Interpreting Quartiles of Ungrouped Data.pptx

Lesson in Grade 10 Math, 4th quarter

1. INTERPRETINGQUARTILES OF UNGROUPED DATA

2. Prayer 2

3. Attendance Check 3 Is there any absent today?

4. Health Check 4 1. How are you feeling today? 2. What is the heat index today? 3. What should you do if you feel so hot?

5. Let’s React! 5 Given the scores of 10 students in a Science quiz: 15, 10, 20, 5, 8, 4, 3, 7, 10, 14, if your score is 15, how will you feel about this score?

6. Let’s React! 6 Your teacher measured your weight and your classmate’s when he computed for your BMI. He told you that 2 of your classmates are heavier than you are. If you are 25 in the class assuming all of you are of similar height, will you be satisfied with your weight?

7. LEARNING OBJECTIVES Compute for Q 1 , Q 2 , and Q 3 of an ungrouped data; Interpret measures of quartile of an ungrouped data; and Solve problems involving quartile of an ungrouped data. 7

8. The Quartiles are the score points which divide a distribution into four equal parts. What is Quartile? 8 Q 1 Q 2 Q 3 25% of the data has a value   50% of the data has a value   75% of the data has a value  

9. Steps in computing the Quartile values STEP 1 Arrange the data in increasing or ascending order. 9 STEP 2 Compute for the position of the quartile values. Position of Q 3 =   Position of Q 2 =   Position of Q 1 =   STEP 3 Locate the quartile value using the position in the set of data.

10. Let’s consider this problem: A group of students obtained the following scores in their latest 30-item quiz in Math 10, find the lower quartile and upper quartile. 7 10 11 19 19 21 24 24 26 27 30 10

11. 11 A group of students obtained the following scores in their latest 30-item quiz in Math 10, find the lower quartile and upper quartile. 7 10 11 19 19 21 24 24 26 27 30 STEP 1 : 7 10 11 19 19 21 24 24 26 27 30 Arrange the data in increasing or ascending order.

12. 12 A group of students obtained the following scores in their latest 30-item quiz in Math 10, find the lower quartile and upper quartile. 7 10 11 19 19 21 24 24 26 27 30 STEP 2 : Compute for the position of the quartile values. Position of Q 1 = (n+1) 4 = (11+1) 4 = 12 4 = 3 Position of Q 2 = 2(n+1) 4 = 2(11+1) 4 = 12 2 = 6 2 or 3 rd Position or 6 th Position Position of Q 3 = 3(n+1) 4 = 3(11+1) 4 = 3(12) 4 = 9 = 36 4 or 9 th Position

13. 13 A group of students obtained the following scores in their latest 30-item quiz in Math 10, find the lower quartile and upper quartile. 7 10 11 19 19 21 24 24 26 27 30 STEP 3 : Locate the quartile value using the position in the set of data distribution. Position of Q 1 = 3 rd Position of Q 2 = 6 th Position of Q 3 = 9 th 7 10 11 19 19 21 24 24 26 27 30 Q 1 Q 2 Q 3 Therefore, Q 1 = 11 Q 2 = 21 Q 3 = 26 How do we interpret these results?

14. Interpreting Q 1 14 7 10 11 19 19 21 24 24 26 27 30 Since, Q 1 = 11 25% of the scores INTERPRETATION: 25% of the scores is less than or equal to 11. (Lower Quartile)

15. Interpreting Q 2 15 7 10 11 19 19 21 24 24 26 27 30 Since, Q 2 = 21 50% of the scores INTERPRETATION: 50% of the scores is less than or equal to 21. (Median)

16. Interpreting Q 3 16 7 10 11 19 19 21 24 24 26 27 30 Since, Q 3 = 26 75% of the scores INTERPRETATION: 75% of the scores is less than or equal to 26. (Upper Quartile)

17. 17   In Rheem’s Coffee Shop, the owner is interested to know the amount of time it takes his Barista to prepare orders per customer. On a particular day, he asked his store manager to record the service times of their Barista for the first 15 costumers. The data for the service time (to the nearest minute) are as follows: 6, 7, 8, 2, 4, 5, 7, 6, 9, 2, 9, 3, 11, 5, 10. What is the lower & upper quartile of the service time recorded? Interpret the result. Guided Practice Let us solve the following problem together!

