Mathematics Grade 10 Quarter 4 Module 1 PDF

10 Mathematics Quarter 4 – Module 1: Measures of Position for Ungrouped Data Mathematics – Grade 10 Quarter 4 – Module 1: Measures of Position for Ungrouped Data First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Go...

10 Mathematics Quarter 4 – Module 1: Measures of Position for Ungrouped Data Mathematics – Grade 10 Quarter 4 – Module 1: Measures of Position for Ungrouped Data First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education – Region XI Development Team of the Module Writers: Joan Loraine D. Bartolome, Vilma E. Tanjay Editors: Vilma E. Tanjay Reviewers: Amelia A. Gumban Illustrator: Layout Artist: Wedzmer B. Munjilul Template Developer: Neil Edward D. Diaz Management Team: Reynaldo M. Guillena Jinky B. Firman Marilyn V. Deduyo Alma C. Cifra Aris B. Juanillo May Ann M. Jumuad Antonio A. Apat Printed in the Philippines by Davao City Division Learning Resources Management Development System (LRMDS) Department of Education – Region XI Office Address: DepEd Davao City Division, E. Quirino Ave., Davao City, Davao del Sur, Philippines Telefax: (082) 224-0100 E-mail Address: [email protected]  10 Mathematics Quarter 4 – Module 1: Measures of Position for Ungrouped Data Introductory Message For the facilitator: As a facilitator, you are expected to orient the learners on how to use this module. You also need to keep track of the learners' progress while allowing them to manage their own learning at home. Furthermore, you are expected to encourage and assist the learners as they do the tasks included in the module. For the learner: As a learner, you must learn to become responsible of your own learning. Take time to read, understand, and perform the different activities in the module. As you go through the different activities of this module be reminded of the following: 1. Use the module with care. Do not put unnecessary mark/s on any part of the module. Use a separate sheet of paper in answering the exercises. 2. Don’t forget to answer Let Us Try before moving on to the other activities. 3. Read the instructions carefully before doing each task. 4. Observe honesty and integrity in doing the tasks and checking your answers. 5. Finish the task at hand before proceeding to the next. 6. Return this module to your teacher/facilitator once you are done. If you encounter any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator. Always bear in mind that you are not alone. We hope that through this material, you will experience meaningful learning and gain deep understanding of the relevant competencies. You can do it! ii  Let Us Learn After going through this module, you are expected to: Ø Illustrates the following measures of position: quartiles, deciles, and percentiles. (M10SP-IVa-1) Specifically, you will; 1. define measures of position 2. locate the specified measures of position of the ungrouped data. 3. find the specified measures of position of the ungrouped data. Let Us Try Encircle the letter of your chosen answer. 1. When the distribution is divided into ten equal parts, how do you call each score point that describes the distribution? A. decile B. interquartile C. percentile D. quartile 2. Which of the following is equivalent to the upper quartile? A. 1st quartile C. 75th percentile B. 5 decile th D. 85th percentile 3. Which of the following measures of position divides the distribution into 100 equal parts? A. decile B. quartile C. quantile D. percentile 4. Which of the following is the difference between the third quartile and the first quartile? A. Interquartile range C. middle quartile B. lower quartile D. upper quartile 5. Which of the following is equivalent to the 5th decile? A. 75th percentile B. 50th percentile C. 25th percentile D. 5th percentile 6. In the given data 16, 14, 17, 19, 15, 18, 13, what is the middle score? A. 15 B. 16 C. 17 D. 18 7. If Mariel is top in a group of 10, how many percent of the students are below on her rank? A. 10 B. 50 C. 70 D. 90 8. Which of the following does NOT belong to the group? I. Q1 