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Data PresentationData PresentationTextualData are presented in paragraph form. It involves enumeration of important characteristics, giving emphasis on significant figures and identifying the important features of the data.Table 1 Distribution of Viewers according to their Opinion on the New TV ProgramChoice/SampleMenWomenChildrenTotalLike the program50 (33%) (43%)56 (37%) (44%)45 (30%) (46%)151 (44%)Indifferent23 (45%) (20%)16 (31%) (13%)12 (24%) (12%)51 (15%)Do not like the program43 (31%) (37%)55 (40%) (43%)40 (29%) (41%)138 (41%)Total116 (34%)127 (37%)97 (28%)340Tabular Presentation of Data

Table number & title It is often used to record and analyze the relation between two or more qualitative variables. It displays the frequency distributionof the variables in a matrixformat. It is also called cross-tabulation.Contingency TableExample:Contingency TableTable 2 Distribution of ICS according to Gender and Mode of Transportation Going to SchoolCommuteCarWalkServiceTotalMale8 (53%) (38%)3 (20%) (50%)3 (20%) (60%)1 (7%) (50%)15 (44%)Female13 (68%) (62%)3 (16%) (50%)2 (11%) (40%)1 (5%) (50%)19 (56%)Total21 (62%)6 (17%)5 (15%)2 (6%)34Frequency Distribution TableIt is a table which shows the data arranged into different classes and the number of cases which fall into each class is tallied. Tabular Presentation of DataUngrouped Frequency Distribution TableTable 3Distribution of a Sample of 1CSF Students According to AgeAgeFrequencyPercentage (%)15121661017132218111819122020610214722582323Total60100Grouped Frequency Distribution TableTable 4 Distribution of a Sample of 1CSF StudentsAgeFrequencyPercentage(%)15 1671217 18244019 20183021 2291523 2423Total60100Class IntervalClass width (i) difference between two consecutive lower limits or upper limits. Ex: The class width of Table 4 is 2.Lower limitUpper limitExample: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58Determine the number of classes (k). Typically, the number of classes chosen is a value between 5 and 20. For this example, let k = 5.

2. Get the class width (i) = and round-up the answer.Frequency Distribution Table

then i = 10 (rounded-up)Frequency Distribution TableExample: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 583. List down the Classes or Class Intervals (LL-UL): Start with the LV as the lower limit (LL) of the first class, then add w to obtain the next lower limit, and so on. Then determine the upper limits (UL). Thus, we have 12 -22 -32 -42 -52 -2131415161See to it that classes do not overlap, each observation can enter a class, and the highest observation enters the last class - sometimes you need to add one more class to be able to do this.Frequency Distribution Table4. Determine the Class Frequencies Count the number of observations falling in each class.12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58ClassesFrequency (f)12 2122 3132 4142 5152 61 Total4653220Frequency Distribution TableThe Percentage column can also be included.

2030251510100Frequency Distribution TableClassesFrequency (f)Percentage%12 2122 3132 4142 5152 61 46532Total20The < Cumulative Frequency, > Cumulative Frequency and Class Mark can be included.16.526.536.546.556.541015182020161052Frequency Distribution TableClassesFrequency (f)Percentage%Class Mark (X)< cumulative frequency> cumulative frequency12 2122 3132 4142 5152 61 465322030251510Total20100

Exercise: Construct a frequency distribution table with 6 classes for the data below. Include classes, frequency, percentage, class mark, < cumulative frequency and > cumulative frequency. 72 78 86 93 106 107 98 82 81 77 87 91 95 92 83 76 78 73 81 86 93 107 99 94 86 81 77 73 76 80 92 88 91 102 88Frequency Distribution TableGRAPHICAL

