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- 1. Presentation of Data Module 6 Basic Statistics SRSTHS Ms. Pegollo
- 2. Presentation of Data Objectives: At the end of the lesson, the students should be able to: 1. Prepare a stem-and-leaf plot 2. Describe data in textual form 3. Construct frequency distribution table 4. Create graphs 5. Read and interpret graphs and tables MCPegollo/Basic Statistics/SRSTHS
- 3. Ungrouped vs. Grouped Data Data can be classified as grouped or ungrouped. Ungrouped data are data that are not organized, or if arranged, could only be from highest to lowest or lowest to highest. Grouped data are data that are organized and arranged into different classes or categories. MCPegollo/Basic Statistics/SRSTHS
- 4. Presentation of Data Textual Method Tabular Method Graphical Method • Rearrangem ent from lowest to highest • Stem-andleaf plot • Frequency distribution table (FDT) • Relative FDT • Cumulative FDT • Contingency Table • Bar Chart • Histogram • Frequency Polygon • Pie Chart • Less than, greater than Ogive MCPegollo/Basic Statistics/SRSTHS
- 5. Textual Presentation of Data Data can be presented using paragraphs or sentences. It involves enumerating important characteristics, emphasizing significant figures and identifying important features of data. MCPegollo/Basic Statistics/SRSTHS
- 6. Textual Presentation of Data Example. You are asked to present the performance of your section in the Statistics test. The following are the test scores of your class: 34 42 20 50 17 9 34 43 50 18 35 43 50 23 23 35 37 38 38 39 39 38 38 39 24 29 25 26 28 27 44 44 49 48 46 45 45 46 45 46 MCPegollo/Basic Statistics/SRSTHS
- 7. Solution First, arrange the data in order for you to identify the important characteristics. This can be done in two ways: rearranging from lowest to highest or using the stem-and-leaf plot. Below is the rearrangement of data from lowest to highest: 9 23 28 35 38 43 45 48 17 24 29 37 39 43 45 49 18 25 34 38 39 44 46 50 20 26 34 38 39 44 46 50 23 27 35 38 42 45 46 50 MCPegollo/Basic Statistics/SRSTHS
- 8. With the rearranged data, pertinent data worth mentioning can be easily recognized. The following is one way of presenting data in textual form. In the Statistics class of 40 students, 3 obtained the perfect score of 50. Sixteen students got a score of 40 and above, while only 3 got 19 and below. Generally, the students performed well in the test with 23 or 70% getting a passing score of 38 and MCPegollo/Basic Statistics/SRSTHS
- 9. Another way of rearranging data is by making use of the stem-and-leaf plot. What is a stem-and-leaf plot? Stem-and-leaf Plot is a table which sorts data according to a certain pattern. It involves separating a number into two parts. In a two-digit number, the stem consists of the first digit, and the leaf consists of the second digit. While in a three-digit number, the stem consists of the first two digits, and the leaf consists of the last digit. In a onedigit number, the stem is zero. MCPegollo/Basic Statistics/SRSTHS
- 10. Below is the stem-and-leaf plot of the ungrouped data given in the example. Stem Leaves 0 9 1 7,8 2 0,3,3,4,5,6,7,8,9 3 4,4,5,5,7,8,8,8,8,9,9,9 4 2,3,3,4,4,5,5,5,6,6,6,8,9 5 0,0,0 Utilizing the stem-and-leaf plot, we can readily see the order of the data. Thus, we can say that the top ten got scores 50, 50, 50, 49, 48, 46, 46, 46,45, and 45 and the ten lowest scores are 9, 17, 18, 20, MCPegollo/Basic Statistics/SRSTHS 23,23,24,25,26, and 27.