II. D2 III. D5 IV. P25 A. I and II B. II and III C. III and IV D. I and IV 1  9. How many percent of the distribution is higher than the first quartile? A. 75% B. 50% C. 25% D. 15% 10. When the distribution is divided into four equal parts, how do you call each score point that describes the distribution? A. decile B. interquartile C. percentile D. quartile Let Us Study Can you still remember the measure of central tendency? If so, let us try to identify the mean, mode, and median in the given data set: A group of students obtained the following scores in their statistics quiz: 8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9 Let’s arrange the given score. We have, 1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9 Questions: 1. What is the sum of the scores? 2. What is the average score? 3. What is the middle score? 4. What scores appeared most of the time? The sum of the scores is 58, therefore, the mean is 5.27, which is obtained by adding the scores and divided by the number of students. The mode is 5 and 8, those are obtained by identifying the number/s which frequently appear. The median is 5, which is obtained by arranging all the numbers in ascending order and identify the middle number. The mean, median, and mode are called measures of central tendency. In our pre-assessment you have noticed, the word quartile, decile, and percentile have been repeatedly mentioned. These are the three different types of measures of position. Measures of position give us a way to see where a certain data point of value falls in a sample or distribution. A measure can tell us whether a value is about average, or whether it is unusually high or low. Measures of position are used for quantitative data that falls on some numerical scale. The Quartile for Ungrouped Data The quartiles are the score points which divide a distribution into 4 equal parts so that each part represents ¼ of the data set. Twenty-five percent (25%) of the 2 distribution is below the first quartile, fifty-percent (50%) are below the second quartile, and seventy-five percent (75%) are below the third quartile. Lower Quartile Median or Upper Quartile 𝑄! Second Quartile 𝑄# 𝑄" a. 25% of the data has a value ≤ 𝑄! b. 50% of the data has a value ≤ 𝑥̅ 𝑜𝑟 𝑄" c. 75% of the data has a value ≤ 𝑄# Using the Mendenhall and Sincich Method: ! Lower Quartile(L) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = " (𝑛 + 1) round to the nearest integer 𝑄! = 𝐿𝑡ℎ 𝑒𝑙𝑒𝑚𝑒𝑛𝑡. If L falls halfway between two integers round up. # Upper Quartile(U) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = " (𝑛 + 1) round to the nearest integer 𝑄# = 𝑈𝑡ℎ 𝑒𝑙𝑒𝑚𝑒𝑛𝑡. If U falls halfway between two integers round down. Interquartile Range is the difference between the Upper quartile and the Lower quartile Examples: 1. A group of students obtained the following scores in their statistics quiz: 8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9. First, arrange the scores in ascending order: 1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9 𝑄! 𝑄" 𝑄# Lower Middle quartile Upper quartile (MEDIAN) quartile Observe how the lower quartile (𝑄! ), middle quartile (𝑄" ), and upper quartile (𝑄# ) of the scores were obtained. Complete the statement below: The first quartile(lower) 3 is obtained by _______________________________________. (observe the position of 3 from 1 to 5) 3 The second quartile(middle) 5 is obtained by ___________________________________. (observe the position of 5 from 1 to 9) The third quartile(upper) 8 is obtained by _______________________________________. (observe the position of 8 from 6 to 9) 2. Given are the scholastic grades in Mathematics of the randomly selected grade 10 students 82, 85, 90, 81, 79, 89, 94, 95, 97, 85, 83, 90 Step 1. Arrange the data in ascending order 79, 81, 82, 83, 85, 85, 89, 90, 90, 94, 95, 97 1 2 3 4 5 6 7 8 9 10 11 12 Step 2. Find its position using the formula below 𝒌 𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒐𝒇 𝑸𝒌 = (𝒏 + 𝟏) 𝟒 Where: k = 1,2,3 n = is the number of elements in a given data