Frequency Distribution (Class-interval- Tally).pptx

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1. STATISTICS Measures of central tendency

2. DEFINITIONS OF TERMS MEAN (Ungrouped Data) is the average of all the elements of a set of data and is denoted by Whereas, = Mean = Sum of all values in a data =Total number of elements in a given data  

3. MEDIAN (UNGROUPED) Is usually denoted by By definition, median is the value at the middle when all the elements in a given set of data are arranged in ascending order. NOTE: If n is odd number, select the middle data value = If n is even number, find the mean of the two middle values. = Midpoint of the set  

4. MEDIAN OF A GROUPED DATA =Median = Lower class boundary = Median Class Frequency = Cumulative frequency before the median class MEDIAN CLASS = Class interval n= Total number of observation  

5. MODE (UNGROUPED) defined as the element in a set of data that has the greatest number of frequencies. It is donated by . The value that occurs most often in a data set. = Most frequent Different types of mode: Unimodal Bimodal Multimodal No mode  

6. MODE (GROUPED) Whereas:  

7. DEFINITIONS OF TERMS FREQUENCY DISTRIBUTION A frequency distribution is a way of presenting and organizing the data connected in tabular form using classes and frequencies. The most convenient method of organizing the data is to construct a frequency distribution in order to describe situations, draw conclusions, or make inferences about events, the researcher must organize the data in some meaningful way.

8. GROUPED FREQUENCY DISTRIBUTION Lower class limit the smallest data value that can be included in the class. Upper class limit the largest data value that can be included in the class. Class boundaries are used to separate classes so that there are no gaps in the frequency distribution. Class marks the midpoint of the classes (average)  

9. GROUPED FREQUENCY DISTRIBUTION Class width the difference between two con secutive lower class limits Cumulative frequency classes are increasing order is the sum of the frequencies for that class and all previous class.

10. Basic types of frequency distribution Ungrouped frequency distribution Classifies a given data set (usually n 30) under a specific category or class. Frequencies of each data is treated as individual data points or a discrete data   grouped frequency distribution Having an interval or a ratio –level data, and beyond the sample size of 30. Frequencies of each data points are clustered in a specific class interval.

11. EXAMPLES Ungrouped frequency distribution AGE TALLY FREQUENCY 19 18 17 16 15 14 grouped frequency distribution CLASS TALLY FREQUENCY 95-99 90-94 85-89 80-84 75-79 70-74

12. Example1 Scores of 15 students in Mathematics I quiz consist of 25 items. The highest score is 25 and the lowest score is 10. Here are the scores: 25, 20, 18, 18,17, 15, 15, 15, 14, 14, 13, 12, 12, 10, 10. Find the mean in the following scores. X (Scores) 25 14 20 14 18 13 18 12 17 12 15 10 15 10 15     15.2  

13. UNGROUPED FREQUENCY DISTRIBUTION Twenty-five positive cases of COVID-19 were given a blood test to determine their blood type. The data set is as follows: A B B AB O O O B AB B B B O A O A O O O AB AB A O B A CLASS TALLY FREQUENCY A B O AB 5 7 9 4 Total (N) = 25

14. Steps in Constructing FDT Arrange the data in ascending order. Determine the range. Decide the class size or the number of classes. Divide the range by the class size to identify the class interval. Construct a frequency distribution table. Tally and count the observations under each classes.

15. Example #2 Grouped frequency distribution Step.1 Arrange the score from lowest to highest. The following are the scores obtained by 40 students of BSIT in 100 item Mathematics quiz. 40 41 42 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 61 62 63 64 64 65 65 65 66 66 70 75 75 76 76 82 84 92 98

16. Example #2 Grouped frequency distribution Step.2 Determine the range. The following are the scores obtained by 40 students of Grade 10 in 100 item MMW quiz. Range= Highest score-Lowest score Range=98-40 R= 58 40 41 42 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 61 62 63 64 64 65 65 65 66 66 70 75 75 76 76 82 84 92 98

17. Example #2 Grouped frequency distribution The following are the scores obtained by 40 students of Grade 10 in 100 item MMW quiz. Sturge rule: Step.3 Determine the class size -A rule for determining the desirable number of groups into which a distribution of observations should be classified. K=1+ 3.322logN K=1+ 3.322log(40) K=6.322 round up K= 7 40 41 42 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 61 62 63 64 64 65 65 65 66 66 70 75 75 76 76 82 84 92 98

18. Example #2 Grouped frequency distribution The following are the scores obtained by 40 students of Grade 10 in 100 item MMW quiz.   Step.4 Find the class width. R=58, K =7   8.286 round up     40 41 42 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 61 62 63 64 64 65 65 65 66 66 70 75 75 76 76 82 84 92 98

19. The following are the scores obtained by 40 students of Grade 10 in 100 item MMW quiz. Step.5 Select as starting point either the lowest score or the lower class limits. Add the class width to the starting point to get the second lower class limits. Then enter the upper class limits. Class Interval Tally Frequency ( f ) Class mark (x) 94-102 I 1 98 85-93 I 1 89 76-84 IIII 4 80 67-75 III 3 71 58-66 IIIII-IIIII-IIII 14 62 49-57 IIIII-IIII 9 53 40- 48 IIIII-III 8 44 Class Interval Tally Frequency ( f ) Class mark (x) 94-102 I 1 98 85-93 I 1 89 76-84 IIII 4 80 67-75 III 3 71 58-66 IIIII-IIIII-IIII 14 62 49-57 IIIII-IIII 9 53 40- 48 IIIII-III 8 44 Class width ( ) =9 number of classes (K)=7   40 41 42 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 61 62 63 64 64 65 65 65 66 66 70 75 75 76 76 82 84 92 98

20. Example #1 Scores of 40 students of BS-Criminology in MMW exam. Construct a frequency distribution table using the class size of 6.

