{"id":311587,"date":"2023-01-30T07:24:00","date_gmt":"2023-01-30T00:24:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=311587"},"modified":"2023-02-06T10:29:39","modified_gmt":"2023-02-06T03:29:39","slug":"desil-dan-persentil","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/desil-dan-persentil\/","title":{"rendered":"Pengertian Desil dan Persentil dengan Cara Menentukannya"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1280\" height=\"853\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pexels-george-pak-7972380-1.webp\" alt=\"\" class=\"wp-image-311590\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pexels-george-pak-7972380-1.webp 1280w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pexels-george-pak-7972380-1-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pexels-george-pak-7972380-1-1200x800.webp 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pexels-george-pak-7972380-1-1170x780.webp 1170w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pexels-george-pak-7972380-1-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pexels-george-pak-7972380-1-263x175.webp?crop=1 263w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, di pembahasan sebelumnya, Quipper Blog sudah pernah membahas tentang mean, modus, dan median kan? Apakah kamu ingat pengertian ketiganya? Mean merupakan istilah lain dari rata-rata, modus merupakan istilah lain untuk data yang sering muncul, sementara median merupakan nilai tengah data. <em>Nah <\/em>di artikel ini, Quipper Blog akan membahas kelanjutan dari ketiga elemen statistika tersebut, yaitu desil dan persentil. Apa yang dimaksud desil dan persentil?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Apa Itu Desil dan Persentil?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Cakupan statistika itu luas. Selain tiga istilah utama mean, modus, dan median, ada istilah lain yang harus dipelajari, yaitu desil dan persentil. Kedua istilah itu berkaitan dengan jangkauan data. Lalu, apa pengertian keduanya?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Pengertian Desil<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Desil adalah suatu istilah yang menunjukkan pembagian data menjadi 10 bagian sama besar. Sebelum menentukan desil, data harus diurutkan terlebih dahulu, ya. Ada sembilan desil yang nantinya bisa membagi data menjadi sepuluh bagian sama besar. Artinya, setiap bagian memiliki persentase yang sama, yaitu 10%. Perhatikan ilustrasi berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/QNY7Opk-akhmk_VA5T06EZB-kS10Zf19AZluegFr2_HNigUlLChgoSH9AtjO3KgVjmtcD1O5nCX-q0x4Xj_xGjwgxBPelUgeCy2IrwTxSOOLTSBSEyRNSa1WWzix1J7qODRDaBsDjNR86cwQwpAU-Uy6g22akH4az_6a28yL3NAyxiy5wX-TkqEljj8sO1BbTnx43GmhLg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Di dalam kehidupan sehari-hari, desil biasa dimanfaatkan untuk mengelompokkan tingkat kesejahteraan rakyat. Misalnya kelompok Desil 1, Desil 2, dan seterusnya.<\/p>\n\n\n\n<div class=\"baca\">\n<p><span class=\"head_baca\">Baca Juga: <\/span> <a href=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/rata-rata\/\">Pengerian Rata-rata Lengkap dengan Rumus dan Contohnya<\/a><\/p>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Pengertian Persentil<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Persentil berasal dari kata persen atau per seratus adalah suatu istilah dalam statistik yang menunjukkan pembagian data menjadi 100 bagian sama besar. Pada prinsipnya, persentil sama dengan desil. Hanya saja, sebaran datanya lebih luas 10 kali lipat.