MEASURES OF POSITION(QUARTILES,DECILES,PERCENTILE) Q3 MATH 10

QUARTER 3 LESSON FOR GRADE 10 MATH

1. Class rules! Treat others with respect at all times. Listen to the teacher when s/he speaks. Be prepared everyday to learn new things. Raise your hand before speaking or leaving your seat Listen and follow directions.

2. Activity 1: legendary R ead the legend of the Chinese Zodiac Sign and answer the questions that follow.

3. The Legend of Chinese Zodiac Sign Long ago, the Jade Emperor made an order to designate animals as the calendar signs. The twelve animals that arrive first in the banquet shall be selected. On that day, the rat got up early and rushed to the banquet. On his way, he met the ox and asked the ox to carry him on his back. As the two were approaching the site, the rat slid in front of the ox, and became the first lucky animal of the Chinese zodiac. Following rat and ox are tiger, rabbit, dragon, snake, horse, sheep, monkey, rooster, dog, and pig.

4. Answer the following questions based on the story. 1) Which of the following belongs to the first 50% that arrived earlier than the rest of the group? A. tiger B. rabbit C. dragon D. all of the above 2) Which of the following belongs to the second 50% that arrived later than the rest of the group? A. horse B. snake C. dragon D. none of the above  3) Which of the following represents the median? A. dragon B. snake C. sheep D. none 4) Which of the following belongs to the first 25% that arrived earlier than the rest of the group? A. tiger B. rabbit C. dragon D. snake 5) How many percent of the animals arrived later than the tiger? A. 25% B. 50% C. 75% D. 100%

5. Answer the following questions based on the story. 1) Which of the following belongs to the first 50% that arrived earlier than the rest of the group? A. tiger B. rabbit C. dragon D. all of the above 2) Which of the following belongs to the second 50% that arrived later than the rest of the group? A. horse B. snake C. dragon D. none of the above 3 ) Which of the following belongs to the first 25% that arrived earlier than the rest of the group? A. tiger B. rabbit C. dragon D. snake 4 ) How many percent of the animals arrived later than the tiger? A. 25% B. 50% C. 75% D. 100%

6. Measure of position -is a measure by which the position of a data is determined through its value. Quartiles Deciles Percentiles

7. Measures of position: the quartile of ungroup data

8. Lesson Objectives illustrate the quartile of ungrouped data; compute for quartile of ungrouped data; and Interpret quartile in real-life situations.

9. What is the position of the tiger in the banquet? ans. The tiger is the third animal that arrived into the banquet.

10. Activity 2: What’s the Truth Analyze the following illustrations and tell me whether it is true or false.

11. 1. The tiger belongs to the first 50% or top 50% of the group that arrived earlier than the rest of the animals. True

12. The tiger belongs to the first 25% or top 25% of the group that arrived earlier than the rest of the animals. True

13. The tiger arrived earlier than 75% of the animals. True

14. median Middle, half means dividing a data set into two equal parts. 1 2

15. quartiles Measure of Position: Quartiles of Ungrouped Data

16. quartiles are the score points which divides a distribution into four equal parts. - There are three quartiles denoted as 𝑄 1 , 𝑄 2 , and Q3.

17. quartiles Quartile 1 (Q1) l ower quartile. Meaning 25% of the distribution are below the first quartile Quartile 2 (Q2) the median Meaning 50% are below the second quartile. Quartile 3 (Q3) is the upper quartile. Indicates that 75% of the distribution is below the third quartile

18. Mendenhall and Sincich Method developed by William Mendenhall and Terry Sincich to find the position of the quartile in the given data. Both experts in the field of statistics Authors of many books in statistics

19. Formula: Lower Quartile (L) = Q1 = * Round up the answer to the nearest integer Median = Q2 = * Retain the original answer Upper Quartile = Q3 = * Round down to the nearest integer   where n is the number of elements in the data.  

20. Steps to solve the quartile of ungrouped data Arrange the data in ascending order (from lowest to highest) Find n or the total number of elements in the given data Use the formulas of Mendenhall and Sincich Method.

