{"id":311765,"date":"2023-01-31T09:56:27","date_gmt":"2023-01-31T02:56:27","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=311765"},"modified":"2023-02-06T10:30:12","modified_gmt":"2023-02-06T03:30:12","slug":"kuartil","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/kuartil\/","title":{"rendered":"Pengertiasn Kuartil dengan Cara Menentukannya"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

Hai Quipperian, saat melakukan percobaan dengan melibatkan banyak data, pasti kamu membutuhkan peran statistika. Misalnya, untuk menentukan rata-rata, nilai tengah, dan besaran-besaran lain. Keseluruhan data yang kamu peroleh bisa dibagi ke dalam beberapa bagian dengan porsi atau persentase yang sama. Jika kamu ingin membagi datamu ke dalam empat kelompok sama banyak, maka kamu harus tentukan dahulu kuartilnya. Lalu, apa yang dimaksud kuartil? Untuk tahu penjelasannya, yuk simak artikel berikut ini.<\/p>\n\n\n\n

Pengertian Kuartil<\/strong><\/h2>\n\n\n\n

Kuartil merupakan suatu istilah kuantitatif yang bisa membagi suatu data menjadi empat bagian sama banyak. Setiap bagian memiliki persentase yang sama, yaitu 25%. Sebelum menentukan kuartil, semua data harus diurutkan terlebih dahulu dari yang paling kecil. Jika tidak diurutkan, hasil yang diperoleh tidak akan akurat. Adapun ilustrasi kuartil adalah sebagai berikut.<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

Untuk membag suatu data menjadi empat bagian sama banyak, dibutuhkan tiga kuartil, yaitu kuartil 1 (Q<\/em>1<\/sub><\/em>), kuartil 2 (Q<\/em>2<\/sub><\/em>), dan kuartil 3 (Q<\/em>3<\/sub><\/em>). Coba kamu perhatikan Q<\/em>2<\/sub><\/em>!<\/p>\n\n\n\n

Oleh karena Q2<\/sub><\/em> membagi data menjadi dua bagian sama banyak, dengan persentase tiap bagian 50%, maka Q2<\/sub><\/em> disebut juga sebagai median.<\/p>\n\n\n\n

\n

Baca Juga: <\/span> Pengertian Desil dan Persentil dengan Cara Menentukannya<\/a><\/p>\n<\/div>\n\n\n\n

Cara Menentukan Kuartil<\/strong><\/h2>\n\n\n\n

Cara menentukan nilai kuartil suatu data itu bergantung pada jenis datanya, misalnya data tunggal atau data berkelompok. Mengingat, cara menentukan kuartil keduanya juga berbeda. Lalu, bagaimana cara menentukan kuartil data tunggal dan data berkelompok? Yuk, simak berikut ini.<\/p>\n\n\n\n

Kuartil Data Tunggal<\/strong><\/h3>\n\n\n\n

Data tunggal adalah data yang tidak disusun dalam bentuk interval. Nah, <\/em>kuartil data tunggal bisa ditentukan dengan rumus berikut.<\/p>\n\n\n\n

Letak Q<\/em>i<\/sub><\/em> <\/em>= <\/sub><\/p>\n\n\n\n

Dengan:<\/p>\n\n\n\n

Q<\/em>i<\/sub><\/em> <\/em> = kuartil ke-i<\/em>;<\/p>\n\n\n\n

i <\/em>= 1, 2, 3 (bergantung letak kuartil yang dicari); dan<\/p>\n\n\n\n

n<\/em> = banyaknya data.<\/p>\n\n\n\n

Untuk memudahkanmu dalam mengerjakan kuartil data tunggal ini, perhatikan rumus SUPER \u201cSolusi Quipper\u201d berikut.<\/p>\n\n\n\n

Kuartil 1 (Kuartil Atas)<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Kuartil 2 (Kuartil Tengah)<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Kuartil 3 (Kuartil Bawah)<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Kuartil Data Berkelompok<\/strong><\/h3>\n\n\n\n