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Cara Menentukan Desil<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Secara umum, bentuk penulisan data dibagi menjadi dua, yaitu data tunggal dan data berkelompok. Cara menentukan desil kedua jenis data juga berbeda, yaitu seperti berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Desil Data Tunggal<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Desil data tunggal bisa ditentukan dengan rumus berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Letak <em>D<\/em><em><sub>i<\/sub><\/em><em> <\/em>= <sub><\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>D<\/em><em><sub>i<\/sub><\/em><em> <\/em>&nbsp;= desil ke-<em>i<\/em>;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>i <\/em>= 1, 2, 3, 4, \u2026, 9 (bergantung letak desil yang dicari); dan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>n<\/em> = banyaknya data.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan desil ke-3 dari data-data berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2, 3, 4, 5, 2, 2, 4, 6, 4, 7, 7, 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, kamu harus mengurutkan data seperti berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Banyaknya data (<em>n<\/em>) = 12<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, gunakan rumus letak desilnya, dengan <em>i<\/em> = 3.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/E46u03JtKd-On-20doEJ2zq0jPmTm37a4n5IxxhaAvmaTiPlVCyoIDTiCXcST7UGXxQcmNXFK9jiihY1sojHbvVh98vkCSxxGmUvEFuqVSPWojeECM27-jERy64K-DHl5HXoD2FnnZijmXJoF_45vKLTt8Zq4qw3cuHKSm4AI_c_XJfViB5YkvkRy9N3prOp_vNfqVU5Bw\" alt=\"\" width=\"83\" height=\"97\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Nilai 3,9 bukan hasil akhirnya, ya. Nilai tersebut menunjukkan letak desil ke-3.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/GUwSfNlYdU3X9Jtboe5akQ7lHg3wmPhs1I7NAaeXC--rqa70J1SVeKS33OPK-GM-puamTHsYcwUBa0zZr37cJ_ZEI7Ec_ckHeZXPQ4Ukvt1XfFWUwZ9ilsHi4lwlwOfkvOWlFd8M-39vejfpEGFD9hTMoWhIUwFJjHJHdDOGH6VeynJhvs8us9ZitJfCaXKzvQfr-Zruqg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Data ke-3nya adalah 2 (lihat kembali data yang telah diurutkan)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lalu, berapakah desil ke-3nya?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk menentukan data desil ke-3, gunakan rumus berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Nilai desil ke-3 = Data ke-3 + (Kelebihan\/sisa letak desil ke-3)(Data ke-4 \u2013 Data ke-3)&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 2 + (0,9)(3 \u2013 2)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 2,9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, desil ke-3nya adalah 2,9.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Desil Data Berkelompok<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Desil data berkelompok dirumuskan sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Letak <em>D<\/em><em><sub>i<\/sub><\/em><em> <\/em>= <sub><\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>D<\/em><em><sub>i<\/sub><\/em><sup> <\/sup>= desil ke-<em>i<\/em>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>i <\/em>= letak desil ke-I; dan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>n<\/em> = banyaknya data.<em>&nbsp;<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Setelah Quipperian tahu letak desil ke-I, gunakan persamaan berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/mgk2Qaeb0ILolc16Ac9mvDUWA5USRn94ndMmXKDjTPUg_3uhk1ZQJaue5povAu8GaqBNvvuBHYlgIv0cg-xVm8C6GBUuZriwAOE6YEw6pb9D9mhllQnIcgF_Za32nygmdqjHYiJiLVSo7HJkBRvJ9ooTKlwiEtRKlUWxAqIgJB2AIR8z8kVns039Ki2CRn0pbkEdwaZSFQ\" alt=\"\" width=\"130\" height=\"72\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>D<\/em><em><sub>i<\/sub><\/em> = desil ke-i;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Tb<\/em><em><sub>i<\/sub><\/em> = tepi bawah kelas desil ke-i;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>p<\/em> = interval kelas;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em><em><sub>k<\/sub><\/em> = frekuensi kumulatif sebelum desil ke-<em>i<\/em>;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em> = frekuensi desil ke-<em>i<\/em>;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>n<\/em> = banyaknya data; dan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>i <\/em>= posisi desil yang dicari (1 \u2013 9).