GROUP-10-Frequency-Distribution-and-Graphical-Representation.pptx

FREQUENCY DISTRIBUTION

1. Frequency Distribution and Their Graphic Representation (Chapter 10)

2. Discussants ADRIAN D. VENTURA PRINCIPAL 1 SAMPALOC ES Gainza District Division of Camarines Sur JAY P. MIRAÑA PRINCIPAL 1 PATAG ES Libmanan District 1 Division of Camarines Sur GEMLIN C. MIRAÑA TEACHER III TARUM ES Libmanan District 1 Division of Camarines Sur

3. Tabulation of scores, showing the number of individuals occur at each class limit arranged from high to low or from low to high Is applicable if the total number of cases (N) is equal to 30 or more. Frequency Distribution

4. In general, a frequency distribution is any arrangement of the data that shows the frequency of occurrence of different values of the variable or the frequency occurrence of values falling within arbitrarily defined ranges of the of the variable known as class intervals Frequency Distribution

5. In general, a frequency distribution is any arrangement of the data that shows the frequency of occurrence of different values of the variable or the frequency occurrence of values falling within arbitrarily defined ranges of the of the variable known as class intervals Frequency Distribution

6. Scores Made by 35 college students in Botany Test STEP 1. Find the range RANGE is equal to highest score minus lowest score R= HS-LS R= 47-12 R = 35 28 40 12 22 20 18 23 28 34 39 33 37 30 21 31 30 14 25 36 27 32 25 29 25 47 42 45 28 22 37 28 16 25 31 25 STEP IN ARRANGING THE SCORES IN A FORM OF FREQUENCY DISTRIBUTION

7. Scores Made by 35 college students in Botany Test STEP 2. Find the Class Interval Class interval is t he difference between the upper and the lower limits of a step of test scores in a grouped of frequency distribution. In finding for the class interval, we simply divide the range (R) by 10 or 20 in order that the size of the class limit or class interval may not be less than 10 and not more than 20 provided that such class will cover the total range of the observations. To illustrate: Range = 35 35/10= 3.5 35/20= 1.75 The class interval ranges from 1.75 to 3.5. Therefore, we choose 3 as our class interval where we will obtain 13 classes. The ideal class limit is 12 to 15. Hence, 13 class limit is within the ideal class. In choosing the class interval, odd number is preferable. 28 40 12 22 20 18 23 28 34 39 33 37 30 21 31 30 14 25 36 27 32 25 29 25 47 42 45 28 22 37 28 16 25 31 25 STEP IN ARRANGING THE SCORES IN A FORM OF FREQUENCY DISTRIBUTION

8. STEP 3. Set up the Classes In setting up the classes, we add C/2 where C is the class interval to the highest score as the upper limit of the highest class and subtract C/2 to the highest score as the lower limit of the highest class. 47+(C/2) = upper limit of the highest class 47+ 1.5 = 48.5 47 – (C/2) = lower limit of the highest class 47 – 1.5 = 45.5 The highest class limit is from 45.5 to 48.5. This setting of class is called the real limit or exact limit and these are sometimes spoken of as class boundaries . Once the highest class is set, subtract 3 as your class interval to the next class until you reach the lowest score. STEP IN ARRANGING THE SCORES IN A FORM OF FREQUENCY DISTRIBUTION Class Limit Real Limits 45.5 – 48.5 42.5 – 45.5 39.5 – 42.5 36.5 – 39.5 33.5 – 36.5 30.5 – 33.5 27.5 – 30.5 24.5 – 27.5 21.5 – 24.5 18.5 – 21.5 15.5 – 18.5 12.5 – 15.5 9.5 – 12.5

9. STEP 3. Set up the Classes There are 2 ways of setting up classes, namely, real limits and integral limits. Integral limits is obtained by adding 0.5 to the lower limit or a class interval and subtracting 0.5 to the upper limit. For instance, the upper class is 45.5 to 48.5 for real limits and 46 to 48 for integral limits. STEP IN ARRANGING THE SCORES IN A FORM OF FREQUENCY DISTRIBUTION Class Limit Real Limits Integral Limits 45.5 – 48.5 42.5 – 45.5 39.5 – 42.5 36.5 – 39.5 33.5 – 36.5 30.5 – 33.5 27.5 – 30.5 24.5 – 27.5 21.5 – 24.5 18.5 – 21.5 15.5 – 18.5 12.5 – 15.5 9.5 – 12.5 46 – 48 43 – 45 40 – 42 37 – 39 34 – 36 31 – 33 28 – 30 25 – 27 22 – 24 19 – 21 16 – 18 13 – 15 10 - 12

