Tugas Statistika Deskriptif Pertemuan 6 [PDF]

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Tugas Statistika Deskriptif Pertemuan 6 Nama : Siti Nur Nadiah NIM



: 64191365



Kelas : 64.3G.01



Soal Esay 1.



Diketahui: Diberikan data skor hasil ujian statistika dari 12 orang mahasiswa sebagai berikut: 62, 65, 58, 90, 75, 79, 82, 91, 75, 75, 75, 95 Ditanya: Rentang, Rentang antar quartil, Simpangan quartil, Koefisien kurtosis, Koefisien kemiringan, Standar deviasi, Varian, Rerata simpangan Jawab: Urutan Data terkecil-terbesar : 58, 62, 65, 75, 75, 75, 75, 79, 82, 90, 91, 95



Rentang 𝑅 = 𝐷𝐵 − 𝐷𝐾 𝑅 = 95 − 58 = 𝟑𝟕



Rentang Antar Quartil 𝑅𝐴𝑄 = 𝑄3 − 𝑄1 𝑅𝐴𝑄 = 82 − 65 = 𝟏𝟕



Simpangan Quartil 𝑆𝑄 = 1⁄2 (𝑄3 − 𝑄1) 𝑆𝑄 = 1⁄2 (82 − 65) = 𝟖, 𝟓 Koefisien Kurtosis 1 (𝑄3 − 𝑄1) 𝛼4 = 2 𝑃90 − 𝑃10



1 (82 − 85) 𝛼4 = 2 93,8 − 59,2 𝛼4 =



8,5 = 𝟎, 𝟐𝟒𝟓 34,6



Koefisien Kemiringan (𝑋̅ − 𝑀𝑜) 𝑠 (76,83 − 75) 𝛼3 = = 𝟎, 𝟏𝟓𝟖 11,53 𝛼3 =



Standar Deviasi ∑𝑓𝑥𝑖 2 − (∑𝑓𝑥𝑖)2 /𝑛 𝑆=√ 𝑛−1 72.304 − (922)2 /12 𝑆=√ 12 − 1 1.463,6 𝑆=√ 11 𝑆 = √133,05 = 𝟏𝟏, 𝟓𝟑



𝒙𝒊 𝒇𝒊 𝒙𝒊𝟐 𝒇𝒊𝒙𝒊 58 1 3.364 58 62 1 3.844 62 65 1 4.225 65 75 4 5.625 300 79 1 6.241 79 82 1 6.724 82 90 1 8.100 90 91 1 8.281 91 95 1 9.025 95 Total 12 922



𝒇𝒊𝒙𝒊𝟐 3.364 3.844 4.225 22.500 6.241 6.724 8.100 8.281 9.025 72.304



Koefisien Varians 𝑠𝑡𝑎𝑛𝑑𝑎𝑟 𝑑𝑒𝑣𝑖𝑎𝑠𝑖 𝑥 100% 𝑟𝑎𝑡𝑎 − 𝑟𝑎𝑡𝑎 11,53 𝐾𝑉 = 𝑥 100% 76,83 𝐾𝑉 =



𝐾𝑉 = 𝟏𝟓, 𝟎𝟏%



Rerata Simpangan 𝑋̅ =



58 + 62 + 65 + 75 + 75 + 75 + 75 + 79 + 82 + 90 + 91 + 95 922 = = 𝟕𝟔, 𝟖𝟑 12 12



𝑅𝑆 =



̅ ∑|𝑥𝑖 − 𝑥| 𝑛



|58−76,83|+|62−76,83|+|65−76,83|+|75−76,83|+|75−76,83|+|75−76,83|+|75−76,83|+|79−76,83|+|82−76,83|+|90−76,83|+|91−76,83|+|95−76,83 𝑋̅ = 12



𝑅𝑆 =



0,04 = 𝟎, 𝟎𝟎𝟑 12



2.



Diketahui: Data sikap terhadap korupsi dari 20 sample acak disajikan sebagai berikut: 55, 54, 64, 68, 59, 75, 66, 68, 80, 53, 54, 98, 77, 80, 62, 79, 75, 68, 62, 84 Ditanya: Rentang, Rentang antar quartil, Simpangan quartil, Koefisien kurtosis, Koefisien kemiringan, Standar deviasi, Varian, Rerata simpangan Jawab: Urutan Data terkecil-terbesar : 53, 54, 54, 55, 59, 62, 62, 64, 66, 68, 68, 68, 75, 75, 77, 79, 80, 80, 84, 98



Rentang 𝑅 = 𝐷𝐵 − 𝐷𝐾 𝑅 = 98 − 53 = 𝟒𝟓



Rentang Antar Quartil 𝑅𝐴𝑄 = 𝑄3 − 𝑄1 𝑅𝐴𝑄 = 66 − 54 = 𝟏𝟐



Simpangan Quartil 𝑆𝑄 = 1⁄2 (𝑄3 − 𝑄1) 𝑆𝑄 = 1⁄2 (66 − 54) = 𝟔 Koefisien Kurtosis 1 (𝑄3 − 𝑄1) 𝛼4 = 2 𝑃90 − 𝑃10 1 (66 − 54) 𝛼4 = 2 83,6 − 54 𝛼4 =



6 = 𝟎, 𝟐𝟎𝟐 29,6



Koefisien Kemiringan 𝛼3 =



(𝑋̅ − 𝑀𝑜) 𝑠



𝛼3 =



(69,05 − 68) = 𝟎, 𝟎𝟖𝟖 11,87



Standar Deviasi ∑𝑓𝑥𝑖 2 − (∑𝑓𝑥𝑖)2 /𝑛 𝑆=√ 𝑛−1 98.039 − (1.381)2 /20 𝑆=√ 20 − 1 2.680,95 𝑆=√ 19 𝑆 = √141,1 = 𝟏𝟏, 𝟖𝟕



Koefisien Varians



𝒙𝒊 𝒇𝒊 𝒙𝒊𝟐 𝒇𝒊𝒙𝒊 53 1 2.809 53 54 2 2.916 108 55 1 3.025 55 59 1 3.481 59 62 2 3.844 124 64 1 4.096 64 66 1 4.356 66 68 3 4.624 204 75 2 5.625 150 77 1 5.929 77 79 1 6.241 79 80 2 6.400 160 84 1 7.056 84 98 1 9.604 98 Total 20 1.381



𝒇𝒊𝒙𝒊𝟐 2.809 5.832 3.025 3.481 7.688 4.096 4.356 13.872 11.250 5.929 6.241 12.800 7.056 9.604 98.039



𝑠𝑡𝑎𝑛𝑑𝑎𝑟 𝑑𝑒𝑣𝑖𝑎𝑠𝑖 𝑥 100% 𝑟𝑎𝑡𝑎 − 𝑟𝑎𝑡𝑎 11,87 𝐾𝑉 = 𝑥 100% 69,05 𝐾𝑉 =



𝐾𝑉 = 𝟏𝟕, 𝟏𝟗%



Rerata Simpangan 𝑋̅ =



53 + 54 + 54 + 55 + 59 + 62 + 62 + 64 + 66 + 68 + 68 + 68 + 75 + 75 + 77 + 79 + 80 + 80 + 84 + 98 20



𝑋̅ =



1.381 = 𝟔𝟗, 𝟎𝟓 20



̅ ∑|𝑥𝑖 − 𝑥| 𝑛 5,68 𝑅𝑆 = = 𝟎, 𝟐𝟖𝟒 20 𝑅𝑆 =



Soal PG 1. 2. 3. 4. 5.



D. 7 C. 23,02 A. C. 12 B. 3