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk lebih jelasnya, perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui tabel data kelompok tinggi badan seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Tinggi badan<\/th><th>Frekuensi (<em>f <\/em>)<\/th><\/tr><\/thead><tbody><tr><td>140 \u2013 143<\/td><td>4<\/td><\/tr><tr><td>144 \u2013 147&nbsp;<\/td><td>3<\/td><\/tr><tr><td>148 \u2013 151<\/td><td>5<\/td><\/tr><tr><td>152 \u2013 155&nbsp;<\/td><td>2<\/td><\/tr><tr><td>Jumlah&nbsp;<\/td><td>14<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan desil ke-5 dari data pada tabel tersebut!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk memudahkanmu, tentukan dahulu frekuensi kumulatif pada tabel.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Tinggi badan (cm)<\/th><th>Frekuensi (<em>f <\/em>)<\/th><th>Frekuensi kumulatif (<em>f<sub>k<\/sub><\/em>)<\/th><\/tr><\/thead><tbody><tr><td>140 \u2013 143<\/td><td>4<\/td><td>4<\/td><\/tr><tr><td>144 \u2013 147&nbsp;<\/td><td>3<\/td><td>7<\/td><\/tr><tr><td>148 \u2013 151<\/td><td>5<\/td><td>12<\/td><\/tr><tr><td>152 \u2013 155&nbsp;<\/td><td>2<\/td><td>14<\/td><\/tr><tr><td>Jumlah&nbsp;<\/td><td>14<\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari tabel di atas, diperoleh panjang kelas (<em>p<\/em>) = 4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, tentukan letak interval desil ke-5 dengan rumus berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Letak <em>D<\/em><em><sub>i<\/sub><\/em><em> <\/em>= <sub><\/sub><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/y8ZmWbq4DW4ixu8DriwWdcgeelUC8ejdaaQcPgfNTJHTc-wkAvFmHCFVE2vqYUJWWxkxNTppLzLGG_Pu2mKvAKvfx11C8xFajAeh0RQ29vZQbs0PCsrW5O-VBbgw8txQY4lh9y_-Ty_Phep7pKU9rWyzhvzZ7d9yVO3lmmcxkE6svUG5_h91kfSdhquFe-uz7yWv_IUpuw\" alt=\"\" width=\"120\" height=\"91\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Oleh karena frekuensi kumulatif 144 \u2013 147 = 7, maka data ke-5 \u2013 ke-7 berada di interval tersebut. Dengan demikian letak <em>D<\/em><em><sub>5<\/sub><\/em> berada di interval 144 \u2013 147.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, tentukan tepi bawah desil ke-5.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Tb<\/em><em><sub>4<\/sub><\/em><em> <\/em>= 144 \u2013 0,5 = 143,5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Setelah semua elemen diketahui, gunakan persamaan desil ke-<em>i<\/em> data berkelompok seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/LZeyTH_zE_BFmikvhyQDF9Fr7BfO-IQuSqTCj8rI2ht02yrMrNOmoeAum5V58_e8lrrUztPETOWL6Q0Snwzkjct4oao4i70bf_Qs5zVenzU5fg0XNSlah4RVe0r0csmqiDQvV7A6gN7-mPq4wI9-MqJc76ccsjRbpA5ayJf6esuweC2iZsmVLYoUBTM4Fxzkjvcv_95-kg\" alt=\"\" width=\"165\" height=\"178\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai desil ke-5 tinggi badan tersebut adalah 147,5 cm.