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. solve the following situations. Show complete solution. _______ Accuracy (50%) Completeness and Organizaution (50%) ] 1. Aqua Running has been promoted as a method for cardiovascular conditioning for the injured uthlctc at: well as for others who desire a low impact aerobic workout. A study reported in the Journal of Sports Medicine investigated the relationship between exercise cadence and heart rate by measuring the heart rates of 20 healthy volunteers at a cadence of 48 cycles per minute (a cycle consisted of two steps). The data are listed here: 87 109 79 80 96 95 90 92 96 98 101 91 78 112 94 98 94 107 81 96 Find the lower and upper quartiles of the data. 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 Q2 = (n * (i + 1) \\ th 4 " = (2- (10 + 12 ) " = (274)"=(2)" = 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 3rd 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 = ( 3 * ( 14 + 1 ) ) the th th 4 " = (3+15) = (+5) = 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