Q4-Lesson-3-Measure-of-Positions-in-Grouped-Data.pptx

math 10 4th quarter measures of position of groped data

1. Measures of Position for Grouped Data

2. Puzzle Game M A T H E M A T I C S M A T H E M A T I C S Arrange the letter tiles to form a word/words.

3. Puzzle Game S A S U R E M E M E A S U R E S O F O S I T I O P N S P O S I T I O N S O F Arrange the letter tiles to form a word/words.

4. Puzzle Game E D O U P G R O U P E D G R Arrange the letter tiles to form a word/words.

5. Puzzle Game C L S I C L A S S A S N T E R V A L I N T E R V A L Arrange the letter tiles to form a word/words.

6. Puzzle Game F R E F R E Q U E N C Y Q U E N C Y Arrange the letter tiles to form a word/words.

7. Puzzle Game N D A L O W E R E R B L O W O U R Y B O U N D A R Y Arrange the letter tiles to form a word/words.

8. Puzzle Game S S C L A S S S I Z E C L A S I Z E Arrange the letter tiles to form a word/words.

9. Puzzle Game L A T C U M U L A T I V E C U I V E M U Arrange the letter tiles to form a word/words.

10. Measures of Position for Grouped Data QUARTILES DECILES PERCENTILES

11. QUARTILES The steps in the computation of the median are also followed in the computation of Q 1 and Q 3 . To calculate the median, determine first the median class. In the same manner, the Q 1 class and the Q 3 class must be determined first before computing for Q 1 and Q 3 . The Q 1 class is the class interval where the th score is contained while the class interval that contains the th score is the Q 3 class. Q 1 and Q 3 (Grouped Data) N 4 3N 4

12. FORMULA Q 1 and Q 3 (Grouped Data) where X LB = lower boundary of Q 1 class N = total frequency cf b = cumulative frequency before Q 1 class fq 1 = frequency of the Q 1 class i = size of the class interval where X LB = lower boundary of Q 3 class N = total frequency cf b = cumulative frequency before Q 3 class fq 3 = frequency of the Q 3 class i = size of the class interval

13. EXAMPLE The following table shows the daily wages of 40 workers. Daily Wages ( ₱) Frequency 426 - 450 3 401 – 425 12 376 – 400 9 351 – 375 8 326 – 350 5 301 - 325 3 Find Q 1 and Q 3 N = 40

14. EXAMPLE Solution : Prepare a cumulative frequency table. Daily Wages ( ₱ ) Frequency < cf 426 - 450 3 401 – 425 12 376 – 400 9 351 – 375 8 326 – 350 5 301 - 325 3 N = 40 3 8 16 25 37 40 Q 1 class: N 4 = 40 4 or 10 th (1 st – 3 rd ) (4 th – 8 th ) (9 th – 16 th ) (17 th – 25 th ) (26 th – 37 th ) (38 th – 40 th ) Q 1 class

15. EXAMPLE Solution : compute for the value of Q 1 . Daily Wages ( ₱ ) Frequency < cf 426 - 450 3 401 – 425 12 376 – 400 9 351 – 375 8 326 – 350 5 301 - 325 3 N = 40 3 8 16 25 37 40 (1 st – 3 rd ) (4 th – 8 th ) (9 th – 16 th ) (17 th – 25 th ) (26 th – 37 th ) (38 th – 40 th ) Class Interval: 351 - 375 X LB = 350.5 cf b = 8 fq 1 = 8 = 25   Q 1 class: N 4 = 40 4 or 10 th

16. EXAMPLE Solution : compute for the value of Q 1 . Class Interval: 351 - 375 X LB = 350.5 cf b = 8 fq 1 = 8 = 25   Q 1 class: N 4 = 40 4 or 10 th     There are 25% of the daily wages are below and 75% are above  

17. EXAMPLE Daily Wages ( ₱ ) Frequency < cf 426 - 450 3 401 – 425 12 376 – 400 9 351 – 375 8 326 – 350 5 301 - 325 3 N = 40 3 8 16 25 37 40 Q 3 class: 3N 4 = 3(40) 4 or 30 th (1 st – 3 rd ) (4 th – 8 th ) (9 th – 16 th ) (17 th – 25 th ) (26 th – 37 th ) (38 th – 40 th ) Q 3 class Solution :

18. EXAMPLE Solution : Daily Wages ( ₱ ) Frequency < cf 426 - 450 3 401 – 425 12 376 – 400 9 351 – 375 8 326 – 350 5 301 - 325 3 N = 40 3 8 16 25 37 40 Q 3 class: 3N 4 = 3(40) 4 or 30 th (1 st – 3 rd ) (4 th – 8 th ) (9 th – 16 th ) (17 th – 25 th ) (26 th – 37 th ) (38 th – 40 th ) Class Interval: 401 - 425 X LB = 400.5 cf b = 25 fq 3 = 12 = 25  

19. EXAMPLE Q 3 class: 3N 4 = 3(40) 4 or 30 th Class Interval: 401 - 425 X LB = 400.5 cf b = 25 fq 3 = 12 = 25       There are 75% of the daily wages are below and 25% are above   Solution : compute for the value of Q 3 .

