1. Training Course on Basic Statistics for Research August 24-28, 2009 STATISTICAL RESEARCH AND TRAINING CENTER J and S Building, 104 Kalayaan Avenue, Diliman, Quezon City Methods of Organizing Data Prepared by: Josefina V. Almeda Professor and College Secretary School of Statistics University of the Philippines, Diliman August 2009

2. 2 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Quantitative Classification of Data * use quantitative classification if the observed values of the data are either a result of count or measurement * organize this type of data in tabular form in the form of a frequency distribution table. Frequency distribution is a summarized table wherein the classes are either distinct values or intervals with a frequency count.

3. 3 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Forms of the Frequency Distribution Single value grouping * is a frequency count of observed values wherein classes are distinct values * range of values is short and with many unique values occurring more than once Grouping by class intervals * is a frequency count of observed values wherein the classes are intervals.

4. 4 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Data for Single Value Grouping Suppose we have data on the number of children of 50 currently married women using any modern contraceptive method. Construct a summary table for the data set below. 0012223344 0012233344 0112233344 0112233345 0112233345

5. 5 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Example of Single Value Grouping Distribution of Currently Married Women Using Any Modern Method of Contraceptive by Number of Children: No. ofFrequency of ChildrenMarried Women% 0714 1816 2 1122 3 1428 4816 52 4 TOTAL 50 100

6. 6 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Definition of Terms Used in a Frequency Distribution Table Class interval contains the numbers defining a class. Class frequency is the number of observations falling under a class interval. Class limits are the end numbers of a class interval. * The lower class limit (LCL) is the lower end of the class interval and the upper class limit (UCL) is the upper end of the class interval. * The number of digits of the class limits should be the same as the number of digits of the raw data. Open class interval is a class interval with either no lower class limit or upper class limit.

7. 7 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Class boundaries are the true class limits. * There are no gaps in the class boundaries. * The number of decimal places is one more than the number of decimal place of the class limits. * The lower class boundary (LCB) is average of the lower class limit of the class interval and the upper class limit of the preceding class interval. * The upper class boundary (UCB) is the average of the upper class limit of the class interval and the lower class limit of the next class interval.

8. 8 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Class size is the size of the class interval. * It is the difference between two successive lower class limits, or two successive upper class limits, or two successive lower class boundaries, or two successive upper class boundaries. Class mark is the midpoint of a class interval. * It is the average of the lower class limit and the upper class limit or the average of the lower class boundary and upper class boundary of a class interval. Modal class is the class interval having the highest frequency.

9. 9 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Steps in Constructing a Frequency Distribution Table 1.Determine an adequate number of classes (K). * The number of classes should not be too many or not too few. * Usually, the number of classes is between 5 and 20. * The class intervals should be non-overlapping. 2. Determine the range (R). Range = Maximum – Minimum 3. Calculate the approximate class size (C’). C’ = R/K 4. Determine the class size (C ) by rounding off C’ to a number that is easy to work with. We recommend class sizes of multiples of 5, 10, 15, 20, etc.

10. 10 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 5.List the required number (K) of class intervals. * Start with the lower class limit of the lowest class interval. * Its value should be less or equal to the minimum value of the data set. * Add the class size (C) to the lower class limit to get the next lower class limit. * The last class interval should include the maximum value. 6.Tally the frequency for each class interval. 7. Sum the frequency column and check against the total number of observations.

