Giải tích 1 - Chapter 2: Tabular and graphical presentations

Chapter 2 TABULAR AND GRAPHICAL PRESENTATIONS MBA Nguyen Tien Dung School of Economics and Management Website: https://sites.google.com/site/nguyentiendungbkhn Email: dung.nguyentien3@hust.edu.vn Main Contents 2.1 Summarising Data for a Categorical Variable 2.2 Summarising Data for a Quantitative Variable 2.3 Summarising Data for Two Variables Using Tables 2.4 Summarising Data for Two Variables Using Graph Displays 2.5 Data Visualisation: Best Practices In Creating Effective © Nguyễn Tiến Dũng Applied Statistics for Business 2 2.1 SUMMARISING DATA FOR A CATEGORICAL VARIABLE ●Frequency Distribution ●Relative Frequency and Percent Frequency ●Bar Charts and Pie Charts © Nguyễn Tiến Dũng Applied Statistics for Business 3 Frequency Distribution Table ● A tabular summary of data showing the number (frequency) of items in each of several nonoverlapping classes. © Nguyễn Tiến Dũng Applied Statistics for Business 4 Relative Frequency and Percent Frequency Distributions © Nguyễn Tiến Dũng Applied Statistics for Business 5 Bar Chart and Pie Chart © Nguyễn Tiến Dũng Applied Statistics for Business 6 2.2 SUMMARISING DATA FOR A QUANTITATIVE VARIABLE ●Frequency Distribution ●Relative Frequency and Percent Frequency Distributions ●Dot Plot ●Histogram ●Cumulative Distributions ●Stem-and-Leaf Display © Nguyễn Tiến Dũng Applied Statistics for Business 7 Frequency Distribution ●Number of nonoverlapping classes ● By a formula ● On purpose: 3-20 ●Width of each class ●The class lower and upper limits © Nguyễn Tiến Dũng Applied Statistics for Business 8 © Nguyễn Tiến Dũng Applied Statistics for Business 9 ●Step 1: Determining the number of classes ● Xmin = 12; Xmax = 33  Max – Min = 33 – 12 = 21. ● Select: k = 4; or k = 5  Textbook: k = 5 ●Step 2: Determining the class width ● Normally: w = (Max – Min)/ k ● Here, textbook: Min (the lower bound of the first class) = 10; Max = 35  w = (35-10)/5 = 5 ●Step 3: Allocating the observed data into classes ● Sorting the data set in the ascending order ● Allocating ●Step 4: Establishing the frequency table © Nguyễn Tiến Dũng Applied Statistics for Business 10 Principles of allocating the data points into classes ●No overlapping cases: one observation must belong to only one class ● If an observation belongs to the upper bound of one class, put it into the next class ● Class 1: 10 – 15 days ● Class 2: 15 – 20 days ● X3 = 15 -> Class 2 © Nguyễn Tiến Dũng Applied Statistics for Business 11 Open-ended classes ●An example: Working years for a company ● Less than 1 years ● 1 – 3 years ● 3 – 5 years ● More than 5 years © Nguyễn Tiến Dũng Applied Statistics for Business 12 ● Audit days: ● Less than 15 ● 15-19 ● 20-29 ● 29-34 ● 35 and more Dot Plot © Nguyễn Tiến Dũng Applied Statistics for Business 13 Histogram = Frequency Distribution Chart © Nguyễn Tiến Dũng Applied Statistics for Business 14 Different Levels of Skewness © Nguyễn Tiến Dũng Applied Statistics for Business 15 Cumulative Distributions © Nguyễn Tiến Dũng Applied Statistics for Business 16 Ogive = Cumulative Frequency Chart © Nguyễn Tiến Dũng Applied Statistics for Business 17 2.3 EXPLORATORY DATA ANALYSIS: THE STEM- AND-LEAF DISPLAY ● Number of questions answered correctly on an aptitude test ● N = 150 © Nguyễn Tiến Dũng Applied Statistics for Business 18 Stem and Leaf Diagram © Nguyễn Tiến Dũng Applied Statistics for Business 19 2.4 CROSSTABULATIONS AND SCATTERED DIAGRAMS ●Crosstabulation ●Simpson’s Paradox ●Scatter Diagram and Trendline © Nguyễn Tiến Dũng Applied Statistics for Business 20 Crosstabulation © Nguyễn Tiến Dũng Applied Statistics for Business 21 Crosstab in Excel: Pivot Table © Nguyễn Tiến Dũng Applied Statistics for Business 22 Simpson’s Paradox ● Be careful in drawing conclusions from a crosstab ● From the same data set, a conclusion based upon aggregated data in a crosstab may be conflicted with a conclusion based on another crosstab based on unaggregated (detailed) data. © Nguyễn Tiến Dũng Applied Statistics for Business 23 Unaggregated data ● Type of court: a hidden variable © Nguyễn Tiến Dũng Applied Statistics for Business 24 Scatter Diagram and Trendline ● A scatter diagram: a dotted graphical presentation of the relationship between two quantitative variables ● A trendline: a line that provides an approximation of the relationship. © Nguyễn Tiến Dũng Applied Statistics for Business 25 ● Excel: Charts >> Scatter >> Add Trendline © Nguyễn Tiến Dũng Applied Statistics for Business 26 Types of Relationship Depicted by Scatter Diagrams © Nguyễn Tiến Dũng Applied Statistics for Business 27 Tabular And Graphical Methods For Summarising Data © Nguyễn Tiến Dũng Applied Statistics for Business 28 Exercises for Homework Section Exercises 2.1 3, 5(2012Names) 2.2 15, 17, 18 2.3 29, 30, 28(Crosstab2) 2.4 37, 38, 39(MPG) © Nguyễn Tiến Dũng Applied Statistics for Business 29