Data berkelompok adalah data yang disusun dalam bentuk interval. Lalu, bagaimana cara menentukan letak kuartilnya? Ikuti langkah berikut ini, ya.<\/p>\n\n\n\n

    \n
  1. Tentukan dahulu letak kuartilnya menggunakan rumus berikut.<\/li>\n<\/ol>\n\n\n\n

    Letak Q<\/em>i<\/sub><\/em> <\/em>= <\/p>\n\n\n\n

    Dengan:<\/p>\n\n\n\n

    Q<\/em>i<\/sub><\/em> <\/sup>= kuartil ke-i<\/em>:<\/p>\n\n\n\n

    i <\/em>= letak desil ke-I; dan<\/p>\n\n\n\n

    n<\/em> = banyaknya data.<\/p>\n\n\n\n

    Mengapa letak kuartil perlu dicari terlebih dahulu? Karena kamu sulit untuk bisa memastikan posisi kuartil ke-i<\/em>  pada kumpulan data yang jumlahnya cukup banyak. Jika datanya hanya ada 4 atau 5, maka letak kuartil bisa dengan mudah diketahui.<\/p>\n\n\n\n

      \n
    1. Setelah tahu letak kuartilnya, tentukan nilai kuartil yang dimaksud menggunakan rumus berikut.<\/li>\n<\/ol>\n\n\n\n
      \"\"<\/figure>\n\n\n\n

      Dengan:<\/p>\n\n\n\n

      Q<\/em>i<\/sub><\/em> = kuartil ke-i<\/em>;<\/p>\n\n\n\n

      Tb<\/em>i<\/sub><\/em> = tepi bawah kelas kuartil ke-i<\/em>;<\/p>\n\n\n\n

      p<\/em> = interval kelas;<\/p>\n\n\n\n

      f<\/em>k<\/sub><\/em> = frekuensi kumulatif sebelum kuartil ke-i<\/em>;<\/p>\n\n\n\n

      f<\/em> = frekuensi kuartil ke-i<\/em>;<\/p>\n\n\n\n

      n<\/em> = banyaknya data; dan<\/p>\n\n\n\n

      i <\/em>= posisi kuartil yang dicari (1 \u2013 3).<\/p>\n\n\n\n

      Jangkauan Kuartil<\/strong><\/h2>\n\n\n\n

      Jangkauan antarkuartil adalah selisih antara kuartil bawah dan kuartil atas. Secara matematis, dirumuskan sebagai berikut.<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Dengan:<\/p>\n\n\n\n

      J<\/em>Q<\/sub><\/em> = jangkauan antarkuartil;<\/p>\n\n\n\n

      Q<\/em>3<\/sub><\/em> = kuartil bawah (kuartil 3); dan<\/p>\n\n\n\n

      Q<\/em>1<\/sub><\/em> = kuartil atas (kuartil 1).<\/p>\n\n\n\n

      Simpangan Kuartil<\/strong><\/h2>\n\n\n\n

      Simpangan kuartil biasa disebut deviasi kuartil merupakan besaran yang menunjukkan tingkat variabilitas suatu data. Secara matematis, simpangan kuartil dirumuskan sebagai berikut.<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Dengan:<\/p>\n\n\n\n

