Please help me on my activity in my math subject about Measures of Position in ungrouped data. Please give accurate and complete solution and explanations. Thank you

A. Calculate what is asked om the folio wing data then interpret. Show complete solution. (18 points) I. Find the 02, DB, and P18 for the following sets of scores of 9 students in Mathematics: 27 30 20 14 17 2] 26 23 16 __-' B. QUARTILE OF UNGROUPED DATA Let i be the number of values in the set of data and n be the number of quartile (e.g. Q1 therefore n = 1). Formula: On = In * (i+1)\\ th 4 where n = 1, 2,3 EXAMPLES: 1. Calculate 1st quartile from the following data: 3, 13, 11, 11, 5, 4, 2 Solution: Arrange the data in ascending order. 2, 3, 4, 5, 11, 11, 13 We let n = 1 since you are finding for quartile 1 and i = 7 since there are 7 observations in the set. So, we have th Q1 =(n * (i+1))th 1 * (7 + 1)\\ 1 * 8) th th 4 4 = 2nd value of the given data Locate the second value: 2, 3, 4, 5, 11, 11, 13 Conclusion: Therefore, 25% of the data is lower than or equal to 3. 2. Calculate the second Quartile from the following students' scores in mathematics 85 96 76 108 85 80 100 85 70 95 Solution: Arrange the data in ascending order. 70 76 80 85 85 85 95 96 100 108we let n = 2 since you are finding for the 2nd quartile and i = 10 since 10 is the total number of observation. So, we have = (2* (10 +1)th th Q2 = n * (i+ 1)) ch 4 4 = (2:14) = (42) = 5.5th value of the given data = 5th + 0.5[6th - 5th] Locate the 5th and 6th value from the data: 70 76 80 85 85 85 95 96 100 108 Q2 = 5th + 0.5[6th - 5th] = 85 + 0.5(85 - 85) = 85 + .5(0) = 85 + 0 = 85 Conclusion: Therefore, 50% of the students' scores is lower than or equal to 85. 3. The list shows the number of bottles of strawberry jam sold in a day 14 different vendors 20 18 16 10 12 15 13 9 11 16 15 16 19 20 a. What is the 3d quartile? b. What percent of the distribution fall under this sale? Solution: Arrange the data in ascending order. 9 10 11 12 13 15 15 16 16 16 18 19 20 20 We let n = 3 since you are finding for the 3'd quartile and i = 14 since there are 14 observations in the set. So, we have Q3 = 3 * (14 + 1)\\ 4 = 11.25th value of the given data = 11th + 0.25[12th - 11th] (a) Locate the 1 1th and 12th value from the data: 9 10 11 12 13 15 15 16 16 16 18 19 20 20 Q3 = 11th + 0.25[12th - 11th] = 18 + 0.25(19 - 18) = 18 + 0.25(1) = 18 + 0.25 = 18.25 Conclusion: (b) Therefore, 75% of the sale distribution fall below 18.5. C. DECILE OF UNGROUPED DATA Let i be the number of values in the set of data and n be the number of Decile (e.g. Dotherefore n = 6). Formula: n * (i + 1)) th Dn = where n = 1, 2, 3, 4, 5, 6, 7, 8, 9 10 EXAMPLES: 1. Calculate Decile 3 from the following data: 3, 13, 11, 11, 5, 4, 2 Solution: Arrange the data in ascending order. 2, 3, 4, 5, 1 1, 11, 13 We let n = 3 since you are finding for decile 3 and i = 7 since there are 7 observations. So, we haveDa = (3*(+1)) "= (218)"= (20) = 2.4 th value of the given data = 2nd + 0.4 (3rd - 2nd) Locate the second and third value: 2, 3, 4, 5, 11, 11, 13 D3 = 2nd + 0.4 (3rd - 2nd) = 3+.4(4 - 3) = 3+.4(1) = 3.4 Conclusion: Therefore, 30% of the data is lower than or equal to 3.4. 2. Calculate the sixth decile from the following students' scores in mathematics 85 96 76 108 85 80 100 85 70 95 Solution: Arrange the data in ascending order. 70 76 80 85 85 85 95 96 100 108 We let n = 6 since you are finding for decile 6 and i = 10 since there are 10 observations. So, we have th D6 = 6 * (10 + 1) \\ " = (6*11) 10 10 = (10 = 6.6 th value of the given data = 6th + 0.6[7th - 6th] Locate the 7th and 6th value from the data: 70 76 80 85 85 85 95 96 100 108 Do = 6th + 0.6[7th - 6th] = 85 + 0.6(95 - 85) = 85 + .6(10) = 85 + 6 = 91 Conclusion: Therefore, 60% of the students' scores is lower than or equal to 91. 3. A quiz has 20 items. The following are the scores of 30 students. 