Data Presentation PDF

Data Presentation Dr. Wilson Cordova, LPT Presentation of Data Numerical quantities focus on expected values, graphical summaries on unexpected values. (John Tukey) Textual Tabular Graphical  Textual Data are...

Data Presentation Dr. Wilson Cordova, LPT Presentation of Data Numerical quantities focus on expected values, graphical summaries on unexpected values. (John Tukey) Textual Tabular Graphical  Textual Data are presented in paragraph form. It involves enumeration of important characteristics, giving emphasis on significant figures and identifying the important features of the data. Example: The data are DSILYTC test scores of 15 students out of 50 items: 47, 48, 49, 42, 42, 36, 38, 40, 35, 50, 44, 45, 45, 50, 50. Make simple analysis by writing findings, drawing conclusions and making an inference. Writing the data in an array form or order 35, 36, 38, 40, 42, 42, 44, 45, 45, 47, 48, 49, may 50, 50, 50. help to analyze the data. Findings: “The lowest score is 35, and the highest is 50. Three students got a perfect score of 50, one got 35, 36, 38, 40, 44, 47, 48 and 49 while 2 got 42 and 45”. If the passing mark is 70%, it shows that nobody failed in the test. Conclusion: “I therefore conclude that the students perform well in the test”. Inference: “If this trend will continue, then it is likely that  Tabular Sometimes we could hardly grasp information from a textual presentation of data. Thus, we may present data using tables. Examples: Table number & Title Table 3a: Distribution of Students in ABS High School According to Year Level Year Level Number of Percentage Students Frequency Freshmen 350 0.3182 Sophomore 300 0.2727 Junior 250 0.2273 Senior 200 0.1818 N = 1,100 Source: ABC College Registrar Table 3b: The Ungrouped Frequency Distribution Table for the Age of 50 Service Crews at Delicious Restaurant Age Frequency Percentage Frequency 18 8 0.1600 19 7 0.1400 20 6 0.1200 21 11 0.2200 22 4 0.0800 23 6 0.1200 24 4 0.0800 25 4 0.0800 N = 50 Table 3c: The Grouped Frequency Distribution for the Age of 50 Service Crews at Delicious Restaurant Age Frequency Percentage Frequency 18-19 15 0.3000 20-21 17 0.3400 22-23 10 0.2000 24-25 8 0.1600 N = 50 Between 5 to 10 is the ideal no. of rows!  is a tabular summary of data showin the frequency (or number) of items each of several non-overlapping class Steps in Constructing Frequency Distribution Table Step 1: Determine the range, denoted by R. R – the difference between the highest value and the lowest value Step 2: Decide on the number of classes, denoted by k. k – no. of non-overlapping intervals Step 3: Compute for the class size, denoted by c. c – quotient of steps 1 and 2. Step 4: Identify the class intervals, CI. Step 5: Identify the frequency in each CI or tallying. Consider the following are the ages of the first 35 early morning customers of McDonalds 18 32 22 12 26 21 34 23 15 27 21 37 23 15 28 18 31 22 10 25 21 39 24 16 28 21 39 24 17 29 20 33 22 14 26 Construct an FDT with Six (6) Classes 18 32 22 12 26 10 18 22 25 31 21 34 23 15 27 12 18 22 26 32 21 37 23 15 28 14 20 22 26 33 18 31 22 10 25 15 21 23 27 34 21 39 24 16 28 15 21 23 28 37 21 39 24 17 29 16 21 24 28 39 20 33 22 14 26 17 21 24 29 39 Construct an FDT with Six (6) Classes 10 18 22 25 31 1: R = HV – LV = 39 – 10 = 29 12 18 22 26 32 2: k = 6 classes 14 20 22 26 33 15 21 23 27 34 3: c = 29/6 = 4.83 ~ 5.0 15 21 23 28 37 4: CI (inclusive) 16 21 24 28 39 17 21 24 29 39 5: Tally (frequency) See next slides for steps 4 and 5 Class Size /Class Width – The difference between the upper (or lower) class limits of consecutive classes. All classes should have the same class width. Lower Class Limit – The least value that can belong to a class. Upper Class Limit – The greatest value that can belong to a class. FDT Class Tally frequenc CI f Interva y l 10- 3 10-14 3 14 15-19 6 15- 6 19 20-24 