18. 18 STEPS ILLUSTRATION Position of Q 1 =         or 4th Position of Q 3 =       or 12th     2 2 3 4 5 5 6 6 7 7 8 9 9 10 11 Q 1 = 4 Q 3 = 9 25% of the time is less than or equal to 4 minutes. 75% of the time is less than or equal to 9 minutes. STEP 1: Arrange the n data entries from lowest to highest. STEP 2: Find the position of the lower & upper quartile using the formula: (Round off to the nearest integer if necessary.) STEP 3: Locate the value of the upper & lower quartile in the distribution. STEP 4: Interpret the results. 6, 7, 8, 2, 4, 5, 7, 6, 9, 2, 9, 3, 11, 5, 10 2 2 3 4 5 5 6 6 7 7 8 9 9 10 11

19. 19 Cardiovascular conditioning improves circulation and strengthens the heart, lungs and blood vessels. It builds endurance and strength for the heart muscle. Moreover, exercise conditions the heart to work more efficiently. 20 aerobics practitioners recorded the average time (in minutes) of their individual workout. The data are listed as follows: 70 72 68 73 43 40 45 40 74 54 80 50 82 50 65 35 62 30 30 55 a.) Arrange the given data from lowest to highest. b.) Solve for the upper and lower quartiles then interpret the results. Guided Practice

20. 20 STEPS ILLUSTRATION Position of Q 1 =         or 5th Position of Q 3 =       or 16th   5.75   Q 1 = 40 Q 3 = 70 25% of the time is less than or equal to 40 minutes. 75% of the time is less than or equal to 70 minutes. STEP 1: Arrange the n data entries from lowest to highest. STEP 2: Find the position of the lower & upper quartile using the formula: (Round off to the nearest integer if necessary.) STEP 3: Locate the value of the upper & lower quartile in the distribution. STEP 4: Interpret the results. 70 72 68 73 43 40 45 40 74 54 80 50 82 50 65 35 62 30 30 55 30 30 35 40 40 43 45 50 50 54 55 62 65 68 70 72 73 74 80 82 30 30 35 40 40 43 45 50 50 54 55 62 65 68 70 72 73 74 80 82

21. 21   Dr. Mabait is a family physician at Family Home Clinic. One morning, he asked her nurse secretary to record the ages of their 15 patients. The following are the data recorded: 22, 24, 10, 33, 15, 12, 17, 31, 25, 30, 29, 27, 20, 17, and 20. Independent Practice Given the problem below, solve for the Q 1, Q 2 , and Q 3 . Then, interpret the result.

22. Let’s Check Your Answers! 22 10 12 15 17 17 20 20 22 24 25 27 29 30 31 33 STEP 1: STEP 2: Position of Q 1 = 4th Position of Q 2 = 8th Position of Q 3 = 12th STEP 3: 10 12 15 17 17 20 20 22 24 25 27 29 30 31 33 Q 1 = 17 Q 3 = 29 Q 2 = 22 STEP 4: 25% of the ages is less than or equal to 17 years old. 50% of the ages is less than or equal to 22 years old. 75% of the ages is less than or equal to 29 years old.

23. Let’s Wrap Up! 23 1. What is Quartile? 2. How do we compute for the quartile values of ungrouped data? 3. How do we interpret the values of Q 1 , Q 2 and Q 3 ?

24. EVALUATION Directions: Study the following situations. Then, answer the questions that follow.  1. Emilio, who is a 14-year-old grade 10 student, believes that he is generally young for his grade level. Upon gathering of data, it has been found out that the first quartile is 15 years old. Would you agree with Emilio? Why? ___________________________________________________________________________________ ___________________________________________________________________________________ 2. Your older sister tells you that you seem to be short for your age. In school, your teacher measures you and your classmates’ height as she computes for your BMI. Your teacher tells you that your height belongs to the upper quartile in the class assuming you and your classmates have similar ages, would you agree with what your sister says? Why? ________________________________________________________________________________ ________________________________________________________________________________