21. Example #1 Scores of 40 students of BS-Criminology in MMW exam. Construct a frequency distribution table using the class size of 6.

22. Example #1 Scores of 40 students of BS-Criminology in MMW exam. Construct a frequency distribution table using the class size of 6. R= HS-LS K=6 R= 50-9 R= 41  

23. Example #1 Scores Tally Frequency Class Boundaries (CB) Class Mark (CM) Less than Cumulative Frequency ( Cf) ( f+Cf ) LCB (LCL-0.5) UCB (UCL+0.5) 44-50 37-43 30-36 23-29 16-22 9-15 i = 7 Scores Tally Frequency Class Boundaries (CB) LCB (LCL-0.5) UCB (UCL+0.5) 44-50 37-43 30-36 23-29 16-22 9-15 i = 7

24. Example #1 Scores Tally Frequency Class Boundaries (CB) Class Mark (CM) Less than Cumulative Frequency ( Cf) ( f+Cf LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 37-43 IIII-I 6 30-36 IIII-II 7 23-29 IIII-IIII-I 11 16-22 IIII-IIII-I 11 9-15 1 1 i = 7 n =40 Scores Tally Frequency Class Boundaries (CB) LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 37-43 IIII-I 6 30-36 IIII-II 7 23-29 IIII-IIII-I 11 16-22 IIII-IIII-I 11 9-15 1 1 i = 7 n =40

25. Example #1 Scores Tally Frequency Class Boundaries (CB) Class Mark (CM) Less than Cumulative Frequency ( Cf) ( f+Cf LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 43.5 37-43 IIII-I 6 36.5 30-36 IIII-II 7 29.5 23-29 IIII-IIII-I 11 22.5 16-22 IIII-IIII-I 11 15.5 9-15 1 1 8.5 i = 7 n =40 Scores Tally Frequency Class Boundaries (CB) LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 43.5 37-43 IIII-I 6 36.5 30-36 IIII-II 7 29.5 23-29 IIII-IIII-I 11 22.5 16-22 IIII-IIII-I 11 15.5 9-15 1 1 8.5 i = 7 n =40

26. Example #1 Scores Tally Frequency Class Boundaries (CB) Class Mark (CM) Less than Cumulative Frequency ( Cf) ( f+Cf LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 43.5 50.5 37-43 IIII-I 6 36.5 43.5 30-36 IIII-II 7 29.5 36.5 23-29 IIII-IIII-I 11 22.5 29.5 16-22 IIII-IIII-I 11 15.5 22.5 9-15 1 1 8.5 15.5 i = 7 n =40 Scores Tally Frequency Class Boundaries (CB) LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 43.5 50.5 37-43 IIII-I 6 36.5 43.5 30-36 IIII-II 7 29.5 36.5 23-29 IIII-IIII-I 11 22.5 29.5 16-22 IIII-IIII-I 11 15.5 22.5 9-15 1 1 8.5 15.5 i = 7 n =40

27. Example #1 Scores Tally Frequency Class Boundaries (CB) Class Mark (CM) Less than Cumulative Frequency ( Cf) ( f+Cf ) LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 43.5 55.5 47 37-43 IIII-I 6 36.5 43.5 40 30-36 IIII-II 7 29.5 36.5 33 23-29 IIII-IIII-I 11 22.5 23.5 26 16-22 IIII-IIII-I 11 15.5 22.5 19 9-15 1 1 8.5 15.5 12 i = 7 n =40 Scores Tally Frequency Class Boundaries (CB) LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 43.5 55.5 47 37-43 IIII-I 6 36.5 43.5 40 30-36 IIII-II 7 29.5 36.5 33 23-29 IIII-IIII-I 11 22.5 23.5 26 16-22 IIII-IIII-I 11 15.5 22.5 19 9-15 1 1 8.5 15.5 12 i = 7 n =40

28. Example #1 Scores Tally Frequency Class Boundaries (CB) Class Mark (CM) Cumulative Frequency (Cf) ( f+Cf ) LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 43.5 55.5 47 40 37-43 IIII-I 6 36.5 43.5 40 36 30-36 IIII-II 7 29.5 36.5 34 30 23-29 IIII-IIII-I 11 22.5 23.5 26 23 16-22 IIII-IIII-I 11 15.5 22.5 19 12 9-15 1 1 8.5 15.5 12 1 i = 7 n =40 Scores Tally Frequency Class Boundaries (CB) Cumulative Frequency (Cf) ( f+Cf ) LCB (LCL-0.5) UCB (UCL+0.5) 44-50 IIII 4 43.5 55.5 47 40 37-43 IIII-I 6 36.5 43.5 40 36 30-36 IIII-II 7 29.5 36.5 34 30 23-29 IIII-IIII-I 11 22.5 23.5 26 23 16-22 IIII-IIII-I 11 15.5 22.5 19 12 9-15 1 1 8.5 15.5 12 1 i = 7 n =40

29. evaluation

30. Construct the problem using frequency distribution. Given 50 multiple choice items in their final test in English, the score of the students are the following:

31. Example #3 Grouped frequency distribution Step.1 Arrange the score from lowest to highest. Construct a frequency distribution table given the set of data. Ages of people going to Boracay 14 29 43 17 32 44 21 34 47 21 35 52 22 35 53 25 36 54 26 37 55 27 39 60 28 41 60 28 42 63

32. Answer the following: 1. Construct a frequency distribution table given the set of data using 6 classes.