10. STEP 4. Tally the Scores Having adopted a set of classes, we are ready to tally them. Taking each score as it comes, locate it within the proper class and tally. After tallying, count the number of tallies in each class and write it in column frequency (f). The frequencies are listed in column 4. The tally should be carefully checked if the sum is equal to the total number of scores in the sample. If there is an unequal frequency from the sample, tallying should be repeated. At the bottom of column 4 the symbol N or ∑ f in which ∑ (capital Greek sigma) stands for the “sum of” equals 35 of the total number of cases (N). STEP IN ARRANGING THE SCORES IN A FORM OF FREQUENCY DISTRIBUTION Classes     Real Limits Integral Limits Tally Frequency 45.5 – 48.5 42.5 – 45.5 39.5 – 42.5 36.5 – 39.5 33.5 – 36.5 30.5 – 33.5 27.5 – 30.5 24.5 – 27.5 21.5 – 24.5 18.5 – 21.5 15.5 – 18.5 12.5 – 15.5 9.5 – 12.5 46 – 48 43 – 45 40 – 42 37 – 39 34 – 36 31 – 33 28 – 30 25 – 27 22 – 24 19 – 21 16 – 18 13 – 15 10 - 12 I I II III III IIII IIII – II IIII III II II I I 1 1 2 3 3 4 7 5 3 2 2 1 1 35 (N or ∑f)

11. CUMULATIVE FREQUENCY DISTRIBUTION 1 2 3 4 Integral Limits f Cf CPf     <  >  <  >  46 – 48 43 – 45 40 – 42 37 – 39 34 – 36 31 – 33 28 – 30 25 – 27 22 – 24 19 – 21 16 – 18 13 – 15 10 - 12 1 1 2 3 3 4 7 5 3 2 2 1 1 35 34 33 31 28 25 21 14 9 6 4 2 1 1 2 4 7 10 14 21 26 29 31 33 34 35 100.00 97.14 94.29 88.57 80.00 71.43 60.00 40.00 25.71 17.14 11.43 5.70 2.86 2.86 5.70 11.43 20.00 28.57 40.00 60.00 74.29 82.86 88.57 94.29 97.14 100 Total 35         Cumulative frequency A frequency obtained by cumulating or successively adding the individual frequencies from the bottom or at the top. “Greater than” cumulative frequency starts adding the frequency successively from the highest class limit and “less than” from the lowest class limit. Cumulative Percentage frequency is obtained by diving the cumulative frequency by the total number of cases (N) time 100, shows the per cent of students falling below or above (< CPf or > CPf ) certain score values. CPf = (Cf/N)100 Legend: f - frequency Cf - Cumulative frequency CPf - Cumulative Percentage frequency < - Lesser than > - Greater than

12. GRAPHICAL REPRESENTATION OF FREQUENCY DISTRIBUTION Frequency Distribution are often represented graphically to enable us to understand the essential features of form of distributions and to compare one frequency distribution with another with another. A graph is a geometrical image or a mathematical picture of a set of data. For this purpose, histogram and frequency polygon are widely used.

13. HISTOGRAM Is a graph in which the frequencies are presented by areas in the form of vertical rectangles or bars. Is called a bar graph. Each bar is equal to the midpoint of class limit and a height corresponding to the absolute frequency Midpoint is obtained by simply adding the lower limit and upper limit and divide this by two.

14. HISTOGRAM 1 Integral Limits Midpoint f Cf     <  >  46 – 48 43 – 45 40 – 42 37 – 39 34 – 36 31 – 33 28 – 30 25 – 27 22 – 24 19 – 21 16 – 18 13 – 15 10 - 12 47 44 41 38 35 32 29 26 23 20 17 14 11 1 1 2 3 3 4 7 5 3 2 2 1 1 35 34 33 31 28 25 21 14 9 6 4 2 1 1 2 4 7 10 14 21 26 29 31 33 34 35 Total 35    

15. FREQUENCY POLYGON Is also called line graph Is done by plotting the frequencies with a dot at their midpoint and connecting the plotted points by the straight lines. Each frequency is plotted as a point directly above the midpoint scores of its limit If there are frequencies of zero, these are plotted on the base line. Then straight lines are drawn to connect the neighboring lines.

