Answer M10SP-IVa-1 and Try these!

Points to Remember for Quartiles 25% of the data is less than or equal to Q1. Therefore 75% of the data is greater than Q1. 50% of the data is less than or equal to Q2. Therefore 50% of the data is greater than Q2 75% of the data is less than or equal to Q3. Therefore 25% of the data is greater than Q3. Points to Remember for Deciles 10% of the data is less than or equal to D1. Therefore 90% of the data is greater than D1. 20% of the data is less than or equal to D2. Therefore 80% of the data is greater than D2 30% of the data is less than or equal to D3. Therefore 70% of the data is greater than D3 90% of the data is less than or equal to Do. Therefore 10% of the data is greater than D, Points to Remember for Percentiles 10% of the data is less than or equal to P10. Therefore 90% of the data is greater than P 10. 20% of the data is less than or equal to P20. Therefore 80% of the data is greater than P20 30% of the data is less than or equal to P30. Therefore 70% of the data is greater than P30 99% of the data is less than or equal to P99. Therefore 1% of the data is greater than Pog Q2 = D5 = P50 Q1 = D2.5 = P25 Q3 = D7.5 = P75 VIVLIOWEE Try these! DICnezIOU Rconbeg DS A. Using the given data at the right, find the value of the following using the formula. Use a separate sheet of paper. 1. Q2 2 4 6 8 9 10 12 14 15 16 18 20 2. D6 3. P70 B. Answer the following questions by giving your reasons. 1. Out of 250 grade 10 students, 50 students' ages 16 years old and 50 is the value of the first quartile. What does this mean? 2. In a 60-items summative test result, 25 is the score which is the upper quartile. What does it imply?To find the Q3 or upper quartile, find the middle data at the right of Q2 including Q2. The middle data is the value of Q3. 2 4 6 7 8 9 10 11 12 Q3 = 10 3. Mendenhall and Sincich Method To find the Q2 or median, locate the middle term and that is the value of Q2 or median. 2 4 6 7 8 9 10 11 12 To find the value of the different quartile including the median, use the formula Qk = -k(n+2) where 4 n is the number of data and k is the quartile number. Example: Find Q1, Q2 and Q3 from the given data above. 05 6XC Solution. Q1 = 1(9+1) = 4 = 2.5 = 3 - 3'd positon. Therefore: 1 6 Note: If the decimal number of quartile 1 is .5, round up So 2.5 become 3. 3(9+1) _ 30 4 =7.5 - 7th position. Therefore: Q3 = 10 Note: If the decimal number of quarter 3 is .5, round down. So 7.5 become 7. 4 4 Q2= 2(9+1) = 20 = 5 -5th position. Therefore: Q2 = 8 C. Finding Quartiles of Ungrouped Data ( Number of Data is Even) Moore and Mccabe Method and Tuckey Method are just the same in finding the value of the quartiles if the number of data is even. To find Q2 or median, locate the two inner most number and add the number divided by two. The result is the value of Q2 or median. 2 3 5 7 8 9 10 12 14 16 Q2 = 8.5 To find Q1, find the middle term of the lower half and that is the value of Q1. 2 3 5 7 8 9 10 12 14 16 Q1 = 5 To find Q3, find the middle term of the upper half and that is the value of Q3. 2 3 5 7 8 9 10 12 14 16 Q3 = 12 D. Formulas in finding Quartiles, Deciles, and Percentiles of ungrouped data. QK = k(n+1) DK =k(n+1) PK = k(n+1) 10 100 Quartile Decile Percentile k - is the quartile, decile, or percentile number n - is the total number of data. Example: From the given data at the right, find the following; 2 4 5 7 8 9 10 12 14 16 n = 10 1. Q3 2. D4 3. P30 4 1. 03 = 3(10+1) = 23 = 8.25 or 8 position Q3= 12 10 10 2. Da= 4(10+1) - 44 = 4.4 or 4th position D4 = 7 3. P30 100 100 30(10+1)-330 = 3.3 or 3'd position P30 = 5Lesson/ Topic: Measure of Position of Ungrouped Data Learning Competencies: Illustrates the following measures of position: quartiles, deciles, and percentiles. A. Definitions of Terms Quantiles - measure of position that divides the distribution into four, ten, and one hundred equal parts. Quartiles - three score points that divide the distribution into four equal parts. (Q1, Q2, Q3) Deciles - nine score points that divide the distribution into ten equal parts. (D1, D2,...Do) Percentiles - ninety-nine score points that divide the distribution into 100 equal parts. (P1, P2,...P99) B. Finding Quartiles of Ungrouped Data (Number of Data is Odd) 1. Moore and Mccabe Method To find the Q2 or median, arrange the data in increasing order and locate the middle term. The middle data is the median since the number of data is ODD. Therefore Q2 = 8 10 17 12 To find the Q1 or lower quartile, find the two inner most data at the left of Q2 excluding Q2. Add these two numbers and divide it by two. The result is the value of Q1. 2 4 6 8 9 10 11 12 To find Q3 or upper quartile, find the two inner most data at the right of Q2 excluding Q2. Add these two numbers and divide it by two. The result is the value of Q3. 2 7 8 9 10 11 12 2. Tukey Method To find the Q2 or median, locate the middle term and that is the value of Q2 or median. 4 6 7 8 9 10 11 12 Q2 = 8 To find the Q1 or lower quartile, find the middle data at the left of Q2 including Q2. The middle data is the value of Q1. 2 4 6 7 8 9 10 11 12 Q1 = 6Directions: Read each question carefully and choose the letter of the best answer. Encircle 7. The 1st quartile of the ages of the 250 the letter that corresponds to your answer. grade 10 students is 16 years old. Which M10SP-IVa-1 of the following statements is TRUE? 1. Which of the following measures of A. Most of the students are below 16 position is a median score? years old. A. 2nd quartile C. 40th percentile B. Twenty-five percent of the B. 6th decile D. 75th percentile students are 16 years old. C. One hundred fifty students are 2. Which of the following measures of younger than 16 years. position has ninety-nine score D. Seventy-five percent of the points? students are 16 years old and A. decile C. quantile above. B. percentile D. quartile 3. What refers to the upper quartile? 8. What measure of position divides a data A. 2nd quartile C. 25th quartile set into 10 equal parts? B. 3d quartile D. 50th quartile A. decile C. quantile 4. Rochelle got a score of 55 which is B. percentile D. quartile equivalent to 70th percentile in a 9. In a group of 55 examinees taking 50- mathematics test. Which of the item test, Rachel obtained a score of 38. following is NOT true? What does it imply to her score? A. Her score is below the 5th decile. A. at 55th percentile B. She scored above 70% of her B. below the 3rd decile classmates. C. at the upper quartile C. Thirty percent of the class got D. below the 50th percentile scores of 55 and above. D. If the passing mark is the first 10. Which of the following data values quartile, she passed the test. is the 50th percentile? {1.52, 5.36, 6.79, 5.21, 0.28, 5. What is the median score in the set of 8.47, 5.52, 6.26, 5.97} score: 14, 17, 10, 22, 19, 24, 8, 12, and A. 0.28 C. 5.52 19? A. 12 B. 14 C. 17 D. 22 B. 5.21 D. 6.36 6. In a 70-item test, Melody got a score of 50 which is the third quartile. What does it mean? END OF MATHEMATICS A. She got the highest score. B. She surpassed 75% of her classmates. C. Her score is higher than 25% of her classmates. D. Seventy-five percent of the class did not pass the test