First Quartile Second Quartile 1 2 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = (𝑛 + 1) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄% = (𝑛 + 1) 4 4 1 1 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = (12 + 1) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄% = (12 + 1) 4 2 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = (0.25)(13) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄" = (0.5)(13) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = 3.25 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄% = 6.5 𝑄! = 3$% 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑄" is the average of the 6th and the 7th element. 𝑄! = 82 85 + 89 25% of the students have a grade 𝑄" = 2 in Mathematics of less than or equal to 82. 𝑄" = 87 50% of the students have a grade in Mathematics of less than or equal to 87. 4 Third Quartile 3 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = (𝑛 + 1) 4 3 𝐼𝑛𝑡𝑒𝑟𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝑅𝑎𝑛𝑔𝑒 = 𝑄# − 𝑄! 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = (12 + 1) 4 𝐼𝑛𝑡𝑒𝑟𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝑅𝑎𝑛𝑔𝑒 = 90 − 82 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = (0.75)(13) 𝐼𝑛𝑡𝑒𝑟𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝑅𝑎𝑛𝑔𝑒 = 8 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = 9.75 𝑄# = 9'( 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 (round down) 𝑄# = 90 75% of the students have a grade in Mathematics of less than or equal to 90 79, 81, 82, 83, 85, 85, 89, 90, 90, 94, 95, 97 𝑄! 𝑄" 𝑄# The first, second, and third quartile can be obtained also using Interpolation. Step 1: Arrange the given data in ascending order. Step 2: Find the position of each quartile. Using the example above: Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = 3.25, therefore, 𝑄! is between the 2nd and 3rd elements. Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄" = 6.5, therefore, 𝑄" is between the 6th and 7th elements. Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = 9.75, therefore, 𝑄# is between the 9th and 10th elements. Step 3. Interpolate to obtain the value of 𝑄! , 𝑄" , and 𝑄# 79, 81, 82, 83, 85, 85, 89, 90, 90, 94, 95, 97 1 2 3 4 5 6 7 8 9 10 11 12 5  For the First Quartile For the Second Quartile Position of 𝑄! = 3.25 Position of 𝑄" = 6.5 Steps: Steps: 1. Subtract the 2nd element 82 − 81 1. Subtract the 6th element 89 − 85 to the 3rd element =1 to the 7th element =4 2. The decimal part 0.25 2. The decimal part 0.5 (position) (position) 3. Multiply the decimal (1)(0.25) 3. Multiply the decimal part (4)(0.5) part and the result in = 0.25 and the result in =2 number 1. number 1. 4. Add the result to the 81 + 0.25 4. Add the result to the 85 + 2 smaller value = 81.25 smaller value = 87 Therefore, 𝑸𝟏 = 𝟖𝟏. 𝟐𝟓 Therefore, 𝑸𝟐 = 𝟖𝟕 For the Third Quartile Position of 𝑄# = 9.75 Steps: 1. Subtract the 10th 94 − 90 element to the 9th =4 element 2. The decimal part 0.75 (position) 3. Multiply the decimal (4)(0.75) part and the result in =3 number 1. 4. Add the result to the 90 + 3 smaller value = 93 Therefore, 𝑸𝟑 = 𝟗𝟑 The Decile for Ungrouped Data The deciles are the nine score points which divide a distribution into ten equal parts. Deciles are denoted as 𝐷! , 𝐷" , 𝐷# , 𝐷) , 𝐷* , 𝐷+ , 𝐷, , 𝐷- , 𝐷.. They are computed in the same way that the quartiles are calculated. 𝐷! 𝐷" 𝐷# 𝐷) 𝐷* 𝐷+ 𝐷, 𝐷- 𝐷. The 1st decile (𝐷! ) is the 10th percentile (𝑃!/ ). It means 10% of the data is less than or equal to the value of 𝑃!/ 𝑜𝑟 𝐷! , and so on. 6 3. Ages of a COVID 19 Patient of a certain district of Davao City. 47 74 19 23 38 36 14 62 62 9 17 34 53 14 23 26 45 45 77 43 7 27 67 23 33 31 40 48 46 15 5 42 `15 34 36 Find the value of the 2nd decile, 6th decile, and 8th decile. SOLUTION: Step 1: Arrange the given data 5 7 9 14 14 15 15 17 19 23 23 23 26 27 31 33 34 34 36 36 38 40 42 43 45 45 46 47 48 53 62 62 67 74 77 Note: In solving the decile, the same process in the quartile should be done. Finding the 2nd decile: 𝑘 Using Linear Interpolation 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷3 = (𝑛 + 1) 10 Since the 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" = 7.2, therefore, 2 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" = (35 + 1) 𝐷" is between the 7th element and the 10 8th element. 