16. FREQUENCY POLYGON 1 Integral Limits Midpoint f Cf     <  >  46 – 48 43 – 45 40 – 42 37 – 39 34 – 36 31 – 33 28 – 30 25 – 27 22 – 24 19 – 21 16 – 18 13 – 15 10 - 12 47 44 41 38 35 32 29 26 23 20 17 14 11 1 1 2 3 3 4 7 5 3 2 2 1 1 35 34 33 31 28 25 21 14 9 6 4 2 1 1 2 4 7 10 14 21 26 29 31 33 34 35 Total 35    

17. CUMULATIVE FREQUENCY POLYGON Lesser than cumulative frequency In plotting the “lesser than” cumulative frequency (<Cf), 35 cumulative frequency be plotted against the top of the upper class limit of the interval, that is 48, the frequency of 28 against 36, 25 cumulative frequency against 33, and so on. Greater than cumulative frequency In plotting the “greater than” cumulative frequency (>Cf), 1 cumulative frequency be plotted against 4, 2 greater cumulative frequency against 45, 4 against 42, 7 against 39 and so on. 1 Integral Limits Midpoint f Cf     <  >  46 – 48 43 – 45 40 – 42 37 – 39 34 – 36 31 – 33 28 – 30 25 – 27 22 – 24 19 – 21 16 – 18 13 – 15 10 - 12 47 44 41 38 35 32 29 26 23 20 17 14 11 1 1 2 3 3 4 7 5 3 2 2 1 1 35 34 33 31 28 25 21 14 9 6 4 2 1 1 2 4 7 10 14 21 26 29 31 33 34 35 Total 35    

18. CUMULATIVE FREQUENCY POLYGON 1 Integral Limits Midpoint f Cf     <  >  46 – 48 43 – 45 40 – 42 37 – 39 34 – 36 31 – 33 28 – 30 25 – 27 22 – 24 19 – 21 16 – 18 13 – 15 10 - 12 47 44 41 38 35 32 29 26 23 20 17 14 11 1 1 2 3 3 4 7 5 3 2 2 1 1 35 34 33 31 28 25 21 14 9 6 4 2 1 1 2 4 7 10 14 21 26 29 31 33 34 35 Total 35    

19. CUMULATIVE PERCENTAGE FREQUENCY POLYGON or OGIVE Is plotted as point against the corresponding score points at the top of the upper class limits of the interval. The lesser than cumulative frequency (< CPf ) of 100 is plotted against 48, 97.14 is plotted against 45 and so on. On the other hand, the greater cumulative than frequency (> CPf ) of 2.86 is plotted against 48, 5.57 against 45 and so on. 1 2 3 Integral Limits Midpoint f CPf     <  >  46 – 48 43 – 45 40 – 42 37 – 39 34 – 36 31 – 33 28 – 30 25 – 27 22 – 24 19 – 21 16 – 18 13 – 15 10 - 12 47 44 41 38 35 32 29 26 23 20 17 14 11 1 1 2 3 3 4 7 5 3 2 2 1 1 100.00 97.14 94.29 88.57 80.00 71.43 60.00 40.00 25.71 17.14 11.43 5.70 2.86 2.86 5.70 11.43 20.00 28.57 40.00 60.00 74.29 82.86 88.57 94.29 97.14 100 Total 35    

20. CUMULATIVE FREQUENCY POLYGON 1 Integral Limits Midpoint f Cf     <  >  46 – 48 43 – 45 40 – 42 37 – 39 34 – 36 31 – 33 28 – 30 25 – 27 22 – 24 19 – 21 16 – 18 13 – 15 10 - 12 47 44 41 38 35 32 29 26 23 20 17 14 11 1 1 2 3 3 4 7 5 3 2 2 1 1 35 34 33 31 28 25 21 14 9 6 4 2 1 1 2 4 7 10 14 21 26 29 31 33 34 35 Total 35    

21. Advantages and Limitations of Histogram and Polygon Frequency polygon Frequency Polygon seems preferable to histogram. It gives a better picture of the distribution. The change from one point to another is direct and gives more correct impressions It is advantageous also in plotting two distributions overlapping on the same base. Gives a clear picture of the comparison.

22. Advantages and Limitations of Histogram and Polygon Histogram Gives a stepwise change from one interval to another It gives a more readily understandable presentation of the number of cases within each class limit; and each measurement occupies exactly a uniform amount of area. It gives a confusing picture when plotting two distribution overlapping on the baseline.

23. Advantages and Limitations of Histogram and Polygon Histogram It gives a confusing picture when plotting two distribution overlapping on the baseline. Class Limit Midpoints Frequency Urban Rural 47-49 44-46 41-43 38-40 35-37 32-34 29-31 26-28 23-25 20-22 17-19 14-16 48 45 42 39 36 33 30 27 24 21 18 15 3 9 14 18 10 9 7 5 4 3 2 1 1 5 10 12 13 18 8 6 5 4 2 1

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