- 11. Exercise: Prepare a stem-and-leaf plot and present in textual form. Stem The ages Leaf teachers in a public of 40 school 23 2 3,6,7,8,8,9 27 28 36 32 42 0,1,2,4,4,5,5,5,6,6,6,6,8,8,8,8,9,9 3 44 54 56 48 55 48 30 31 35 36 47 48 4 0,0,0,2,3,4,4,5,5,7,8,8,8 26 28 29 45 34 5 4,5,6 38 39 38 36 35 34 36 35 38 39 40 43 38 45 44 40 40 MCPegollo/Basic Statistics/SRSTHS
- 12. Tabular Presentation of Data Below is a sample of a table with all of its parts indicated: Table Number Table Title Column Header Row Classifier Body Source Note http://www.sws.org.ph/youth.htm MCPegollo/Basic Statistics/SRSTHS
- 13. Frequency Distribution Table A frequency distribution table is a table which shows the data arranged into different classes(or categories) and the number of cases(or frequencies) which fall into each class. The following is an illustration of a frequency distribution table for ungrouped data: MCPegollo/Basic Statistics/SRSTHS
- 14. Sample of a Frequency Distribution Table for Ungrouped Data Table 1.1 Frequency Distribution for the Ages of 50 Students Enrolled in Statistics Age Frequency 12 2 13 13 14 27 15 4 16 3 17 1 N = 50 MCPegollo/Basic Statistics/SRSTHS
- 15. Sample of a Frequency Distribution Table for Grouped Data Table 1.2 Frequency Distribution Table for the Quiz Scores of 50 Students in Geometry Scores Frequency 0-2 1 3-5 2 6-8 13 9 - 11 15 12 - 14 19 MCPegollo/Basic Statistics/SRSTHS
- 16. Lower Class Limits are the smallest numbers that can actually belong to different classes Rating Frequency 0-2 1 3-5 2 6-8 13 9 - 11 15 12 - 14 19
- 17. Lower Class Limits are the smallest numbers that can actually belong to different classes Rating 0-2 Lower Class Limits Frequency 1 3-5 2 6-8 13 9 - 11 15 12 - 14 19
- 18. Upper Class Limits are the largest numbers that can actually belong to different classes Rating Frequency 0-2 1 3-5 2 6-8 13 9 - 11 15 12 - 14 19
- 19. Upper Class Limits are the largest numbers that can actually belong to different classes Rating Upper Class Limits Frequency 0-2 1 3-5 2 6-8 13 9 - 11 15 12 - 14 19
- 20. Class Boundaries are the numbers used to separate classes, but without the gaps created by class limits
- 21. Class Boundaries number separating classes Rating - 0.5 0-2 20 3-5 14 6-8 15 9 - 11 2 2.5 5.5 8.5 Frequency 11.5 12 - 14 14.5 1
- 22. Class Boundaries number separating classes Rating - 0.5 0-2 20 3-5 14 6-8 15 9 - 11 2 2.5 Class Boundaries 5.5 8.5 Frequency 11.5 12 - 14 14.5 1
- 23. Class Midpoints The Class Mark or Class Midpoint is the respective average of each class limits
- 24. Class Midpoints midpoints of the classes Rating Class Midpoints Frequency 0- 1 2 20 3- 4 5 14 6- 7 8 15 9 - 10 11 2 12 - 13 14 1
- 25. Class Width is the difference between two consecutive lower class limits or two consecutive class boundaries Rating Frequency 0-2 20 3-5 14 6-8 15 9 - 11 2 12 - 14 1
- 26. Class Width is the difference between two consecutive lower class limits or two consecutive class boundaries Rating Frequency 3 Class Width 0-2 20 3 3-5 14 3 6-8 15 3 9 - 11 2 3 12 - 14 1
- 27. Guidelines For Frequency Tables 1. Be sure that the classes are mutually exclusive. 2. Include all classes, even if the frequency is zero. 3. Try to use the same width for all classes. 4. Select convenient numbers for class limits. 5. Use between 5 and 20 classes. 6. The sum of the class frequencies must equal the number of original data values.
- 28. Constructing A Frequency Table 1. Decide on the number of classes . 2. Determine the class width by dividing the range by the number of classes (range = highest score - lowest score) and round up. range class width round up of number of classes 3. Select for the first lower limit either the lowest score or a convenient value slightly less than the lowest score. 4. Add the class width to the starting point to get the second lower class limit, add the width to the second lower limit to get the third, and so on. 5. List the lower class limits in a vertical column and enter the upper class limits. 6. Represent each score by a tally mark in the appropriate class. Total tally marks to find the total frequency for each class.