      Q<\/em>D<\/sub><\/em> = simpangan kuartil;<\/p>\n\n\n\n

      Q<\/em>3<\/sub><\/em> = kuartil bawah (kuartil 3); dan<\/p>\n\n\n\n

      Q<\/em>1<\/sub><\/em> = kuartil atas (kuartil 1).<\/p>\n\n\n\n

      Contoh Soal<\/strong><\/h2>\n\n\n\n

      Untuk mengasah kemampuanmu, yuk simak contoh soal berikut ini.<\/p>\n\n\n\n

      Contoh Soal 1<\/strong><\/h3>\n\n\n\n

      Tentukan kuartil ke-1 dari data-data berikut.<\/p>\n\n\n\n

      3, 2, 2, 4, 4, 1, 1, 3, 4, 2, 2, 5, 7, 6, 8<\/p>\n\n\n\n

      Pembahasan:<\/p>\n\n\n\n

      Mula-mula, kamu harus mengurutkan data seperti berikut.<\/p>\n\n\n\n

      1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6, 7, 8<\/p>\n\n\n\n

      Banyaknya data (n<\/em>) = 15<\/p>\n\n\n\n

      Selanjutnya, gunakan rumus letak kuartil, dengan i<\/em> = 1.<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Dengan demikian, kuartil 1 terletak pada data urutan ke-4, yaitu 2.<\/p>\n\n\n\n

      Jadi, kuartil atasnya  adalah 2.<\/p>\n\n\n\n

      \n

      Baca Juga: <\/span> Pengerian Rata-rata Lengkap dengan Rumus dan Contohnya<\/a><\/p>\n<\/div>\n\n\n\n

      Contoh Soal 2<\/strong><\/h3>\n\n\n\n

      Berikut ini merupakan tabel penjualan buah di Toko A dan Toko B pada 6 bulan pertama.<\/p>\n\n\n\n

      Bulan<\/th>Toko A (kg)<\/th>Toko B (kg)<\/th><\/tr><\/thead>
      Bulan ke-1<\/td>20<\/td>25<\/td><\/tr>
      Bulan ke-2<\/td>32<\/td>30<\/td><\/tr>
      Bulan ke-3<\/td>34<\/td>32<\/td><\/tr>
      Bulan ke-4<\/td>40<\/td>41<\/td><\/tr>
      Bulan ke-5<\/td>56<\/td>58<\/td><\/tr>
      Bulan ke-6<\/td>60<\/td>62<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Tentukan perbandingan jangkauan antarkuartil penjualan buah Toko A dan Toko B!<\/p>\n\n\n\n

      Pembahasan:<\/p>\n\n\n\n

      Pertama, kamu harus menentukan jangkauan antarkuartil masing-masing toko.<\/p>\n\n\n\n

      Jangkauan antarkuartil Toko A<\/strong><\/p>\n\n\n\n

      Untuk menentukan jangkauan antarkuartil Toko A, carilah nilai kuartil atas dan bawahnya terlebih dahulu.<\/p>\n\n\n\n

      Letak kuartil atas:<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Nilai kuartil atas (Q<\/em>1<\/sub><\/em>) = 20 + (0,75)(32 \u2013 20 )<\/p>\n\n\n\n

                                            = 29<\/p>\n\n\n\n

      Letak kuartil bawah:<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Nilai kuartil bawah (Q<\/em>3<\/sub><\/em>) = 56 + (0,25)(60 \u2013 56 )<\/p>\n\n\n\n

                                                 = 57<\/p>\n\n\n\n

      Jangkauan antarkuartil Toko A (J<\/em>Q<\/sub><\/em>) = Q<\/em>3<\/sub><\/em> \u2013 Q<\/em>1<\/sub><\/em><\/p>\n\n\n\n

                                                                      = 57 \u2013 29<\/p>\n\n\n\n

                                                                      = 28 <\/p>\n\n\n\n

      Jangkauan antarkuartil Toko B<\/strong><\/p>\n\n\n\n

      Untuk menentukan jangkauan antarkuartil Toko B, carilah nilai kuartil atas dan bawahnya terlebih dahulu.<\/p>\n\n\n\n

      Letak kuartil atas:<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Nilai kuartil atas (Q<\/em>1<\/sub><\/em>) = 25 + (0,75)(30 \u2013 25 )<\/p>\n\n\n\n

                                            = 28,75<\/p>\n\n\n\n

      Letak kuartil bawah:<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Nilai kuartil bawah (Q<\/em>3<\/sub><\/em>) = 58 + (0,25)(62 \u2013 58 )<\/p>\n\n\n\n

                                                 = 59<\/p>\n\n\n\n

      Jangkauan antarkuartil Toko B (J<\/em>Q<\/sub><\/em>) = Q<\/em>3<\/sub><\/em> \u2013 Q<\/em>1<\/sub><\/em><\/p>\n\n\n\n

