Question

MTH 139 207 Sp 2020 sara shuaibi & I @ 02/27/20 1:39 AM Homework: HW 2 Save 7 of 18 (5 complete) HW Score: 26.39%, 4.75 of 18 pts Score: 0 of 1 pt 3.1.13 Question Help College students and surfers Rex Robinson and Sandy Hudson collected data on the self-reported number of days surfed in a month for 30 longboard surfers and 30 shortboard surfers. Complete parts a and b below. Full data set Longboard:13, 19, 17. 12. 4.9.22. 13, 15, 20, 20, 4, 18, 11, 6,5 18. 12. 12, 15, 13, 14, 7, 9, 11, 17, 14. 6. 22. 10 Shortboard: 13.9. 11. 9. 9. 18. 4. 18, 8, 16. 12. 20. 11. 4. 19. 8. 7. 7. 13, 19, 15, 12.48. 18. 19. 14. 11.4.8. 16 a. Compute the means for both longboards and shortboards The mean for longboards is days. (Round to one decimal places as needed.) Enter your answer in the answer box and then click Check Answer Clear All parts remaining VIZIO

Answer 1

Solution-

The mean for Longboard is 12.9 days.

The mean for Shortboard is 12.3 days.

• Calculations and other Descriptive Statistics

For Longboard

The sample size is n = 30. The provided sample data along with the data required to compute the sample mean X and sample variance s- are shown in the table below: Longboard Longboard2 13 169 361 289 144 16 484 169 225 400 400 16 324 121 36 25 324 144 144 225 169 196 49 121 289 196 36 484 100 Sum = 5818

The sample mean X is computed as follows: Ñ -Iry_388 -= 12.933 1 na i= 1 Also, the sample variance s? is 1 3882 - (2x -+(3x))= –(115 - sost) = 2:02 58 = 27.582 n - 1 30 – 1 Therefore, the sample standard deviation s is s = Vs2 = V27.582 = 5.252

Since the sample size n = 30 is even, we have that (n + 1)/2 = (30 + 1)/2 = 15.5 is not an integer value, the median is computing by taking the average of the values at the positions 15th and 16th, as shown below 13+13 - 13 median = Quartiles The quartiles are computed using the table with the data in ascending order > For Q1 we have to compute the following position: 25 25 pos(Q1) = (n + 1) = 7.75 Since 7.75 is not an integer number, Q1 is computed by interpolating between the values located in the 7th and 8th positions, as shown in the formula below Q1 = 9+ (7.75 – 7) x (9 – 9) = 9 For Q3 we have to compute the following position: pos(Q;) = (n + 1) 766 = (30 + 1) 766 = 23.25 100 Since 23.25 is not an integer number, Q3 is computed by interpolating between the values located in the 23th and 24th positions, as shown in the formula below Q3 = 17 + (23.25 - 23) x (18 – 17) = 17.25 Also, from the information above we get that min = 4, max = 22, which means that the range is Range = max - min = 22 - 4 = 18 Finally, the 5-Number summary is min = 4, Q1 = 9, median = 13, Q3 = 17.25, max = 22 which completes the basic descriptive statistics analysis.

For Longboard

The sample size is n = 30. The provided sample data along with the data required to compute the sample mean X and sample variance sa are shown in the table below: Shortboard Shortboard 169 81 121 81 324 16 324 64 256 144 400 121 16 361 64 49 169 361 225 144 324 324 361 196 121 64 256 Sum = 5282

The sample mean 7 is computed as follows: * = Š x = 370 = 12.333 Also, the sample variance sa is In 1 3702 *** (**?- ! (3x)) = - +1 (52 - ) 2 782 5282 - = 24.782 n - 1 30 – 1 30 Therefore, the sample standard deviation s is s = V 52 = V24.782 = 4.978

Since the sample size n = 30 is even, we have that (n+1)/2 = (30+1)/2 = 15.5 is not an integer value, the median is computing by taking the average of the values at the positions 15th and 16th, as shown below 12+ 12 = 12 median = Quartiles The quartiles are computed using the table with the data in ascending order For Q1 we have to compute the following position: pos(Q1) = (n +1) 726 = (30 + 1) 256 = 7.75 100 Since 7.75 is not an integer number, Q1 is computed by interpolating between the values located in the 7th and 8th positions, as shown in the formula below Q1 = 8+ (7.75 – 7) * (8 – 8) = 8 > For Q3 we have to compute the following position: pos(Q3) = (n + 1) -) = (n+1) 75 = (30+1) 75 = 23.25 Since 23.25 is not an integer number, Q3 is computed by interpolating between the values located in the 23th and 24th positions, as shown in the formula below Q3 = 18+ (23.25 – 23) x (18 – 18) = 18 Also, from the information above we get that min = 4, max = 20, which means that the range is Range = max - min = 20 – 4= 16 Finally, the 5-Number summary is min = 4, Q1 = 8, median = 12, Q3 = 18, max = 20

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