- 29. Homework Gather data on the ages of your classmates’ fathers, include your own. Construct a frequency distribution table for the data gathered using grouped and ungrouped data. What are the advantages and disadvantages of using ungrouped frequency distribution table? What are the advantages and disadvantages of using grouped frequency distribution table? MCPegollo/Basic Statistics/SRSTHS
- 30. Relative Frequency Table relative frequency = class frequency sum of all frequencies
- 31. Relative Frequency Table Rating Frequency Relative Rating Frequency 0-2 20 0-2 38.5% 3-5 14 3-5 26.9% 6-8 15 6-8 28.8% 9 - 11 2 9 - 11 3.8% 12 - 14 1 12 - 14 1.9% 20/52 = 38.5% Total frequency = 52 Table 2-5 14/52 = 26.9% etc.
- 32. Cumulative Frequency Table >cf Rating Frequency <cf 0-2 20 20 52 3–5 14 34 32 6–8 15 49 18 9 – 11 2 51 3 12 – 14 1 52 1 Table 2-6 Cumulative Frequencies
- 33. Frequency Tables Rating Frequency Rating Relative Frequency Rating Cumulative Frequency 0-2 20 0-2 38.5% 0–2 20 3-5 14 3-5 26.9% 3–5 34 6-8 15 6-8 28.8% 6–8 49 9 - 11 2 9 - 11 3.8% 9 – 11 51 12 - 14 1 12 - 14 1.9% 12 – 14 52 Table 2-3 Table 2-5 Table 2-6
- 34. Complete FDT A complete FDT has class mark or midpoint (x), class boundaries (c.b), relative frequency or percentage frequency, and the less than cumulative frequency (<cf) and the greater than cumulative frequency (>cf). MCPegollo/Basic Statistics/SRSTHS
- 35. Complete Frequency Table Table 2-6 Grouped Frequency Distribution for the Test Scores of 52 Students in Statistics Class Frequency Class Intervals (f) Mark (x) (ci) Class Relative Boundary Frequency <cf (cb) (rf) >cf 0-2 20 1 -0.5 – 2.5 38.5% 20 52 3–5 14 4 2.5 – 5.5 26.9% 34 32 6–8 15 7 5.5 – 8.5 28.8% 49 18 9 – 11 2 10 8.5 – 11.5 3.8% 51 3 12 – 14 1 13 11.5 – 14.5 1.9% 52 1
- 36. Exercise: For each of the following class intervals, give the class width(i), class mark (x), and class boundary (cb) Class interval (ci) Class Width Class Mark Class Boundary a. 4 – 8 b. 35 – 44 c. 17 – 21 d. 53 – 57 e. 8 – 11 f. 108 – 119 g. 10 – 19 h. 2.5 – 2. 9 i. 1. 75 – 2. 25 MCPegollo/Basic Statistics/SRSTHS
- 37. Construct a complete FDT with 7 classes The following are the IQ scores of 60 student applicants in a certain high school 106 128 96 94 85 75 113 103 96 91 94 70 109 113 109 100 81 81 103 113 91 88 78 75 106 103 100 88 81 81 113 106 100 96 88 78 96 109 94 96 88 70 103 102 88 78 95 90 99 89 87 96 95 104 89 99 101 105 103 125 MCPegollo/Basic Statistics/SRSTHS
- 38. Contingency Table This is a table which shows the data enumerated by cell. One type of such table is the “r by c” (r x c) where the columns refer to “c” samples and the rows refer to “r” choices or alternatives. MCPegollo/Basic Statistics/SRSTHS
- 39. Example Table 1 The Contingency Table for the Opinion of Viewers on the TV program “Budoy” Choice/Sample Men Women Children Total Like the Program 50 56 45 151 Indifferent 23 16 12 51 Do not like the program 43 55 40 138 Total 116 127 97 340 Give as many findings as you can, and draw as many conclusions from your findings. The next table can help you identify significant findings. MCPegollo/Basic Statistics/SRSTHS
- 40. Example Table 1 The Contingency Table for the Opinion of Viewers on the TV program “Budoy” Choice/Sampl e Men Women Children Total Like the Program 50 (33%) 56(37%) (43%) (44%) 45(30%) (46%) 151 (44%) Indifferent 23(45%) (20%) 16(31%) (13%) 12(24%) (12%) 51 (15%) Do not like the program 43(53%) (37%) 55(40%) (43%) 40(29%) (41%) 138(41%) Total 116 (34%) 127 (37%) 97 (28%) 340 Do not use this table for presentation because the percentages might confuse the readers. Can you explain the percentages in each cell? MCPegollo/Basic Statistics/SRSTHS

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