 59.5-69.5 = 10 • Class limits are the smallest and largest observations (data, events etc) in each class. Therefore, each class has two limits: a lower and upper. E.g. 60 – 69 • Class Boundaries (true class limits) are numbers that do not occur in the sample data but are halfway between the upper limit of one class and the lower limit of the next class. Therefore, each class has an upper and lower class boundary. E.g. 59.5 – 69.5 29
- 30. Grouped Frequency Distribution • Determine Class Boundaries (Limit) Class limits are the lower and upper values of the classes. Class Boundaries are the lower and upper values of a class that mark common points between classes. Class 50-59 70-79 80-89 100-109 60-69 90-99 Lower boundary =59.5 Lower boundary =89.5 Upper boundary =69.5 Upper boundary =99.5 Lower Limit=60 Lower Limit=90 Upper Limit=69 Upper Limit=99 30
- 31. • Compute Class Midpoints: Class Mid-points are situated in the centre of the classes. They can be identified as being mid-way between the upper and lower boundaries (or limits) • Count observations and assign to classes Class 50-59 70-79 80-89 100-109 60-69 90-99 Class width= 10 (69.5-59.5) Mid-point= (60+69)/2=64.5 (NOT 65) Class width= 10 (99.5-89.5) Mid-point= (90+99)/2=94.5 (NOT 95) Grouped Frequency Distribution 31
- 32. Grouped Frequency Distribution For William Auto Repair, if we choose six classes: Approximate Class Width = (109 - 52)/6 = 9.5 10 Parts Cost ($) Boundary Class Mid point (x) Tally Frequency(f) 50-59 49.5-59.5 54.5 II 2 60-69 59.5-69.5 64.5 IIII IIII III 13 70-79 69.5-79.5 74.5 IIII IIII IIII I 16 80-89 79.5-89.5 84.5 IIII II 7 90-99 89.5-99.5 94.5 IIII II 7 100-109 99.5-109.5 104.5 IIII 5 Total 50 32
- 33. Relative Frequency and Percent Frequency Distributions 2/50 .04(100) Only 4% of the parts costs are in the $50- 59 class. 30% of the parts costs are under $70. The greatest percentage (32% or almost one-third) of the parts costs are in the $70-79 class. 10% of the parts costs are $100 or more. 7/50 .14(100) Insights Gained from the Percent Frequency Distribution Parts Cost ($) Frequency (f) Relative Frequency Percent Frequency 50-59 2 0.04 4 60-69 13 0.26 26 70-79 16 0.32 32 80-89 7 0.14 14 90-99 7 0.14 14 100-109 5 0.10 10 Total 50 1.00 100 33
- 34. More on Frequency Distributions • Cumulative Frequency Distribution – a summary of a set of data that displays the number of observations with values less than or equal to the upper limit of each of its classes • Cumulative Relative Frequency Distribution – a summary of a set of data that displays the proportion of observations with values less than or equal to the upper limit of each of its classes
- 35. Example: DVD Movies Owned
- 36. Graphic Presentation of a Frequency Distribution: Histogram • A Graph That Displays a Frequency Distribution – Horizontal Axis Contains the Possible Outcomes for the Variable of Interest – Vertical Axis Shows the Frequency for Each Possible Outcome – No Gaps Between Bars
- 37. Frequency Histogram Number of Late Deliveries Per Month
- 38. Frequency Histogram Tesco, Penang Product Categories Frequency Distribution Tesco Customer Product Categories
- 39. Line Charts and Scatter Diagrams • Line Chart – A two-dimensional chart showing time on the horizontal axis and the variable of interest on the vertical axis – Use to Display Time-Series
- 41. Constructing Line Charts • Step 1: Identify the time-series variable of interest and determine the maximum value and the range of time periods covered in the data. • Step 2: Construct the horizontal axis for the time periods. Construct the vertical axis with a scale appropriate for the range of values. • Step 3: Plot the points of the graph and connect them with straight lines
- 42. Line Chart Example – Separate Charts
- 43. Line Chart Example – Both Variables on Same Chart
- 44. Improved Line Chart – Two Vertical Axes
- 45. A two-dimensional graph of plotted points in which the vertical axis represents values of one quantitative variable and the horizontal axis represents values of the other quantitative variable. Scatter Diagram
- 46. Scatter Diagram • Also called the scatter plot • Shows the relationship between two quantitative variables • Dependent Variable – Values are thought to be a function of another variable • Independent Variable – Values are thought to impact the values of the dependent variable
- 47. Scatter Diagrams Reveal Relationships
- 48. Constructing Scatter Diagrams • Step 1: Identify the dependent and independent variable. • Step 2: Collect values for the two variables. • Step 3: Construct the horizontal axis using the independent variable. Construct the vertical axis using the dependent variable • Step 4: Plot the points of the graph. (don’t connect the points.)
- 49. Scatter Diagram Example Volume per day Cost per day 23 125 26 140 29 146 33 160 38 167 42 170 50 188 55 195 60 200
Editor's Notes
- #7: At issue: How do we summarize the information in the above box?