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Descriptive Statistics: Tabular and Graphical Presentations

Descriptive Statistics: Tabular and Graphical Presentations. Chapter 2 BA 201 – Spring 2011. Summarizing Data Using Tabular and Graphical Presentations. Categorical Data. Quantitative Data. Frequency, Relative Frequency, and Percent Frequency Distributions Dot Plot Histogram

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Descriptive Statistics: Tabular and Graphical Presentations

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  1. Descriptive Statistics:Tabular and Graphical Presentations Chapter 2 BA 201 – Spring 2011

  2. Summarizing Data Using Tabular and Graphical Presentations Categorical Data Quantitative Data Frequency, Relative Frequency, and Percent Frequency Distributions Dot Plot Histogram Cumulative Distributions Ogive Cross Tabulations Stem-and-Leaf Scatter Diagrams • Frequency, Relative Frequency, and Percent Frequency Distributions • Bar Chart • Pie Chart • Cross Tabulations

  3. Frequency Distribution • A frequency distribution is a tabular summary of data showing the frequency (or number) of items in each of several non-overlapping classes.

  4. Frequency Distribution Categorical Data Marada Inn Ratings – customer ratings Below Average Above Average Above Average Average Above Average Average Above Average Average Above Average Below Average Poor Excellent Above Average Average Above Average Above Average Below Average Poor Above Average Average Count ratings in each category

  5. Frequency Distribution Categorical Data Poor Below Average Average Above Average Excellent 2 3 5 9 1 Total 20 Rating Frequency Count for class

  6. Frequency DistributionQuantitative Data Hudson Auto Repair – cost of parts in tune-up

  7. Frequency DistributionQuantitative Data • Determine the number of non-overlapping classes. • 5 to 20 classes based on quantity of data. • Determine the width of each class. • Equal width. • =(largest value – smallest value)/# of classes • Determine the class limits. • Each item in one class only.

  8. Frequency Distribution Using six classes. Largest = 109, Smallest = 52. Hudson Auto Repair Approximate Class Width = (109 - 52)/6 = 9.5   10 50-59 60-69 70-79 80-89 90-99 100-109 2 13 16 7 7 5 Total 50 Parts Cost ($) Frequency

  9. Relative Frequency Distribution • A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class. • The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class.

  10. Percent Frequency Distribution • A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class. • The percent frequency of a class is the relative frequency multiplied by 100.

  11. Relative Frequency andPercent Frequency Distributions Relative Frequency Percent Frequency Rating Poor Below Average Average Above Average Excellent 10 15 25 45 5 100 .10 .15 .25 .45 .05 1.00 .10(100) = 10 Total 1/20 = .05

  12. Bar Chart • A bar chart is a graphical device for depicting qualitative data. • Horizontal axis – labels for classes. • Vertical axis – frequency scale.

  13. 10 9 8 7 6 5 4 3 2 1 Bar Chart Marada Inn Quality Ratings Frequency Rating Excellent Poor Average Above Average Below Average

  14. Pareto Diagram • Bar Chart • Bars arranged in descending order from left to right.

  15. 10 9 8 7 6 5 4 3 2 1 Pareto Diagram Marada Inn Quality Ratings Frequency Rating Excellent Poor Average Above Average Below Average

  16. Pie Chart • First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class. • Since there are 360 degrees in a circle, a class with a relative frequency of .25 would consume .25(360) = 90 degrees of the circle.

  17. Pie Chart Marada InnQuality Ratings Excellent 5% Poor 10% Below Average 15% Above Average 45% Average 25%

  18. Frequency Distribution Practice

  19. Dot Plot • A horizontal axis shows the range of data values. • Each data value represented by a dot above the axis.

  20. Dot Plot Hudson Auto Repair Tune-up Parts Cost 5060708090100110 Cost ($)

  21. Histogram • Variable of interest is on the horizontal axis. • A rectangle is drawn above each class interval with its height corresponding to the interval’s frequency, relative frequency, or percent frequency. • No separation between classes.