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Cara Menentukan Persentil<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Pada prinsipnya, cara menentukan persentil sama dengan desil. Perbedaannya terletak pada nilai pembaginya saja. Jika nilai pembagi desil 10, maka persentil 100. Untuk lebih jelasnya, simak rumus berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Persentil Data Tunggal<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Letak persentil data tunggal bisa ditentukan dengan rumus berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Letak <em>P<\/em><em><sub>i<\/sub><\/em><em> <\/em>= <sub><\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>P<\/em> <sub>i<\/sub> = persentil ke-i;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>i<\/em> = 1 \u2013 99; dan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>n<\/em> = banyaknya data.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan persentil ke-25 dari data berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">33 33 34 34 34 36 36 37 38 38 39 40 41 41 42 43 44 44 45 45<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dari data di atas, banyak datanya (<em>n<\/em>) = 20.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lalu, tentukan letak persentil ke-25 dengan rumus berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/kANv6NE88IHNv0UyLlA6lEKTSGRiD0T0niFY1aLx3cxnMLzButbsuyABd-u4VtEO8RMaUVn_U-BOlbsXq6cm4j1EG5p0_7nULs_1POb6GCIbVvXyEFrqTPIodritBKRC_Bmome0UcHOaVlBTabRzbzK30dUSn5GXKG9JXUDxvv-nF9KW7jS-SYrFVwsHNT86XIe3bj2LLw\" alt=\"\" width=\"173\" height=\"163\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Artinya, <em>P<\/em><em><sub>25<\/sub><\/em> terletak di data urutan ke-5 lebih 0,25.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/RzrQsD3GEWQDGMOgrHkx6TEn4SL29hD2eHMtowZimM9R2q_JEKF6VEwrO3qBFZtj_cQTw5pLw6LdxueWPnt7eVJ4cs_vMHJj46rbQNagbp5bGgyxBdW2wwsIv5gVYTlYF_8tQJRIQmuqnXV_EOTSvvRW98hjGjEunnnebDi8JTY2Vr1EmXSUcuhaaa9A43ZwUFN-fRJBUw\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Berdasarkan data pada soal, urutan data ke-5 ditempati oleh 34. Sementara data ke-6 = 36. Dengan demikian:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Nilai persentil ke-25 = Data ke-5 + (Kelebihan\/sisa letak persentil ke-25)((Data ke-6) \u2013 (Data ke-5))&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/wOTif73L0z5cooglRcLxT_8HKbCF_Nx4-YVtWBtHHbUy4R7oii44fZOa4q9He69Bp4z2_5EHqGwCcJ-zpOTT8cR_pBbg7nLHWuWrGV9MXgyMsSym8rs1TYNty-oMSDmNCagDLNipgIiGcwxvFhXMsR4aXRvUNX390IGV3eAEGkTrPgnAsanuB_bTkXH4Rab-gASt1xrZwg\" alt=\"\" width=\"182\" height=\"104\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, persentil ke-25 dari data tersebut adalah 34,5.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Persentil Data Kelompok<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Cara menentukan persentil data kelompok sama dengan desil data kelompok, yaitu sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan dahulu letak interval persentilnya dengan rumus berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Letak <em>P<\/em><em><sub>i<\/sub><\/em><em> <\/em>= <sub><\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>P<\/em><em><sub>i<\/sub><\/em><sup> <\/sup>= persentil ke-<em>i<\/em>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>i <\/em>= letak persentil ke-i; dan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>n<\/em> = banyaknya data.<em>&nbsp;<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Setelah letak persentil diketahui, gunakan persamaan berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/UyNN8J4Slzb7m8QEuOkqKzeZ5no-AKFqDkR581RLdNLqA8d2uglg7JeeJOKS3Io-_AKT96Nh8VgZocUoOVZkbAhol3_iWmo3fmgDCLuIJF_xuPoP0A3Y08vE82sclGF_kpQ4vP6f29YW1vkKdx10YXuH363UXJ5xrDHc2ef0HEAmSpONyZOwHsBAhD_X_62DVuS2ZnlrMw\" alt=\"\" width=\"142\" height=\"81\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>P<\/em><em><sub>i<\/sub><\/em> = persentil ke-<em>i<\/em>;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Tb<\/em><em><sub>i<\/sub><\/em> = tepi bawah kelas desil ke-i;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>p<\/em> = interval kelas;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em><em><sub>k<\/sub><\/em> = frekuensi kumulatif sebelum persentil ke-<em>i<\/em>;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em> = frekuensi persentil ke-<em>i<\/em>;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>n<\/em> = banyaknya data; dan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>i <\/em>= posisi persentil yang dicari (1 \u2013 99).