11. 11 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 TABLE 3. Magnitude of Poor Population in the Philippines: 2000 NCR 848,962 Region 2 820,786Region 4a 1,699,333 (National1st District120,663(CagayanBatanes2,535(CALABARZON)Batangas440,603 Capital2nd District229,301Valley)Cagayan251,222 Cavite244,712 Region) 1 3rd District292,611Isabela424,580 Laguna207,184 4th District206,387Nueva Vizcaya82,895 Quezon667,385 CAR 536,169Quirino59,555 Rizal139,449 (CordilleraAbra110,937Region 3 1,695,227Region 4b 1,030,987 AdministrativeApayao28,770(CentralAurora59,985(MIMAROPA)Marinduque113,553 Region)Benguet122,762Luzon)Bataan68,659 Occidental Mindoro177,823 Ifugao113,719Bulacan147,812 Oriental Mindoro340,690 Kalinga83,844Nueva Ecija532,961Region 5 2,540,618 Mt. Province76,137Pampanga331,739(BicolAlbay553,629 Region 1 1,447,638Tarlac360,109Region)Camarines Norte301,147 (IlocosIlocos Norte115,116Zambales193,962 Camarines Sur765,373 Region)Ilocos Sur190,297 Catanduanes116,866 La Union253,382 Masbate483,651 Pangasinan888,844 Sorsogon319,952

12. 12 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Region 6 2,765,055Region 8 1,646,371Region 10 1,580,249 (WesternAklan186,813(EasternBiliran58,135(NorthernBukidnon449,647 Visayas)Antique208,169Visayas) Eastern Samar202,680Mindanao)Camiguin41,017 Capiz328,635 Leyte680,536 Lanao Del Norte424,819 Guimaras37,838 Northern Samar240,228 Misamis Occidental260,764 Iloilo690,639 Southern Samar116,738 Misamis Oriental404,002 Negros Occidental1,312,961 Western Samar348,054Region 11 1,222,367 Region 7 2,017,162Region 9 1,254,884(Davao Davao del Norte637,298 (CentralBohol590,926(Zamboanga Zamboanga del Norte433,091Region)Daval del Sur412,442 Visayas)Cebu973,490Peninsula) Zamboanga del Sur821,793 Davao Oriental172,627 Negros Oriental427,509 Zamboanga 2 Sibugay Compostela 4 Valley Siquijor25,237 Isabela City 3

13. 13 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Region 12 1,596,785Region 13 1,071,005ARMM 1,648,441 (SOCCSKSAR GEN)North Cotabato509,463(Caraga)Agusan del Norte259,475 (Autonomous RegionBasilan123,825 Saranggani223,279 Agusan del Sur353,825 in Muslim Mindanao Lanao del Sur432,307 South Cotabato469,874 Surigao del Norte232,065 Maguindanao534,628 Sultan Kudarat344,172 Sulu397,119 Cotabato City49,997 Tawi-tawi160,562 1 Districts of NCR cover the following: 1st District – Manila; end District – Mandaluyong, Marikina, Pasig, Quezon City and San Juan; 3rd District - Valenzuela, Kaloocan City, Malabon and Navotas; and 4th District – Las Pinas, Makati, Muntinlupa, Paranaque, Pasay City, Pateros, and Taguig. 2 Zamboanga Sibugay was part of Zamboanga del Sur in 2000. Thus, 2000 estimates of Zamboanga del Sur includes Zamboanga Sibugay 3 Isabela City was part of Basilan in 2000. Thus, 2000 estimates of Basilan still includes Isabela City. 4 Davao del Norte estimates for 2000 include Compostela Valley. Source: National Statistical Coordination Board

14. 14 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 TABLE 4. Sorted Data (Array) of Magnitude of Poor Population for the 82 provinces of the Philippines: 2000 2,535 76,137 122,762 193,962 240,228 331,739 424,819 534,628 973,490 25,237 82,895 123,825 202,680 244,712 340,690 427,509 553,629 1,312,961 28,770 83,844 139,449 206,387 251,222 344,172 432,307 590,926 37,838 110,937 147,812 207,184 253,382 348,054 433,091 637,298 41,017 113,553 160,562 208,169 259,475 353,825 440,603 667,385 49,997 113,719 170,917 223,279 260,764 360,109 449,647 680,536 58,135 115,116 172,627 225,640 292,611 397,119 469,874 690,639 59,555 116,738 177,823 228,004 301,147 404,002 483,651 765,373 59,985 116,866 186,813 229,301 319,952 412,442 509,463 821,793 68,659 120,663 190,297 232,065 328,635 424,580 532,961 888,844