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" = (0.2)(36) 1. 8th element – 17 − 15 = 2 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" = 7.2 7th element 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" ≈ 7th element 2. decimal part 0.2 of 7.2 𝐷" = 15 3. Multiply the (2)(0.2) = 0.4 result in 1 20% of the COVID 19 Patient and 2 is younger or equal to 15 4. Add it to the 15 + 0.4 = 15.4 years old. smaller value Therefore, 𝐷" = 15.4, 20% of the COVID 19 Patient is younger or equal to 15.4 years old. 7 Finding the 6th Decile 𝑘 Using Linear Interpolation 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷3 = (𝑛 + 1) 10 Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷+ = 21.6, therefore, 6 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷+ = (35 + 1) 𝐷+ is between the 21st element and the 10 22nd element. 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷+ = (0.6)(36) 1. 22nd element – 21st 40 − 38 = 2 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷+ = 21.6 element 𝐷+ ≈ 224% 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 2. decimal part of 21.6 0.6 𝐷+ ≈ 40 3. Multiply the result (2)(0.6) = 1.2 in 1 and 2 60% of the COVID 19 Patient 4. Add it to the 38 + 1.2 = 39.2 is younger or equal to 40 smaller value years old. Therefore, 𝐷+ = 39.2, 60% of the COVID 19 Patient is younger or equal to 39.2 years old. Finding 𝑫𝟖 𝑘 Using Linear Interpolation 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷3 = (𝑛 + 1) 10 Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷- = 28.8, therefore, 8 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷- = (35 + 1) 𝐷- is between the 28th element and the 10 29th element. 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷- = (0.8)(36) 1. 29th element – 28th 48 − 47 = 1 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷- = 28.8 element 𝐷- ≈ 29'( 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 2. decimal part of 28.8 0.8 𝐷- ≈ 48 3. Multiply the result (1)(0.8) = 0.8 in 1 and 2 80% of the COVID 19 Patient 4. Add it to the 47 + 0.8 = 47.8 is younger or equal to 48 smaller value years old Therefore, 𝐷- = 47.8, 80% of the COVID 19 Patient is younger or equal to 47.8 years old. The Percentile for Ungrouped Data The percentiles are the ninety-nine score points which divide a distribution into one hundred equal parts so that each part represents the data set. Percentiles indicate the percentage of scores that a given value is higher or greater than. 8  For example, the first percentile (P1) separates the lowest 1% from the other 99%. 𝑄! 𝑄" 𝑄# 𝑃"* 𝑃*/ 𝑃,* 𝐷! 𝐷" 𝐷# 𝐷) 𝐷* 𝐷+ 𝐷, 𝐷- 𝐷. 𝑃!/ 𝑃"/ 𝑃#/ 𝑃)/ 𝑃*/ 𝑃+/ 𝑃,/ 𝑃-/ 𝑃./ 4. Using the above data on Ages of Covid 19 Patient of a certain District in Davao City, find the 40th Percentile and the 75th Percentile. 5 7 9 14 14 15 15 17 19 23 23 23 26 27 31 33 34 34 36 36 38 40 42 43 45 45 46 47 48 53 62 62 67 74 77 Finding the 40th Percentile 𝑘 Using Linear Interpolation 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃3 = (𝑛 + 1) 100 Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃)/ = 14.4, therefore, 40 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃)/ = (35 + 1) 100 𝑃)/ is between the 14th element and the 15th element. 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃)/ = (0.4)(36) 1. 15th element – 14th 31 − 27 = 4 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃)/ = 14.4 element 𝑃)/ ≈ 14'( 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 2. decimal part of 14.4 0.4 𝑃)/ ≈ 27 3. Multiply the result (4)(0.4) = 1.6 in 1 and 2 40% of the COVID 19 Patient 4. Add it to the 27 + 1.6 = 28.6 is younger or equal to 27 smaller value years old Therefore, 𝑃)/ = 28.6, 40% of the COVID 19 Patient is younger or equal to 28.6 years old. 9 Finding the 75th Percentile 𝑘 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃3 = (𝑛 + 1) 100 75 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃,* = (35 + 1) 100 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃,* = (0.75)(36) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃,* = 27 𝑃,* = 27'( 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑃,* = 46 75% of the COVID 19 Patient is younger or equal to 46 years old Let Us Practice Study the given data and answer the questions that follow. Show your solution. 