CHAPTER 3: FREQUENCY DISTRIBUTION ..pptx

statistic

1. Minimal Chapter 3 FREQUENCY DISTRIBUTION REPORTER: BEVERLY A. SERADA

2. Definition Frequency indicates how often something occurs.

3. YOUR LOGO Definition Frequency distribution: A frequency distribution shows the frequency of repeated items in a graphical form or tabular form. It gives a visual display of the frequency of items or shows the number of times they occurred.

4. Definition A frequency distribution table has two or three columns.  The first column has all the outcomes as individual values or in the form of class intervals.  The second column of the table includes tally marks of each outcome, which also tells us about the frequency using vertical lines. The third column tells us about the frequency of each outcome. 

5. PART OE Given below are marks obtained by 20 students in Math out of 25. 21, 23, 19, 17, 12, 15, 15, 17, 17, 19, 23, 23, 21, 23, 25, 25, 21, 19, 19, 19 Marks Obtained Tally Marks Frequency 12 I 1 15 II 2 17 III 3 19 IIII 5 21 III 3 23 IIII 4 25 II 2

6. PART OE PARTS OF FREQUENCY TABLE Class limits groupings or categories define by lower and upper limits Lower class limits are the smallest numbers that belongs to the different classes. Upper class limits are the highest numbers that belongs to the different classes

7. Class limits Examples: 16-20 21-25 26-30 PARTS OF FREQUENCY TABLE Upper limit of the first interval Lower limit of the second interval

8. 2 . Class Size refers to the number of data points that fall within specific intervals or classes. PARTS OF FREQUENCY TABLE class size- 5 L.L U.P 16 - 20 21 - 25

9. 3. Class Boundaries used to separate class but without gaps created by class limits the number to be added or subtracted is half the difference between the upper limit of one class and the lower limit of the next class PARTS OF FREQUENCY TABLE

10. Topic 1 Presentations are communication tools. PARTS OF FREQUENCY TABLE

11. Topic 1 Presentations are communication tools. PARTS OF FREQUENCY TABLE 4. Class Marks the midpoint of the lower and upper limit add the lower and the upper limit then divide by 2 Example: C.L. Class Mark 16 - 20 18 21 - 25 23 26 - 30 28 31 - 35 33

12. Topic 1 Presentations are communication tools. PARTS OF FREQUENCY TABLE 1. Class limits 2. Class Size 3. Class Boundaries 4. Class Marks

13. STEPS IN CONSTRACTING THE FREQUENCY DISTRIBUTION TABLE

14. Consider the given data below which shows the scores of 60 students in a statistical test. 5 13 8 6 13 10 5 13 15 16 8 12 15 10 12 16 12 9 3 7 11 15 11 7 15 2 13 5 9 12 13 9 12 9 9 14 12 11 19 13 16 18 3 13 18 10 15 14 18 11 10 12 6 9 5 17 9 6 9 18

15. : S teps in Constracting the Frequency Distribution table 1. Find the range of the values Range = highest value – lowest value Example: R = 19-2 R = 17 5 13 8 6 13 10 5 13 15 16 8 12 15 10 12 16 12 9 3 7 11 15 11 7 15 2 13 5 9 12 13 9 12 9 9 14 12 11 19 13 16 18 3 13 18 10 15 14 18 11 10 12 6 9 5 17 9 6 9 18

16. Steps in Constracting the Frequency Distribution table Presentations are communication tools. 2. Determine the class width using Sturge’s Formula k= 1 + 3.3 log n where: k = number of class interval n = total number of observation Example: k = 1 + 3.3 log 60 k = 1 + 3.3 (1.77815) = 6.867 k = 7 class interval thus, C= = 2.42 = 3  

17. Topic Presentations are communication tools. 3. Set up the class limits of each class Examples Class Limit 2-4 5-7 8-10 11-13 14-16 17-19 Steps in Constracting the Frequency Distribution table

18. 4. Set the class boundaries then lower boundary = lower limit –V and upper boundary = upper limit +V in the example hence the first lower boundary is 2 – 0.5 = 1.5 and the first upper boundary is 4 + 0.5= 4.5   S teps in Constracting the Frequency Distribution table

19. S teps in Constracting the Frequency Distribution table Examples Class Limit 2-4 5-7 8-10 11-13 14-16 17-19 Upper limit of the first interval Lower limit of the second interval

20. Examples: S teps in Constracting the Frequency Distribution table Class boundaries 1.5 - 4.5 4.5 - 7.5 7.5 -10.5 10.5 - 13.5 13.5 - 16.5 16.5 - 19.5 Class Limit 2-4 5-7 8-10 11-13 14-16 17-19

21. 240+ Short description Presentations are communication tools that can be used as speeches, reports, and more. 5. Tally the scores in the appropriate classes and then add the tallies for each class in order to obtain the frequency Class Limit Class Boundaries Tally frequency (f) 2-4 1.5 - 4.5 lll 3 5-7 4.5 - 7.5 llll-llll 9 8-10 7.5 - 10.5 llll-llll - llll 14 11-13 10.5- 13.5 llll-llll - llll 18 14-16 13.5- 16.5 llll-llll 10 17-19 16.5- 19.5 llll-l 6 N=60 S teps in Constracting the Frequency Distribution table