12 20- 12 25-29 7 24 30-34 4 25- 7 35-39 3 29 30- 4 34  Additional Info about FDT Class Boundaries (CB)– the numbers that separate classes without forming gaps between them. Class Mark / Midpoint (CM) – the middle value of each data class. To find the class midpoint, average the upper and lower class limits. Relative Frequency (RF)– obtained by dividing the frequency of the given class by the total number of observations. FDT Class frequenc Class Class Relative Interva y Boundary Mark Frequenc l / Tally y 10-14 3 9.5-14.5 12 0.0857 15-19 6 14.5- 17 0.1714 19.5 20-24 12 19.5- 22 0.3429 24.5 25-29 7 24.5- 27 0.2000 29.5 30-34 4 29.5- 32 0.1143 34.5  Additional Info about FDT Less than CF (CF) – total number of observations within a class whose values are not less than the lower limit of the class Cumulative frequency of a data class – the number of data elements in that class and all previous classes. (may be ascending or descending.) FDT CI f CB CM RF CF 10-14 3 9.5-14.5 12 0.0857 3 35 15-19 6 14.5- 17 0.1714 9 32 19.5 20-24 12 19.5- 22 0.3429 21 26 24.5 25-29 7 24.5- 27 0.2000 28 14 29.5 30-34 4 29.5- 32 0.1143 32 7 34.5 35-39 3 34.5- 37 0.0857 35 3 39.5 Presentation of Data Graphical Types of Graphs: 1] Pie chart/ circle graph – any data MOST POPULAR 2] Bar graph - Bar chart [with gaps between bars] – discrete data - Histogram [no gaps between bars] – continuous data 3] Line graph - Frequency polygon – continuous data  Graphical Rules to remember in constructing graphs: 1] Labels: - Figure number [below the graph] - Figure title [below the graph] - for Pie chart, % should be indicated - for Bar graph, axis should be labeled 2] Textual explanation should also follow any graph  Show how to Graph Table 3a: Distribution of… 400 Year Level Freq. 350 300 Frosh 350 250 Sophomore 300 200 150 Junior 250 100 Senior 200 50 N=1,100 0 Frosh Sophomore Junior Senior 12 10 8 6 4 2 0 18 19 20 21 22 23 24 25  12 Bar Chart 10 Base: Class Interval 8 Height: Frequency (c.i) f 10 - 14 3 6 15 - 19 6 4 20 - 24 12 2 25 - 29 7 0 10 to 14 20 to 24 30 to 34 30 - 34 4 35 - 39 3 Figure 1: The Bar Chart for the ‘Frequency’ of Ages of 35 early morning customers at McDo Take Note !! There are gaps between bars. This is appropriate to use for discrete variables!  12 Histogram 10 Base: Class Boundary Height: 8 Frequency CI f CB 6 10 - 14 3 9.5-14.5 4 15 - 19 6 14.5-19.5 2 20 - 24 12 19.5-24.5 25 - 29 7 24.5-29.5 0 30 - 34 4 29.5-34.5 14.5 19.5 24.5 29.5 39.5 34.5 9.5 35 - 39 3 34.5-39.5 Figure 2: The Histogram for the ages of 35 early morning customers at McDo Take Note !! There is no gap between bars. This is appropriate to use for continuous variables!  14 Frequency 12 Polygon (CI) f CM 10 8 10 - 14 3 12 6 15 - 19 6 17 20 - 24 12 22 4 Base: Class Mark 25 - 29 7 27 2 Height: Frequency 30 - 34 4 32 35 - 39 3 37 0 Take Note !! 7 12 17 22 27 32 37 42 Additional “X” are Figure 3: The Frequency Polygon for the ages of added on both ends in order 35 early morning customers at McDo to close the polygon.  Base: Upper Class Boundary < Ogive Height: < cf CB CF Take Note !! CB >CF 40 There is additional 9.5-14.5 35 35 Lower c.b. “39.5” with 14.5-19.5 32 30 >cf equal to 0. 19.5-24.5 26 25 24.5-29.5 14 20 29.5-34.5 7 34.5-39.5 3 15 39.5- 0 10 >O giv 5 e >cf & Lower c.b. 0 9.5 14.5 19.5 24.5 29.5 34.5 39.5  Ogives Base: Class Interval Height: Cumulative Frequency c.b. cf 40 9.5-14.5 3 35 < Ogive 35 14.5-19.5 9 32 19.5-24.5 21 26 30 24.5-29.5 28 14 25 29.5-34.5 32 7 20 34.5-39.5 35 3 15 10 > Ogive cf & Lower c.b. 0 9.5 14.5 19.5 24.5 29.5 34.5 39.5  SW / Assignment # 2 Consider the test scores of 30 students in an exam. Construct a FDT with 5 classes showing the following information (CI, f, CB, CM, RF, CF). 37 41 48 21 29 31 35 27 38 30 29 50 33 19 48 21 32 33 26 36 31 32 30 37 27 35 42 45 34 42 Draw the following: 1. Frequency Histogram 2. Frequency Polygon 3. Ogives