                                                                      = 59 \u2013 28,75<\/p>\n\n\n\n

                                                                      = 30,25<\/p>\n\n\n\n

      Dengan demikian, perbandingan jangkauan antarkuartil Toko A dan Toko B adalah sebagai berikut.<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Jadi, perbandingannya adalah 112 : 121.<\/p>\n\n\n\n

      Contoh Soal 3<\/strong><\/h3>\n\n\n\n

      Diketahui tabel data kelompok perolehan skor olimpiade seperti berikut.<\/p>\n\n\n\n

      Tinggi badan<\/th>Frekuensi (f <\/em>)<\/th><\/tr><\/thead>
      140 \u2013 143<\/td>4<\/td><\/tr>
      144 \u2013 147 <\/td>3<\/td><\/tr>
      148 \u2013 151<\/td>5<\/td><\/tr>
      152 \u2013 155 <\/td>2<\/td><\/tr>
      Jumlah <\/td>14<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Tentukan kuartil bawah dari data pada tabel tersebut!<\/p>\n\n\n\n

      Pembahasan:<\/p>\n\n\n\n

      Untuk memudahkanmu, tentukan dahulu frekuensi kumulatif pada tabel.<\/p>\n\n\n\n

      Tinggi badan (cm)<\/th>Frekuensi (f <\/em>)<\/th>Frekuensi kumulatif (fk<\/sub><\/em>)<\/th><\/tr><\/thead>
      <\/td><\/td><\/td><\/tr>
      140 \u2013 143<\/td>4<\/td>4<\/td><\/tr>
      144 \u2013 147 <\/td>3<\/td>7<\/td><\/tr>
      148 \u2013 151<\/td>5<\/td>12<\/td><\/tr>
      152 \u2013 155 <\/td>2<\/td>14<\/td><\/tr>
      Jumlah <\/td>14<\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Dari tabel di atas, diperoleh panjang kelas (p<\/em>) = 4.<\/p>\n\n\n\n

      Selanjutnya, tentukan letak interval kuartil ke-3 dengan rumus berikut.<\/p>\n\n\n\n

      Letak Q<\/em>i<\/sub><\/em> <\/em>= <\/sub><\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Oleh karena frekuensi kumulatif 148 \u2013 151 = 12, maka letak kuartil bawahnya (kuartil 3) berada di interval tersebut. Dengan demikian letak Q<\/em>3<\/sub><\/em> berada di interval 148 \u2013 151.<\/p>\n\n\n\n

      Selanjutnya, tentukan tepi bawah kuartil ke-3.<\/p>\n\n\n\n

      Tb<\/em>3<\/sub><\/em> <\/em>= 148 \u2013 0,5 = 147,5<\/p>\n\n\n\n

      Setelah semua elemen diketahui, gunakan persamaan kuartil ke-i<\/em> data berkelompok seperti berikut.<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Jadi, nilai kuartil bawah perolehan skor olimpiade tersebut adalah 148,2 cm.<\/p>\n\n\n\n

      Itulah pembahasan Quipper Blog kali ini. Semoga bisa bermanfaat, ya. Untuk mendapatkan materi lengkapnya, yuk buruan gabung Quipper Video. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"

      Hai Quipperian, saat melakukan percobaan dengan melibatkan banyak data, pasti kamu membutuhkan peran statistika. Misalnya, untuk menentukan rata-rata, nilai tengah, dan besaran-besaran lain. Keseluruhan…<\/p>\n","protected":false},"author":156447303,"featured_media":311769,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384865],"tags":[679385147],"ppma_author":[679386823,679386836],"class_list":["post-311765","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-materi-matematika-kelas-12"],"acf":[],"yoast_head":"\nPengertiasn Kuartil dengan Cara Menentukannya - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Kuartil merupakan suatu istilah kuantitatif yang bisa membagi suatu data menjadi empat bagian sama banyak. 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