22. Consider the given data below which shows the scores of 60 students in a statistical test. 5 13 8 6 13 10 5 13 15 16 8 12 15 10 12 16 12 9 3 7 11 15 11 7 15 2 13 5 9 12 13 9 12 9 9 14 12 11 19 13 16 18 3 13 18 10 15 14 18 11 10 12 6 9 5 17 9 6 9 18

23. Education. Presentations are communication tools that can be used as demonstrations, lectures, speeches, reports, and more. Most of the time, they're presented before an audience. What is cumulative frequency distribution ? Cumulative means totalling or gradually building up . In statistics, cumulative frequency is found by adding up all successive frequencies in a frequency distribution table. In statistics, the frequency of the first-class interval is added to the frequency of the second class, and this sum is added to the third class and so on then, frequencies that are obtained this way are known as cumulative frequency (c.f.). A cumulative frequency table is a simple visual representation of the cumulative frequencies for each distinct value or category.

24. Class boundaries Frequency Cumulative frequency 1.5-4.5 3 3 4.5-7.5 9 9 + 3 =1 3 7.5-10.5 14 1 3 +1 4 = 27 10.5-13.5 18 27 + 18 = 45 13.5-16.5 10 45+10= 55 16.5-19.5 6 55+6=61 Examples:

25. Education. Presentations are communication tools that can be used as demonstrations, lectures, speeches, reports, and more. Most of the time, they're presented before an audience. Types Of Cumulative Frequency Distribution. There are two types of cumulative frequency distributions. <  Less than cumulative frequency distribution: It is obtained by adding successively the frequencies of all the previous classes including the class against which it is written. The cumulate is started from the lowest to the highest size. > More than cumulative frequency distribution: It is obtained by finding the cumulate total of frequencies starting from the highest to the lowest class.

26. Education. Presentations are communication tools that can be used as demonstrations, lectures, speeches, reports, and more. Most of the time, they're presented before an audience. CL 2-4 5-7 8-10 11-13 14-16 17-19 Tally (t) /// //// / - //// //// / - //// / - //// ///// - ///// - ///// - /// ///// - ///// ///// - / Freq (f) 3 9 14 1 8 10 6 N = 60 X (Class Mark) 3 6 9 12 15 18 CB LCB - UCB 1.5-4.5 4.5-7.5 7.5-10.5 10.5-13.5 13.5-16.5 16.5-19.5 Cuf < > 3 60 12 51 26 37 44 19 54 9 60 3

27. Education. Presentations are communication tools that can be used as demonstrations, lectures, speeches, reports, and more. Most of the time, they're presented before an audience. Relative Frequency Distribution: A relative frequency distribution is made by dividing each frequency of a distribution by the total frequency and expressing the result either as a decimal or as a percent(Percentage frequency distribution).

28. Education. Presentations are communication tools that can be used as demonstrations, lectures, speeches, reports, and more. Most of the time, they're presented before an audience. CL 2-4 5-7 8-10 11-13 14-16 17-19 Tally (t) /// //// / - //// //// / - //// / - //// ///// - ///// - ///// - /// ///// - ///// ///// - / Freq (f) 3 9 14 1 8 10 6 N = 60 X 3 6 9 12 15 18 CB LCB - UCB 1.5-4.5 4.5-7.5 7.5-10.5 10.5-13.5 13.5-16.5 16.5-19.5 Cuf < > 3 60 12 51 26 37 44 19 54 9 60 3 rel f 3/60(100)= 5 9/60(100)= 15 14 /60(100)= 23.33 18 /60(100)= 30 /60(100)= 16 /60(100)= 10

29. Education. Presentations are communication tools that can be used as demonstrations, lectures, speeches, reports, and more. Most of the time, they're presented before an audience. Example- 2 The following data show the weights (in pounds) of 30 students of a school . Find relative frequency distribution. Find percentage frequency distribution . (c ) What percentage of the student‘s weight is less 117 pounds . (d ) What percentage of the student‘s weight is over 117 pounds . (e) What percentage of the student‘s weight is in between 100 and 126 pounds . Class Interval Frequency 91 - 99 3 100 – 108 7 109 – 117 11 118 – 126 7 127 – 135 2   30

30. Solution : (a) And (b) Class Interval Frequency Relative Frequency Percentage Frequency 91 - 99 3 100 – 108 7 109 – 117 11 118 – 126 7 127 – 135 2   30 1 100 Class Interval Frequency 91 - 99 3 100 – 108 7 109 – 117 11 118 – 126 7 127 – 135 2   30 1 100

31. (c) From column four Percentage of the student's weight is less 117 pounds = 10% + 23.33% + 36.67% Percentage of the student's weight is less 117 pounds = 70 %   (d) From column four Percentage of the student's weight is over 117 pounds = 23.33% + 6.67% Percentage of the student's weight is over 117 pounds = 30%

32. Topic 1 Presentations are communication tools. (e) From column four Percentage of the student's weight is in between 100 and 126 pounds = 23.33% + 36.67 % + 23.33 % Percentage of the student's weight is in between 100 and 126 pounds = 83.33%

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