Data PresentationFREQUENCY number of measurements in each category

Frequency Table RELATIVE FREQUENCY proportion of measurements in each category

Percentage of measurements in each categoryPie Chart Course %BSBA-CA 50BSBA-HRM 34BSBA-EM 10BS-IS 3AB-FDM 3Figure 5 Distribution of Math101 Students According to CourseA circular chart divided into sectors, illustrating proportion / percentages. Base: Class IntervalHeight: Frequency (c.i) f10 - 14 315 - 19 620 24 1225 - 29 730 - 34 435 - 39 3There are gaps between bars. This is appropriate to use for discrete variables!Note !!Bar ChartFigure 1 Distribution of Movies Watched by Math103 Students Last Year.A chart with rectangular bars with lengths proportional to the values they represent.Base: CoursesHeight: Frequency Course fBSBA-CA 19BSBA-HRM 13BSBA-EM 4BS-IS 1AB-FDM 1Bar charts can also be used for qualitative variables.Bar ChartFigure 2 Distribution of Math101 Students According to Course Base: Class MarkHeight: Frequency (c.i) f X 10 - 14 3 1215 - 19 6 1720 - 24 12 2225 - 29 7 2730 - 34 4 3235 - 39 3 37There is no gap between bars. This is appropriate to use for continuous variables.HistogramFigure 3 Distribution of Training Participants according to Age121722273237 Base: Class MarkHeight: Frequency (c.i) f X 10 - 14 3 1215 - 19 6 1720 - 24 12 2225 - 29 7 2730 - 34 4 3235 - 39 3 3702468101214712172227323742This is also appropriate to use for continuous variables.Additional X are added on both ends in order to close the polygon. Frequency PolygonFigure 4 Distribution of Training Participants according to Age Base: Class BoundariesHeight: Cumulative Frequency05101520253035409.514.519.524.529.534.539.5< Ogive> Ogive c.b. cf 9.5 - 14.5 3 3514.5 - 19.5 9 3219.5 - 24.5 21 2624.5 - 29.5 28 1429.5 - 34.5 32 734.5 - 39.5 35 3OgivesA distributive curve in which the frequencies are cumulative.Exercise 1.10Fifty people are grouped into four categories A, B, C, and D and the people who fall into each category is shown in the table:CategoryFrequencyA11B14C20D5a.) Construct a pie chart to describe the data.b.) Construct a bar chart to describe the data.CategoryFrequencyRelative FreqPercentAngleA110.222279.2B140.2828100.8C200.440144D50.11036Pie Charts and Bar ChartsExercise 1.29Statistics of the worlds religions are only very rough approximations, since many religions do not keep track of their membership numbers. An estimate of these numbers (in millions) is shown in the table:

Construct a pie chart and bar chart to describe the total membership in the worlds organized religions.ReligionMembers (millions)ReligionMembers (millions)Buddhism375Judaism15Christianity2100Sikhism25Hinduism851Other21Islam1300-when a quantitative variable is recorded over time at equally spaced intervals, the data set forms a time series.

Line ChartsExercise 1.24The value of a quantitative variable is measured once a year for a 10-year period. Here are the data:

Create a line chart to describe the variable as it changes over time.

YearMeasurementYearMeasurement161.5658.2262.3757.5360.7857.5459.8956.15581056YearMeasurement161.5262.3360.7459.8558658.2757.5857.5956.11056Figure 5: Measuring over TimeDot Plot90707070757065686074709575706865406570Table 1.7: Prices of Walking Shorts

405060708090455565758595Dot Plot for the data in Table 1.7

Stem and Leaf Plot90707070757065686074709575706865406570Table 1.7: Prices of Walking Shorts

4567890

0 5 5 5 8 80 0 0 0 0 0 0 4 5 5 0 5Leaf unit = 1stemleafRules for Constructing Graphs The following are the main rules to construct a graph:Every graph must have a suitable title which should clearly convey the main idea, the graph intends to portray. The graph must suit the size of the paper. The scale of the graph should be in even numbers or in multiples. Graph should be as simple as possible.Rules for Constructing Graphs The following are the main rules to construct a graph: A graph should be neat and clean. It should be appealing to the eyes. The test of a good graph depends on the case with which the observer can interpret it. Thank you!Table 4

Distribution of Students in ABC College

According to Year Level

Year Level

Number of Students

First year300

Second year250

Third year285

Fourth year215

N = 1050

Source: ABC College Registrar