1. Ages of the SSG Officers of Dacudao NHS: 14, 15, 17, 16, 18, 15, 15, 16, 17, 16, 15, 17, 14, 17, 15, 15, 16, 14, 15, 18. Find the following using Mendenhall and Sincich Method. a. First Quartile b. 4th Decile c. 80 Percentile 2. The new cases of COVID 19 in the Philippines as of February 21, 2021, are as follows: REGION NEW CASES NCR NATIONAL CAPITAL REGION 618 CAR CORDILLERA ADMINISTRATIVE REGION 176 I ILOCOS REGION 49 II CAGAYAN VALLEY 45 III CENTRAL LUZON 101 IV A CALABARZON 160 IV B MIMAROPA 4 V BICOL REGION 11 VIII EASTERN VISAYAS 30 VI WESTERN VISAYAS 93 VII CENTRAL VISAYAS 404 10  IX ZAMBOANGA PENINSULA 24 X NORTHERN MINDANAO 31 XI DAVAO REGION 60 XII SOCCKSARGEN 45 XIII CARAGA REGION 34 BARMM BANGSAMORO AUTONOMOUS REGION IN 8 MUSLIM MINDANAO a. Arrange the data from the lowest number of cases to the highest number of cases, indicating the region and the number of cases. b. What region belongs to the first quartile? c. What are the regions below the first quartile? d. How many cases belong to the 75th percentile? e. Is Davao Region belong to the 5th Decile? f. What region/s belong to the upper 10% of having most of the new cases? g. How many new cases that belong to 30% percentile and below? h. What are the Regions or areas that are higher or equal to the 60th percentile? i. What will be your contribution to minimize the number of new cases in your area? Let Us Practice More Complete the Cross Quantile puzzle by finding the specified measures of position using linear interpolation. (In filling the boxes, disregard the decimal point. Show your solution.) Given: Ages of selected teachers: 23, 25, 27, 30, 33, 38, 40, 41, 43, 43, 45, 48, 53 1 2 3 Across 1. 𝐷! 4 4. 𝑃,- 5. 𝑃-* 5 8. 𝑃)- Down 10. 𝐷- 6 2. 𝑃#* 3. 𝑃)* 7 8 9 5. 𝑄# 6. 𝑃-- 7. 𝑃!* 10 9. 𝐷+ SOLUTION: 11  FINAL Find POSITION SUBTRACT MULTIPLY ADD VALUE 𝐷" 2 (14) = 2.8 27 − 25 = 2 (2)(0.8) = 1.6 25 + 1.6 = 26.6 𝐷" = 26.6 10 1. 𝐷! 2. 𝑃#* 3. 𝑃)* 4. 𝑃,- 5. 𝑃-* 5. 𝑄# 6. 𝑃-- 7. 𝑃!* 8. 𝑃)- 9. 𝐷+ 10. 𝐷- Let Us Remember Measures of Positions Quartiles – divides the distribution into 4 equal parts. 𝒌 𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒐𝒇 𝑸𝒌 = 𝟒 (𝒏 + 𝟏), where 𝑘 = 1,2,3 and n is the number of elements in a given data Deciles – divides the distribution into 10 equal parts. 𝒌 𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒐𝒇 𝑫𝒌 = 𝟏𝟎 (𝒏 + 𝟏), where 𝑘 = 1,2,3,4,5,6,7,8,9 Percentiles – divides the distribution into 100 equal parts. 𝒌 𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒐𝒇 𝑷𝒌 = 𝟏𝟎𝟎 (𝒏 + 𝟏), where 𝑘 = 1, 2, 3, 4, … , 99 12  Let Us Assess 1. When the distribution is divided into four equal parts, how do you call each score point that describes the distribution? A. decile B. interquartile C. percentile D. quartile 2. When the distribution is divided into ten equal parts, how do you call each score point that describes the distribution? A. decile B. interquartile C. percentile D. quartile 3. Which of the following measures of position divides the distribution into 100 equal parts? A. decile B. quartile C. quantile D. percentile 4. Which of the following is equivalent to the upper quartile? A. 1st quartile C. 75th percentile B. 5th decile D. 85th percentile 5. Which of the following is equivalent to the 5th decile? A. 75th percentile B. 50th percentile C. 25th percentile D. 5th percentile 6. How many percent of the distribution is higher than the first quartile? A. 75% B. 50% C. 25% D. 15% For numbers 7 to 10, please refer to the data below: The Number of released modules per section of grade 10 level. 40, 37. 