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk lebih jelasnya, perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui tabel data kelompok tinggi badan seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Tinggi badan<\/th><th>Frekuensi (<em>f <\/em>)<\/th><\/tr><\/thead><tbody><tr><td>140 \u2013 143<\/td><td>4<\/td><\/tr><tr><td>144 \u2013 147&nbsp;<\/td><td>3<\/td><\/tr><tr><td>148 \u2013 151<\/td><td>5<\/td><\/tr><tr><td>152 \u2013 155&nbsp;<\/td><td>2<\/td><\/tr><tr><td>Jumlah&nbsp;<\/td><td>14<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan persentil ke-60 dari data pada tabel tersebut!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk memudahkanmu, tentukan dahulu frekuensi kumulatif pada tabel.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Tinggi badan (cm)<\/th><th>Frekuensi (<em>f <\/em>)<\/th><th>Frekuensi kumulatif (<em>f<sub>k<\/sub><\/em>)<\/th><\/tr><\/thead><tbody><tr><td>140 \u2013 143<\/td><td>4<\/td><td>4<\/td><\/tr><tr><td>144 \u2013 147&nbsp;<\/td><td>3<\/td><td>7<\/td><\/tr><tr><td>148 \u2013 151<\/td><td>5<\/td><td>12<\/td><\/tr><tr><td>152 \u2013 155&nbsp;<\/td><td>2<\/td><td>14<\/td><\/tr><tr><td>Jumlah&nbsp;<\/td><td>14<\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari tabel di atas, diperoleh panjang kelas (<em>p<\/em>) = 4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, tentukan letak interval persentil ke-60 dengan rumus berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Letak <em>P<\/em><em><sub>i<\/sub><\/em><em> <\/em>= <sub><\/sub><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/_7SQ04vWEXIOZ3C7CUFrsx1XdrED1KyF1hQXbsrUx7EqDzyhJut00pKv8tmWOMlWKat4dla6Ml6TGPUpmRMUw1GTbTbB7VHyc9O_w0QHm2YznIj25k2vN5eX-hDMMEgZnsp6lPtn63abNRRqaNokzov9_KkjjsBKaHqQb8gU7rQyJJ27EI6aX-732fSikNg33iwEanVU7g\" alt=\"\" width=\"165\" height=\"118\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian letak <em>P<\/em><em><sub>60<\/sub><\/em> berada di interval 148 \u2013 151.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, tentukan tepi bawah persentil ke-60.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Tb<\/em><em><sub>4<\/sub><\/em><em> <\/em>= 148 \u2013 0,5 = 147,5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Setelah semua elemen diketahui, gunakan persamaan persentil ke-<em>i<\/em> data berkelompok seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/IhoOtwj-pVFxO4hNfuanRDQYv7w8nep1LtTq4HQNQnxNfti-wgL2JQetMnqXi0H7vup-unIEfxDDMdEjtWPbcyKukJTnKzFzCGTPWRFHwTTUo6M91NgAxEXchxftofqeLL-gVO8B9wG5TDVo1J9g7FSRYvfYSQYIx8C_LewV4LfG3LpW7zYTLc4AUe6j46bXN6unH9KTDA\" alt=\"\" width=\"218\" height=\"225\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai persentil ke-60 tinggi badan tersebut adalah 148,62 cm.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh Soal<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Tabel perolehan nilai siswa kelas 3 dinyatakan pada tabel berikut.