18 15 10 12 20 20 15 12 10 12 15 16 18 20 8 9 20 19 19 13 11 10 17 14 12 a. What score is at the 7th decile? b. At which decile is the score of 15? Solution: Arrange the 30 scores in ascending order. 6 7 8 8 9 10 10 10 11 11 12 12 12 12 13 14 15 15 15 16 17 18 18 19 19 20 20 20 20 a. We let n = 7 since you are finding for decile 6 and i = 30 since there are 30 scores. So, we have 7 * (30 + 1)\\ D, = (7* 10 = 21.7 th value of the given data = 21st + 0. 7[22nd - 21st] Locate the 22nd and 21st value from the data: 5 6 7 8 8 9 10 10 10 11 12 12 12 13 14 15 15 15 16 17 18 18 19 19 20 20 20 20D7 = 21st + 0.7[22nd - 21sc] = 16 + 0.7(17 - 16) = 16 + 0.7 (1) = 16 + 0.7 = 16.7 Conclusion: Therefore, 70% of the students' scores is lower than or equal to 16.7. b. The 18th, 19th, and the 20th scores are the same: 15. So, we get the average of these ranks: 18 + 19 + 20 57 = 19 3 3 Thus, 19th score is 15 (Dn = 15) and i = 30. By substitution, we have n * (i+ 1)\\ th Dn = 1 10 n * (30 + 1) 19 = 10 n(31) 19 = 10 31n 19 = 10 190 = 31n 31n 190 31 31 n = 6.13th Conclusion: Thus, the score 15 is in decile 6.13 or 6.13th decile. D. PERCENTILE OF UNGROUPED DATA Let i be the number of values in the set of data and n be the number of percentile (e.g. Pootherefore n = 86). Formula: Pn = in * (i + 1)\\th 100 where n = 1, 2, 3, ....,99 EXAMPLES: 1. Calculate 20th percentile from the following data: 3, 13, 11, 11, 5, 4, 2 Solution: Arrange the data in ascending order. 2, 3, 4, 5, 11, 11, 13 We let n = 20 since you are finding for percentile 20 and i = 7 since there are 7 is the total number of data. So, we have P20 = 20 * (7 + 1) ) th (20 * 8) th 160) th 100 =( 100 100 = 1.6 th value of the given data = 1st + 0.6 (2nd - 1st) Locate the first and second value: 2, 3, 4, 5, 11, 11, 13 P20 = 1st + 0.6 (2nd - 1st) = 2 +.4(3 - 2) = 2+.4(1) = 2.4 Conclusion: Therefore, 20% of the data is lower than or equal to 2.4.2. Calculate the 45 percentile from the following students' scores in mathematics 85 96 76 108 85 80 100 85 70 95 Solution: Arrange the data in ascending order. 70 76 80 85 85 85 95 96 100 108 We let n = 45 since you are finding for percentile 45 and i = 10 since 10 is the total number of data. So, we have (45 * 11 th 495 th 45 * (10 + 1) \\ th PAS = = 100 100 100 = 4.95 th value of the given data = 4th + 0. 95[5th - 4th] Locate the 5th and 4th value from the data: 70 76 80 85 85 85 95 96 100 108 P45 = 4th + 0.95[5th - 4th] = 85 + 0.95(85 - 85) = 85 + .95(0) = 85 + 0 = 85 Conclusion: Therefore, 45% of the students' scores is lower than or equal to 85. 3. The height (in cm) of twelve students were measured as follows: 148 157 152 166 164 161 150 160 165 159 140 155 a. What height is at the 85th percentile rank? b. 70% of the students are shorter what height? Solution: Arrange the 12 students from shortest to tallest. 140 148 150 152 155 157 159 160 161 164 165 166 a. We let n = 85 since you are finding for percentile 85 and i = 12, since there are 12 students. So, we have (1105) th P85 = 85 * (12 + 1)\\th (85 * 13) =: 100 100 100 = 11.05 th value of the given data = 11th + 0. 05[12th - 11th] Locate the 12th and 1 1th value from the data: 140 148 150 152 155 157 159 160 161 164 165 166 Pas = 11th + 0.05[12th - 11th] = 165 + 0.05(166 - 165) = 165 + 0.05(1) = 165 + 0.05 = 165. 05 Conclusion: Therefore, the height at the 85th percentile is 165.05 cm. have b. We let n = 70 since you are finding for percentile 70 and i = 12 since there are 12 students. So, we P70 = 70 * (12 + 1) \\th (70 * 13 th (910) the 100 100 (100) = 9.01 th value of the given data = 9th + 0.01[10th - 9th]Locate the 10th and 9th value from the data: 140 148 150 152 155 157 159 160 161 164 165 166 Pro = 9th + 0.01[10th - 9th] = 161 + 0.01(164 - 161) = 161 + 0.01(3) = 161 + 0.03 = 161.03 Conclusion: Therefore, the height at the 70th percentile is 161.03 cm