21. Activity 3. Let’s make it real

22. Read and Answer Problem 1. The grade 10 students are having a practice for their upcoming festival dance. They were asked to form a line with eleven members according to their heights and below is the list of their heights in centimeters. Locate the position of Q1, Q2, Q3. Student Height (cm) A 154 B 156 C 168 D 155 E 150 F 170 G 167 H 160 I 159 J 163 K 152

23. Problem 2 : From the legend of the Chinese Zodiac Sign, the first 12 animals that arrived to the banquet were designated as Calendar Signs. Those animals are as follows. Calculate the Q1, Q2 and Q3. Arranged in ascending order Pig, Dog, rooster, monkey, sheep, horse, snake, dragon, rabbit, tiger, ox, rat.

24. Activity 4. your turn Find the first quartile(Q1), Second Quartile (Q2) and Third Quartile (Q3), given the scores of 10 students in their mathematics activity using Mendenhall and Sincich Method. 4, 9, 7, 14, 10, 8, 12, 15, 6, 11

25. Translate it! Give the meaning of th ese words in Engligh , Filipino or in your own dialect. Ascending Arrive Banquet Lower Ungrouped Upper Median

26. Translate it! Ascending – increasing, from low to high ( mula sa mababa-pataas ) Arrive – reach, come to a place ( dumating ) Banquet – a formal evening meal ( piging o salu-salo ) Lower – downward,below (mas mababa ) Ungrouped – separate items ( walang pangkat o grupo ) Upper- above, higher (mas mataas , itaas ) Median – middle ( gitna )

27. Let’s sum it up What was our lesson all about?  What is a quartile? Was the Mendenhall and Sincich Method helpful in solving the quartile of ungrouped data? Why?  How do we calculate the lower quartile?  How about the upper quartile?  What is referred to as the median?

28. Activity 6. boys vs. girls

29. Situation 1 Given 50 multiple-choice items in the final test, you got 43 correct answers and it falls in the 3rd quartile, how would you feel about you score? Explain your answer.

30. Situation 2 Anton is a secretary in a big company. His salary is in the 1 st quartile. Should Anton be glad about his salary or not? Explain you answer.

31. Scoring Rubrics 5 Explains all points in the situation clearly and comprehensively using concept of quartiles. 4 Explains some points in the situation comprehensively using concept of quartiles. 3 Explains few points in the situation using concept of quartiles. 2 Explains the situation without any application of mathematical concept

32. Quiz! Get ¼ sheet of paper and answer the following 1. Which of the following measures where exactly 25% of the distribution or data set are below it? A. First Quartile C. Third Quartile B. Second quartile D. fourth quartile 2. What measure is also known as the median? A. First Quartile C. Third Quartile B. Second quartile D. fourth quartile 3. In how many parts does the quartile divides a distribution? A. 2 equal parts C. 4 equal parts B. 3 equal parts D. 10 equal parts 4-5. Given the following time record (in seconds) of 7 athletes in 100-meter run, compute the lower quartile (Q1) and the median(Q2). 11, 11. 50, 12, 12.40, 12. 45, 12.5, 13

33. Get ¼ sheet of paper and answer the following 1. Which of the following measures where exactly 25% of the distribution or data set are below it? A. First Quartile C. Third Quartile B. Second quartile D. fourth quartile 2. What measure is also known as the median? A. First Quartile C. Third Quartile B . Second quartile D. fourth quartile 3. In how many parts does the quartile divides a distribution? A. 2 equal parts C . 4 equal parts B. 3 equal parts D. 10 equal parts 4-5. Given the following time record (in seconds) of 7 athletes in 100-meter run, compute the lower quartile (Q1) and the median(Q2). 11, 11. 50, 12, 12.40, 12. 45, 12.5, 13 Ans: Q2 = 4 th =12.40sec Q1 = 2 nd = 11.50sec

34. Additional Activity Make an online survey with your classmates. Think of a question that will prompt you and your classmates to give a quantitative data. Find your position based on the data values and make an interpretation. Then send your output to your teacher via e-mail or Messenger.

35. Thank you!