15. 15 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 TABLE 5. Frequency Distribution Table on Magnitude of Poor Population for the 82 Provinces of the Philippines: 2000 TABLE 5a CLASS LIMITS LCLUCLf 2,500 152,49924 152,500 302,49924 302,500 452,49918 452,500 602,4997 602,500 752,4994 752,500 902,4993 902,500 1,052,4991 1,052,500 1,202,4990 1,202,500 1,352,4991 82 TABLE 5b CLASS LIMITS LCLUCLf 2,500 202,49931 202,500 402,49926 402,500 602,49916 602,500 802,4995 802,500 1,002,4993 1,002,500 1,202,4990 1,202,500 1,402,4991 82

16. 16 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 TABLE 5c CLASS LIMITS LCLUCLf 2,500 192,49930 192,500 382,49926 382,500 572,49916 572,500 762,4995 762,500 952,4993 952,500 1,142,4991 1,142,500 1,332,4991 82

17. 17 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Example: This illustrates the use of appropriate column labels in a frequency distribution table. TABLE 6. Frequency Distribution Table of the Magnitude of Poor Population in the Phils: 2000 Magnitude ofPoor PopulationNo. of Provinces 2,500- 192,49930 192,500- 382,49926 382,500- 572,49916 572,500- 762,4995 762,500- 952,4993 952,500- 1,142,4991 1,142,500- 1,332,4991 Total 82

18. 18 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 TABLE 7. Frequency Distribution Table with Class Boundaries and Class Marks Class Limits Class Boundaries LCLUCLLCBUCBClass Markf 2,500- 192,499 2,500- 192,499 97,50030 192,500- 382,499 192,500- 382,499 287,50026 382,500- 572,499 382,500- 572,499 477,50016 572,500- 762,499 572,500- 762,499 667,5005 762,500- 952,499 762,500- 952,499 857,5003 952,500- 1,142,499 952,500- 1,142,499 1,047,5001 1,142,500- 1,332,499 1,142,500- 1,332,499 1,237,5001 82

19. 19 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Relative Frequency and Relative Frequency Percentage Relative frequency * divide the class frequency of a class interval to the number of observations * the sum of the relative frequency column is one Relative frequency percentage * multiply the relative frequency by 100 * the sum of the relative frequency percentage column is one hundred percent.

20. 20 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 TABLE 8. Frequency Distribution Table with Relative Frequency and Relative Frequency Percentage Relative Class Limits RelativeFrequency LCLUCLfFrequencyPercentage 2,500- 192,499300.36636.6 192,500- 382,499260.31731.7 382,500- 572,499160.19519.5 572,500- 762,499 50.0616.1 762,500- 952,499 30.0373.7 952,500-1,142,499 10.0121.2 1,142,500-1,332,499 10.0121.2 821.000 100.0

21. 21 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 TABLE 9. Frequency Distribution Table with Less than Cumulative Frequency and Greater than Cumulative Frequency Distributions Class Limits Less than cumulative Greater than Cumulative Frequency LCLUCLfFrequency 2,500- 192,49930 82 192,500- 382,499265652 382,500- 572,499167226 572,500- 762,499 57710 762,500- 952,499 3805 952,500-1,142,499 1812 1,142,500-1,332,499 1821

22. 22 Statistical Research and Training Center Training Course on Basic Statistics for Research August 24 - 28, 2009 Graphical Representation of the Frequency Distribution  Frequency Histogram - use the class frequency on the vertical axis and the class boundaries on the horizontal axis  Frequency Polygon - use the class frequency on the vertical axis and the class mark on the horizontal axis

23. Training Course on Basic Statistics for Research August 24-28, 2009 STATISTICAL RESEARCH AND TRAINING CENTER J and S Building, 104 Kalayaan Avenue, Diliman, Quezon City Thank you.