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Nilai<\/th><th>Frekuensi<\/th><\/tr><\/thead><tbody><tr><td>56 \u2013 60&nbsp;<\/td><td>5<\/td><\/tr><tr><td>61 \u2013 65&nbsp;<\/td><td>7<\/td><\/tr><tr><td>66 \u2013 70&nbsp;<\/td><td>3<\/td><\/tr><tr><td>71 \u2013 75&nbsp;<\/td><td>8<\/td><\/tr><tr><td>76 \u2013 80&nbsp;<\/td><td>2<\/td><\/tr><tr><td>81 \u2013 85&nbsp;<\/td><td>10<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari tabel tersebut, 30% siswa dinyatakan tidak lulus. Jika Hani mendapatkan nilai 68, apa yang akan terjadi? Apakah ia lulus atau tidak lulus?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dari soal diketahui bahwa 30% siswa dinyatakan tidak lulus. Artinya, kamu harus menentukan dahulu batas nilai maksimal siswa yang tidak lulus.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Batas nilai maksimal yang tidak lulus = persentil ke-30<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk memudahkanmu, tentukan dahulu frekuensi kumulatif pada tabel.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Nilai<\/th><th>Frekuensi<\/th><th>Frekuensi kumulatif<\/th><\/tr><\/thead><tbody><tr><td>56 \u2013 60&nbsp;<\/td><td>5<\/td><td>5<\/td><\/tr><tr><td>61 \u2013 65&nbsp;<\/td><td>7<\/td><td>12<\/td><\/tr><tr><td>66 \u2013 70&nbsp;<\/td><td>3<\/td><td>15<\/td><\/tr><tr><td>71 \u2013 75&nbsp;<\/td><td>8<\/td><td>23<\/td><\/tr><tr><td>76 \u2013 80&nbsp;<\/td><td>2<\/td><td>25<\/td><\/tr><tr><td>81 \u2013 85&nbsp;<\/td><td>10<\/td><td>35<\/td><\/tr><tr><td>Jumlah<\/td><td>35<\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari tabel di atas, diperoleh panjang kelas (<em>p<\/em>) = 5.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, tentukan letak interval persentil ke-30 dengan rumus berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Letak <em>P<\/em><em><sub>i<\/sub><\/em><em> <\/em>= <sub><\/sub><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/UVm2F0_cO1DWCKl86OiWgXQGs80VXxGLicnUBIrC_mf4nDbFeof57Q7UV_2gbGh_1dEmupxe4y-2uHdLPtzDkqNhIvB23kmywpENJFwnNhNgeYNLX8Wq7fd6tW8Rh5dCmRfdTCXQ69IFWBTt-3HWoynd2GD4f4uKHYyMChE7qTKY7ZVFA1PT_x02A3f7k7Wbpu8YAK2sgQ\" alt=\"\" width=\"164\" height=\"117\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian letak <em>P<\/em><em><sub>30<\/sub><\/em> berada di interval 61-65.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, tentukan tepi bawah persentil ke-30.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Tb<\/em><em><sub>30<\/sub><\/em><em> <\/em>= 61 \u2013 0,5 = 60,5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Setelah semua elemen diketahui, gunakan persamaan persentil ke-<em>i<\/em> data berkelompok seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/K1lozd6chIWHePakf0JGWlDbBm3KavdSmXjQPfJQxMKKRBFPEQwss0DP5okCrvOnYb_K22TqJFOce7LlVrnG4wYmFPhOiA6UN5-_Uy9hg1Pr-ze2vzkTPwZHLTbZr3ljEr2a18obJVNN3HJGK7P4hFDvxw4RlhOYiEUtvtmy9B2hOMg_63kWtCPdeuSOAiLDfC7u_PLVDQ\" alt=\"\" width=\"216\" height=\"228\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, batas nilai maksimal siswa yang tidak lulus adalah 64,43. Oleh karena Hani mendapatkan nilai 68, maka Hani dinyatakan lulus.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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":"<p>Hai Quipperian, di pembahasan sebelumnya, Quipper Blog sudah pernah membahas tentang mean, modus, dan median kan? Apakah kamu ingat pengertian ketiganya? Mean merupakan istilah&hellip;<\/p>\n","protected":false},"author":156447303,"featured_media":311590,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384865],"tags":[679385147],"ppma_author":[679386823,679386836],"class_list":["post-311587","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-materi-matematika-kelas-12"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pengertian Desil dan Persentil dengan Cara Menentukannya - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Apa itu desil dan persentil? 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