40, 41, 40, 35, 32, 26, 37, 40, 35, 38, 38, 37, 35, 38 7. What is the first quartile? A. 32 B. 35 C. 37 D. 38 8. What is the 75th percentile? A. 37 B. 38 C. 40 D. 41 9. What is the interquartile range? A. 3 B. 4 C. 5 D. 6 10. What is the 6th Decile? A. 37 B. 38 C. 40 D. 41 13  Let Us Enhance Take a survey of 15 of your classmates. 1. Choose one of the following categories: a. Weight in kilogram b. Height in centimeters c. Number of Facebook friends Write the name of your classmates and their corresponding value of the chosen category. 2. Arrange the given data from lowest to highest. 3. Find two values of each quantile. One lower and one upper. Show your solution. Example: 𝑄! 𝑎𝑛𝑑 𝑄# , 𝐷% 𝑎𝑛𝑑 𝐷' , 𝑃#( 𝑎𝑛𝑑 𝑃'( RUBRICS: TOTAL POINTS 70 OUSTANDING SATISFACTORY DEVELOPING BEGINNING CRITERIA RATING 10 8 4 2 DATA The Data is The data The values are Values not GATHERI complete, with gathered has arranged from arranged. NG name of the name but no lowest to correspondents values. highest. and values. The values are The values are arranged from arranged from lowest to highest. lowest to highest. Accuracy The The The The (Per computations computations are computations computation measures are accurate. accurate. Use of are erroneous s are of Position A wise use of key concepts of and show erroneous solved) key concepts of measures of some use of and do not measures of position is key concepts show some position is evident. of measures of use of key evident. position. concepts of measures of position. OVERALL RATING 14  Let Us Reflect We encountered so many difficulties and challenges in our different lives especially this time of the pandemic. We have to stand our position, whether we have to protect ourselves and our loved ones by staying at home or enjoy life as long as we live by going outside. Don’t lose hope. We have to remember that for every problem there will always be a solution and an answer so we have to be patient in solving the problem or might be a part of the solution and not be part of the problem. Understanding Level: A. Color your level of understanding about Measures of Position, whether it is 10%, 20%, 30% … or 100% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% B. Write the things you’ve learned about measures of position depending on your level of understanding. 10% equivalent to 1 sentence. 15  16 Let Us Assess Let Us Practice More 1. D 1 2 3 1. 𝐷! = 23.8 2. A 2 3 8 3 2. 𝑃%& = 32.7 3. D 4 3. 𝑃'& = 38.6 4. C 2 4 4 8 4 4. 𝑃(# = 44.84 5. B 5 5. 𝑃#& = 47.7 6. A 4 7 7 6 5. 𝑄% = 44 7. B 6. 𝑃## = 49.6 8. C 6 7. 𝑃!& = 25.2 9. C 4 4 8. 𝑃'# = 39.44 10. B 7 8 9 9. 𝐷" = 41.8 2 3 9 4 4 10. 𝐷# = 45.6 10 4 5 6 6 1 2 8 Let Us Practice: b. Eastern Visayas c. Mimaropa, 1. a. 𝑄! = 15 b. 𝐷" = 16 c. 𝑃#$ = 17 Bangsamoro, Bicol 2. a. Region, and REGION NEW Zamboanga CASES Peninsula IVB MIMAROPA 4 d. 101 BARMM BANGSAMORO AUTONOMOUS 8 e. No, Davao Region is REGION IN MUSLIM MINDANAO above the 5th Decile. V BICOL REGION 11 f. National Capital IX ZAMBOANGA PENINSULA 24 Region VIII EASTERN VISAYAS 30 g. 77 X NORTHERN MINDANAO 31 h. Davao Region, XIII CARAGA REGION 34 Western Visayas, XII SOCCKSARGEN 45 Central Luzon, Calabarzon, II CAGAYAN VALLEY 45 Cordillera I ILOCOS REGION 49 Autonomous Region, XI DAVAO REGION 60 Central Visayas and VI WESTERN VISAYAS 93 National Capital III CENTRAL LUZON 101 Region. IVA CALABARZON 160 i. Answer may vary CAR CORDILLERA ADMINISTRATIVE 176 REGION VII CENTRAL VISAYAS 404 NCR NATIONAL CAPITAL REGION 618 Let Us Try: 1. A 6. B 2. C 7. D 3. D 8. B 4. A 9. A 5. B 10. D Answer Key  References Callanta, Melvin M., et.al, Mathematics Learner’s Module, Department of Education, 2015, pp 355 – 378. “Updates on Covid on Davao Region”, Department of Health Davao Region Facebook Page, February 21, 2021. “New Cases by Region: COVID-19 Philippines in Numbers”, covid19stats.ph, February 22, 2021. For inquiries or feedback, please write or call: Department of Education – Davao City Division Elpidio Quirino Ave., Poblacion District, Davao City, 8000 Davao del Sur Telefax: (082) 224-3274, (082) 222-1672 E-mail Address: [email protected]