Data organization and presentation (statistics for research)
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The document discusses various methods of presenting data, including textual, tabular, and graphical displays. It provides examples and definitions of key terms used in data presentation, such as frequency distribution tables, class intervals, class boundaries, class marks, and cumulative frequencies. The document also outlines steps for constructing a frequency distribution table, including determining the number of classes, range, class size, and class limits.
Data organization and presentation (statistics for research)
- 1. Methods of Data Presentation Remark: One of the most important aspects in any statistical investigation is the manner by which the researcher presents the data. Various Modes of Data Presentation I. Textual II. Tabular III. Graphical Displays
- 2. Methods of Data Presentation I. Textual Presentation – the data are presented in the form of texts, phrases or paragraphs. - common among newspaper reports depicting specifically the salient or important findings. Example: The Philippine Stock Exchange composite index lost 7.19 points to 2,099.12 after trading between 2,095.30 and 2,108.47. Volume was 1.29 billion shares worth 903.15 million pesos (16.7 million dollars). The broader all share index gained 5.21 points to 1,221.34. (From: Freeman dated March 17, 2005)
- 3. Methods of Data Presentation II. The Tabular Display – a more reliable and effective way of showing relationships or comparisons of data through the use of tables. - the tables must be accompanied by a short narrative explanation to make the facts clearer and more understandable.
- 4. Methods of Data Presentation Example: The following newspaper report presents a tabular data presentation . Country Peso United States Japan United Kingdom Hongkong Switzerland Canada Singapore 50. 7890 0.4140 72.5267 6.5116 28.7382 32.9756 28.7382
- 5. Methods of Data Presentation III. The Graphical Display – the most effective way of presenting data through the use of statistical graph. - can easily attract the attention as well as the interest of the reader.
- 6. Types of Graph I. Bar Graph – uses rectangular bars the length of which represents the quantity or frequency of each type or category. II. Multiple Bar Graph – useful when the researcher wants to compare figures on two or more different occurrence. - a legend is especially helpful in guiding the viewer in analyzing the data.
- 7. Types of Graph III. Pie Chart – used to present quantities that make up a whole. - constructed using percents and the slices of the pie are drawn in proportion to the different values of each class, item, group or category. IV. Line Chart – useful in showing trends over a period of time.
- 8. Data Organization: The Frequency Distribution Table Definition: Data in its original form and structure are called raw data. Example: The following data represent the quarterly sales tax receipts (in thousand dollars) submitted to the comptroller of Gmoserville Township for the period ending March 2010 by all 50 business establishments in that locale: 10.3 11.1 9.6 9.0 14.5 13.0 6.7 11.0 8.9 8.4 10.3 13.0 11.2 7.3 5.3 12.5 8.0 10.1 11.8 10.2 11.1 9.9 9.8 11.6 15.1 12.5 11.5 6.5 7.5 10.0 12.9 9.2 10.0 12.8 12.5 9.3 9.3 10.4 12.7 10.5 9.3 11.5 10.7 11.6 8.6 7.8 10.5 7.6 10.1 8.9
- 9. Remark: When these scores are arranged in either ascending or descending magnitude, then such an arrangement is called an array. Remark: It is usually helpful to put the raw data in an array because it is easy to identify the extreme values or the values where the scores most cluster. Definition: When the data are placed into a system wherein they are organized, then these partake the nature of grouped data. Definition: The procedure of organizing data into groups is called a Frequency Distribution Table (FDT)
- 10. Example: The following presents a frequency distribution table of the scores of fifteen Behavioral Statistics Graduate Students. Scores Frequency 20 – 29 5 30 – 39 4 40 – 49 3 50 – 59 2 60 – 69 1 15
- 11. Components of a Frequency Distribution Table I. Class Interval – these are the numbers defining the class. - consist of the end numbers called the class limits namely the lower limit and upper limit. II. Class Frequency (f) – shows the number of observations falling in the class. III. Class Boundaries – these are the so called “true class limits” classified as: - Lower Class Boundary (LCB) is defined as the middle value of the lower class limits of the class and the upper class limit of the preceding class.
- 12. Components of a Frequency Distribution Table - Upper Class Boundary is defined as the middle value between the upper class limit of the class and the lower limit of the next class. IV. Class Size – the difference between two consecutive upper limits or two consecutive lower limits. V. Class Mark (CM) – midpoint or the middle value of a class interval.
- 13. Components of a Frequency Distribution Table VI. Cumulative frequency – shows the accumulated frequencies of successive classes. Types of Cumulative Frequencies A. Greater than CF (> CF) – shows the number of observations greater than LCB. B. Less than CF (< CF) - shows the number of observations less than UCB.
- 14. The following are the suggested steps in constructing a Frequency Distribution Table. Determine the number of classes. For first approximation, it is suggested to use the Sturge’s Approximation Formula. K = 1 + 3.322 log n where K = approximate number of classes n = number of cases 2. Determine the range R, where R = maximum value – minimum value 3. Determine the approximate class size C using the formula C = R / K. It is usually convenient to round off C to a nearest whole number
- 15. 4. Determine the lowest class interval (or the first class). This class should include the minimum value in the data set. For uniformity, let us agree that for our purposes, the lower limit of the class interval should start at the minimum value. 5. Determine all class limits by adding the class size C to the limits of the previous class. 6. Tally the scores / observations falling in each class.