Data presented in a grouped frequency distribution are easier to analyze and to describe. However, the identity of individual score is lost due to grouping.
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Presentation of DataModule 6Basic StatisticsSRSTHSMs. Pegollo
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Presentation of DataObjectives: At the end of the lesson, the students should be able to:1. Prepare a stem-and-leaf plot2. Describe data in textual form3. Construct frequency distribution table4. Create graphs5. Read and interpret graphs and tables MCPegollo/Basic Statistics/SRSTHS
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Ungrouped vs. Grouped DataData can be classified as grouped or ungrouped.Ungrouped data are data that are notorganized, or if arranged, could only befrom highest to lowest or lowest tohighest.Grouped data are data that areorganized and arranged into differentclasses or categories. MCPegollo/Basic Statistics/SRSTHS
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Presentation of Data Textual Tabular Graphical Method Method Method• Rearrangem • Frequency • Bar Chart ent from distribution • Histogram lowest to table (FDT) • Frequency highest • Relative Polygon• Stem-and- FDT • Pie Chart leaf plot • Cumulative • Less than, FDT greater than • Contingency Ogive Table MCPegollo/Basic Statistics/SRSTHS
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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
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Textual Presentation of DataExample. 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
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SolutionFirst, 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
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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
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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 whichsorts data according to a certain pattern. Itinvolves separating a number into two parts.In a two-digit number, the stem consists ofthe first digit, and the leaf consists of thesecond digit. While in a three-digitnumber, the stem consists of the first twodigits, and the leaf consists of the last digit.In a one-digit number, the stem is zero. MCPegollo/Basic Statistics/SRSTHS
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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 0,0,0Utilizing the stem-and-leaf plot, we can readily see theorder of the data. Thus, we can say that the top tengot scores 50, 50, 50, 49, 48, 46, 46, 46,45, and 45and the ten lowest scores are 9, 17, 18, 20, MCPegollo/Basic Statistics/SRSTHS23,23,24,25,26, and 27.
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Exercise:Prepare a stem-and-leaf plot and present in textual form.The ages Leaf teachers in a public Stem of 40 school 2 3,6,7,8,8,9 23 27 28 36 35 38 39 40 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 43 38 4 0,0,0,2,3,4,4,5,5,7,8,8,8 34 26 28 29 45 34 45 44 5 4,5,6 36 38 39 38 36 35 40 40 MCPegollo/Basic Statistics/SRSTHS
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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 Notehttp://www.sws.org.ph/youth.htm MCPegollo/Basic Statistics/SRSTHS
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Frequency Distribution TableA 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
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Sample of a Frequency DistributionTable 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
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Sample of a FrequencyDistribution Table for GroupedData 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
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Lower Class Limitsare the smallest numbers that can actually belongto different classes Rating Frequency 0-2 1 3-5 2 6-8 13 9 - 11 15 12 - 14 19
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Lower Class Limits are the smallest numbers that can actually belong to different classes Rating Frequency 0-2 1Lower Class 3-5 2Limits 6-8 13 9 - 11 15 12 - 14 19
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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
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Upper Class Limits are the largest numbers that can actually belong to different classes Rating FrequencyUpper Class 0-2 1Limits 3-5 2 6-8 13 9 - 11 15 12 - 14 19
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Class Boundariesare the numbers used to separateclasses, but without the gaps created by classlimits
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Class Boundaries number separating classes Rating Frequency - 0.5 0-2 20 2.5Class 3-5 14 5.5Boundaries 6-8 15 8.5 9 - 11 2 11.5 12 - 14 1 14.5
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Class MidpointsThe Class Mark or Class Midpoint is the respective average of each class limits
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Class Midpoints midpoints of the classes Rating Frequency 0- 1 2 20Class 3- 4 5 14Midpoints 6- 7 8 15 9 - 10 11 2 12 - 13 14 1
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Class Widthis the difference between two consecutive lower classlimits or two consecutive class boundaries Rating Frequency 0-2 20 3-5 14 6-8 15 9 - 11 2 12 - 14 1
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Class Width is the difference between two consecutive lower class limits or two consecutive class boundaries Rating Frequency 3 0-2 20 3 3-5 14Class Width 3 6-8 15 3 9 - 11 2 3 12 - 14 1
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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.
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Constructing A Frequency Table1. Decide on the number of classes .2. Determine the class width by dividing the range by the number ofclasses (range = highest score - lowest score) and roundup. range class width round up of number of classes3. 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.
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HomeworkGather 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
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Relative Frequency Table class frequencyrelative frequency = sum of all frequencies
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Complete FDTA 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
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Complete Frequency Table Table 2-6 Grouped Frequency Distribution for the Test Scores of 52 Students in Statistics Class Class Relative Frequency ClassIntervals Boundary Frequency <cf >cf (f) Mark (x) (ci) (cb) (rf) 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
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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
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Construct a complete FDT with 7classes 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
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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
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Example Table 1 The Contingency Table for the Opinion of Viewers on the TV program “Budoy”Choice/Sample Men Women Children TotalLike the Program 50 56 45 151Indifferent 23 16 12 51Do not like the 43 55 40 138programTotal 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
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Example Table 1 The Contingency Table for the Opinion of Viewers on the TV program “Budoy”Choice/Sampl Men Women Children TotaleLike the 50 (33%) 56(37%) 45(30%) 151Program (43%) (44%) (46%) (44%)Indifferent 23(45%) 16(31%) 12(24%) 51 (20%) (13%) (12%) (15%)Do not like the 43(53%) 55(40%) 40(29%) 138(41%)program (37%) (43%) (41%)Total 116 127 97 340 (34%) (37%) (28%)Do not use this table for presentation because the percentages mightconfuse the readers. Can you explain the percentages in each cell? MCPegollo/Basic Statistics/SRSTHS