  22. 18 16 14 12 10 8 6 4 2 Histogram Hudson Auto Repair Tune-up Parts Cost Frequency Parts Cost ($) 50-59 60-69 70-79 80-89 90-99 100-110

  23. Skewness Symmetric Skewed Right Skewed Left

  24. Histogram Practice b. Start the first class at zero.

  25. Cumulative Distributions • Shows items with values less than or equal to upper limit of class: • Frequency – number of items. • Relative frequency – proportion of items. • Percent frequency – percentage of items.

  26. Cumulative Distributions Hudson Auto Repair Cumulative Relative Frequency Cumulative Percent Frequency Cumulative Frequency < 59 < 69 < 79 < 89 < 99 < 109 Cost ($) 2 15 31 38 45 50 .04 .30 .62 .76 .90 1.00 4 30 62 76 90 100 .30(100) 2 + 13 15/50

  27. Ogive • An ogive is a graph of a cumulative distribution. • Data values on horizontal axis. • Cumulative measure on vertical axis. • Frequency of each class plotted as a point. • Straight lines connect points.

  28. 100 80 60 40 20 Ogive with Cumulative Percent Frequencies Hudson Auto Repair Tune-up Parts Cost Cumulative Percent Frequency Parts Cost ($) 50 60 70 80 90 100 110

  29. Stem-and-Leaf Display • Easy way to show shape of rank order and shape of the distribution. • Leaf = right most digit. • Stem = left most digit(s).

  30. Stem-and-Leaf Display Hudson Auto Repair 5 6 7 8 9 10 2 7 2 2 2 2 5 6 7 8 8 8 9 9 9 1 1 2 2 3 4 4 5 5 5 6 7 8 9 9 9 0 0 2 3 5 8 9 1 3 7 7 7 8 9 1 4 5 5 9 a stem a leaf

  31. Example of Leaf Unit = 0.1 If we have data with values such as 8.6 11.7 9.4 9.1 10.2 11.0 8.8 a stem-and-leaf display of these data will be Leaf Unit = 0.1 8 9 10 11 6 8 1 4 2 0 7

  32. Stretched Stem-and-Leaf Display Hudson Auto Repair 5 5 6 6 7 7 8 8 9 9 10 10 2 7 2 2 2 2 5 6 7 8 8 8 9 9 9 1 1 2 2 3 4 4 5 5 5 6 7 8 9 9 9 0 0 2 3 5 8 9 1 3 7 7 7 8 9 1 4 5 5 9

  33. Stem and Leaf Practice

  34. Crosstabulation • A crosstabulation is a tabular summary for two variables. • Left and top margins define classes for variables.

  35. Crosstabulation Finger Lakes Homes The number of Finger Lakes homes sold for each style and price for the past two years is shown below. Home Style Price Range Colonial Log Split A-Frame Total 18 6 19 12 55 45 < $200,000 > $200,000 12 14 16 3 30 20 35 15 Total 100

  36. Crosstabulation Frequency distribution for the price range variable Finger Lakes Homes Home Style Price Range Colonial Log Split A-Frame Total 18 6 19 12 55 45 < $200,000 > $200,000 12 14 16 3 30 20 35 15 Total 100 Frequency distribution for the home style variable

  37. Crosstabulation: Row Percentages Finger Lakes Homes Home Style Price Range Colonial Log Split A-Frame Total 32.73 10.91 34.55 21.82 100 100 < $200,000 > $200,000 26.67 31.11 35.56 6.67 Note: row totals are actually 100.01 due to rounding. (Colonial and > $200K)/(All > $200K) x 100 = (12/45) x 100

  38. Crosstabulation: Column Percentages Finger Lakes Homes Home Style Price Range Colonial Log Split A-Frame 60.00 30.00 54.29 80.00 < $200,000 > $200,000 40.00 70.00 45.71 20.00 100 100 100 100 Total (Colonial and > $200K)/(All Colonial) x 100 = (12/30) x 100

  39. Cross Tabulation Practice

  40. Scatter Diagram and Trendline • A scatter diagram is a graphical presentation of the relationship between two quantitative variables. • A trendline provides an approximation of the relationship.

  41. Scatter Diagram Panthers Football Team The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored. Number of Interceptions Number of Points Scored 14 24 18 17 30 1 3 2 1 3

  42. 35 30 25 20 15 10 5 0 1 0 2 3 4 Scatter Diagram Number of Points Scored Number of Interceptions

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