20. The deciles are the score-points that divide a distribution into ten equal parts. The deciles are computed in the same way as the median, the quartile, and the percentiles were calculated. The Deciles (D 1 , D 2 , D 3 ,…, D 9 ) Grouped Data DECILES

21. FORMULA Deciles (Grouped Data)

22. EXAMPLE Use the frequency distribution to calculate a. D 2 b. D 5 c. D 8 Class Interval f < cf 134 - 139 10 50 128 – 133 9 40 122 – 127 8 31 116 – 121 1 23 110 – 115 5 22 104 – 109 2 17 98 – 103 9 15 92 – 97 5 6 86 - 91 1 1 N = 50 D 2 class: 2N 10 = 2(50) 10 or 10 th Class Interval: 98 - 103 X LB = 97.5 cf b = 6 fd 2 = 9 = 6         20% are below 100.17 and 80% are above 100.17

23. EXAMPLE Use the frequency distribution to calculate a. D 2 b. D 5 c. D 8 Class Interval f < cf 134 - 139 10 50 128 – 133 9 40 122 – 127 8 31 116 – 121 1 23 110 – 115 5 22 104 – 109 2 17 98 – 103 9 15 92 – 97 5 6 86 - 91 1 1 N = 50 D 5 class: 5N 10 = 5(50) 10 or 25 th Class Interval: 122 - 127 X LB = 121.5 cf b = 23 fd 5 = 8 = 6         50% are below and above 123

24. EXAMPLE Use the frequency distribution to calculate a. D 2 b. D 5 c. D 8 Class Interval f < cf 134 - 139 10 50 128 – 133 9 40 122 – 127 8 31 116 – 121 1 23 110 – 115 5 22 104 – 109 2 17 98 – 103 9 15 92 – 97 5 6 86 - 91 1 1 N = 50 D 8 class: 8N 10 = 8(50) 10 or 40 th Class Interval: 128 - 133 X LB = 127.5 cf b = 31 fd 8 = 9 = 6         80% are below 133.5 and 20% are above 133.5

25. PERCENTILES Finding P c for ungrouped data is seldom used because it involves a larger population. Hence, the formula for the computation of P c for grouped data is generally preferred. The steps in the computation of the median are also to be followed in the computation of the percentiles. P 1 , P 2 , P 3 , …, P 98 , P 99 (Grouped Data)

26. FORMULA Percentiles (Grouped Data) where X LB = lower boundary of P 5 class N = total frequency cf b = cumulative frequency before P 5 class fp 5 = frequency of the P 5 class i = size of the class interval where X LB = lower boundary of P 80 class N = total frequency cf b = cumulative frequency before P 80 class fp 80 = frequency of the P 80 class i = size of the class interval

27. EXAMPLE The table below shows the hourly wages of the 50 workers in the Paradise Farm. Calculate: a. P 10 b. P 30 c. P 75 Hourly Wages of 50 Workers in Paradise Farm Class Interval f < cf 134 - 139 10 128 – 133 9 122 – 127 8 116 – 121 1 110 – 115 5 104 – 109 2 98 – 103 9 92 – 97 5 86 - 91 1 N = 50 1 6 15 17 22 23 31 40 50

28. EXAMPLE The table below shows the hourly wages of the 50 workers in the Paradise Farm. Hourly Wages of 50 Workers in Paradise Farm Class Interval f < cf 134 - 139 10 128 – 133 9 122 – 127 8 116 – 121 1 110 – 115 5 104 – 109 2 98 – 103 9 92 – 97 5 86 - 91 1 N = 50 1 6 15 17 22 23 31 40 50 P 10 class: 10N 100 = 10(50) 100 or 5 th Class Interval: 92 - 97 X LB = 91.5 cf b = 1 fp 10 = 5 = 6         10% of the workers are below ₱ 96.3 and 90% are above ₱ 96.3.

29. EXAMPLE The table below shows the hourly wages of the 50 workers in the Paradise Farm. Hourly Wages of 50 Workers in Paradise Farm Class Interval f < cf 134 - 139 10 128 – 133 9 122 – 127 8 116 – 121 1 110 – 115 5 104 – 109 2 98 – 103 9 92 – 97 5 86 - 91 1 N = 50 1 6 15 17 22 23 31 40 50 P 30 class: 30N 100 = 30(50) 100 or 15 th Class Interval: 98 - 103 X LB = 97.5 cf b = 6 fp 30 = 9 = 6         30% of the workers are below ₱ 103.5 and 70% are above ₱ 103.5.

30. EXAMPLE The table below shows the hourly wages of the 50 workers in the Paradise Farm. Hourly Wages of 50 Workers in Paradise Farm Class Interval f < cf 134 - 139 10 128 – 133 9 122 – 127 8 116 – 121 1 110 – 115 5 104 – 109 2 98 – 103 9 92 – 97 5 86 - 91 1 N = 50 1 6 15 17 22 23 31 40 50 P 75 class: 75N 100 = 75(50) 100 or 37.5 Class Interval: 128 - 133 X LB = 127.5 cf b = 31 fp 75 = 9 = 6         75% of the workers are below ₱ 131.83 and 25% are above ₱ 131.83.

31. Percentiles are used when you need to know the relative standing of a score or value. For example, a grade 10 student who has a score of 38 from a 50-item test during online assessment, and he wants to know his relative standing in relation to the 250 grade-10 students handled by a particular teacher. If he is in the 125th position, what is his corresponding percentile? Ans. 50th percentile (P50). Solution: Solve for k using the locator L = 𝑘𝑛 100 where L = 125, and n = 250 125 = 𝑘 (250) 100 so k = 50. This means that there are 50% grade 10 students, or 125 students scored less than or equal to 38. Generalization: