{"id":308686,"date":"2022-11-26T11:05:00","date_gmt":"2022-11-26T04:05:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=308686"},"modified":"2023-02-06T10:24:50","modified_gmt":"2023-02-06T03:24:50","slug":"standar-deviasi","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/standar-deviasi\/","title":{"rendered":"Pengertian Standar Deviasi, Fungsi, Rumus dan Cara Menghitungnya"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

Hai Quipperian, mungkin kamu sudah tak asing lagi dengan istilah penelitian ilmiah. Tanpa adanya penelitian ilmiah, ilmu pengetahuan tidak akan berkembang. Saat melakukan penelitian, data yang digunakan oleh seorang peneliti tidak hanya satu, tetapi bisa jadi puluhan atau bahkan ratusan. Nah, untuk mengecek kesesuaian semua data itu terhadap rata-rata, dibutuhkanlah suatu standar deviasi. Apa yang dimaksud standar deviasi? Yuk, simak selengkapnya!<\/p>\n\n\n\n

Pengertian Standar Deviasi<\/strong><\/h2>\n\n\n\n

Standar deviasi adalah suatu nilai yang menunjukkan tingkat penyebaran data terhadap nilai rata-rata data tersebut. Lambang standar deviasi adalah s<\/em>. Biasanya, kamu mengenal istilah ini sebagai simpangan baku. Di awal artikel ini sudah disinggung tentang banyaknya data-data penelitian yang digunakan oleh para peneliti. Data-data tersebut tentu beragam, kan? Nah, itulah mengapa dibutuhkan beberapa sampel untuk kemudian dicari standar deviasinya, lalu dibandingkan dengan rata-rata. Memangnya, apa hubungan standar deviasi dengan rata-rata? Jika standar deviasinya lebih besar dari mean, artinya data semakin beragam. Jika standar deviasinya lebih kecil dari mean, artinya data kurang beragam. Satuan dari standar deviasi sama dengan satuan data yang digunakan. Jika kamu ingin mencari standar deviasi pengukuran massa yang satuannya gram, maka standar deviasinya juga bersatuan gram.<\/p>\n\n\n\n

Fungsi Standar Deviasi<\/strong><\/h2>\n\n\n\n

Adapun fungsi standar deviasi dalam penelitian adalah sebagai berikut.<\/p>\n\n\n\n

    \n
  1. Memastikan bahwa sampel yang digunakan sudah mewakili populasi penelitian.<\/li>\n\n\n\n
  2. Memudahkan peneliti untuk menganalisis ukuran penyebaran data yang diperoleh.<\/li>\n\n\n\n
  3. Menunjukkan tingkat keragaman data penelitian.<\/li>\n\n\n\n
  4. Sebagai tolok ukur keakuratan data di dalam penelitian.<\/li>\n<\/ol>\n\n\n\n

    Kapan Standar Deviasi Digunakan?<\/strong><\/h2>\n\n\n\n

    Mungkin kamu penasaran, kapan sih standar deviasi itu digunakan? Apakah setiap penelitian harus menggunakannya? Sebaiknya, standar deviasi digunakan untuk setiap data penelitian, terlebih data-data yang jumlahnya cukup banyak. Untuk data yang jumlahnya banyak, seorang peneliti hanya perlu mengambil beberapa sampel saja.<\/p>\n\n\n\n

    Rumus Standar Deviasi<\/strong><\/h2>\n\n\n\n

    Rumus standar deviasi dibagi menjadi dua, yaitu rumus standar deviasi data tunggal dan standar deviasi data berkelompok. Adapun rumus keduanya adalah sebagai berikut.<\/p>\n\n\n\n

    Rumus standar deviasi data tunggal<\/strong><\/h3>\n\n\n\n

    Data tunggal adalah data-data yang hanya memiliki satu rentang nilai saja atau data asli penelitian, misalnya 12, 23, 35, dan seterusnya. Untuk data-data demikian, kamu bisa mencari standar deviasinya dengan rumus berikut.<\/p>\n\n\n\n

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

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

    s <\/em>= standar deviasi atau simpangan baku;<\/p>\n\n\n\n

    x<\/em>i<\/sub> = data ke-i;<\/p>\n\n\n\n

    x= rata-rata (mean<\/em>); dan<\/p>\n\n\n\n

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

    Rumus standar deviasi data berkelompok<\/strong><\/h3>\n\n\n\n

    Data berkelompok adalah data yang dinyatakan dalam bentuk interval, misalnya 22 \u2013 25, 26 \u2013 29, 30 \u2013 33, dan seterusnya. Standar deviasi untuk data berkelompok bisa dicari dengan rumus berikut.<\/p>\n\n\n\n

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

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

    s <\/em>= standar deviasi atau simpangan baku;<\/p>\n\n\n\n

    x<\/em>i<\/sub> = data tengah (median dari tiap interval);<\/p>\n\n\n\n

    x= rata-rata (mean<\/em>); dan<\/p>\n\n\n\n

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

    Jika diperhatikan, rumus di atas hampir sama dengan rumus varians. Lalu, apa hubungan standar deviasi dan varians? Hubungannya adalah standar deviasi merupakan bentuk akar dari varians.<\/p>\n\n\n\n

    Cara Menghitung Standar Deviasi<\/strong><\/h2>\n\n\n\n

    Langkah-langkah untuk menghitung standar deviasi data tunggal adalah sebagai berikut.<\/p>\n\n\n\n

      \n
    1. Tentukan dahulu mean atau rata-rata data penelitiannya (x). Data yang dimaksud mencakup semua data, bukan sampel.<\/li>\n\n\n\n
    2. Ambil beberapa sampel yang ingin dicari standar deviasinya, misalnya data ke-1 sampai ke-5. \u2192 Misal (x<\/em>1<\/sub> \u2013 x<\/em>5<\/sub>)<\/li>\n\n\n\n
    3. Setelah menentukan sampel, selanjutnya tentukan selisih antara setiap data pada poin 2 dan rata-ratanya lalu kuadratkan. \u2192 Misal (x<\/em>1<\/sub> – x)2<\/sup>, (x<\/em>2<\/sub> – x)2<\/sup>, (x<\/em>3<\/sub> – x)2<\/sup>, dan seterusnya<\/li>\n\n\n\n
    4. Jumlahkan semua selisih yang diperoleh pada poin 3, lalu kuadratkan hasilnya. \u2192 Misal ((x<\/em>1<\/sub> – x)2<\/sup> + (x<\/em>2<\/sub> – x)2<\/sup> + (x<\/em>3<\/sub> – x)2<\/sup> + \u2026 + \u2026)<\/li>\n\n\n\n
    5. Hasil penjumlahan kuadrat itu dibagi dengan banyaknya data sampel \u2013 1 (n<\/em> \u2013 1).<\/li>\n\n\n\n
    6. Terakhir, akarkan semua hasil yang diperoleh.<\/li>\n<\/ol>\n\n\n\n

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

      Setelah mempelajari materi ini, yuk asah kemampuanmu melalui contoh soal berikut ini.<\/p>\n\n\n\n

      Contoh soal standar deviasi data tunggal<\/strong><\/h3>\n\n\n\n

      Sebanyak 8 siswa kelas XA5 mengikuti ujian susulan untuk mata pelajaran Matematika karena tidak hadir saat ujian berlangsung. Adapun perolehan nilai ke-8 siswa tersebut adalah 75, 80, 66, 90, 89, 90, 85, 87. Tentukan simpangan baku dari data nilai tersebut!<\/p>\n\n\n\n

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

      Mula-mula, kamu harus menentukan nilai rata-rata (mean<\/em>).<\/p>\n\n\n\n

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

      Untuk memudahkanmu, buatlah tabel seperti berikut.<\/p>\n\n\n\n

      Siswa ke-<\/th>xi<\/sub><\/em><\/th>x<\/th>(xi<\/sub> <\/em>– x)2<\/sup><\/th><\/tr><\/thead>
      1<\/td>75<\/td>82,75<\/td>60,0625<\/td><\/tr>
      2<\/td>80<\/td>82,75<\/td>7,5625<\/td><\/tr>
      3<\/td>66<\/td>82,75<\/td>280,5625<\/td><\/tr>
      4<\/td>90<\/td>82,75<\/td>52,5625<\/td><\/tr>
      5<\/td>89<\/td>82,75<\/td>39,0625<\/td><\/tr>
      6<\/td>90<\/td>82,75<\/td>52,5625<\/td><\/tr>
      7<\/td>85<\/td>82,75<\/td>5,0625<\/td><\/tr>
      8<\/td>87<\/td>82,75<\/td>18,0625<\/td><\/tr>
      <\/td><\/td><\/td>515,5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Dengan demikian, standar deviasinya dirumuskan sebagai berikut.<\/p>\n\n\n\n

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

      Jadi, simpangan bakunya adalah 8,58.<\/p>\n\n\n\n

      Contoh soal standar deviasi data berkelompok<\/strong><\/h3>\n\n\n\n

      Dalam rangka sosialisasi pentingnya vaksinasi pada anak dan dewasa, Dinas Kesehatan Kota X mengadakan penyuluhan pada 60 orang dengan rentang usia yang berbeda-beda seperti berikut.<\/p>\n\n\n\n

      Rentang usia (th)<\/th>Jumlah peserta<\/th><\/tr><\/thead>
      16 \u2013 20<\/td>4<\/td><\/tr>
      21 \u2013 25<\/td>10<\/td><\/tr>
      26 \u2013 30<\/td>6<\/td><\/tr>
      31 \u2013 35<\/td>15<\/td><\/tr>
      36 \u2013 40<\/td>8<\/td><\/tr>
      41 \u2013 45<\/td>14<\/td><\/tr>
      46 \u2013 50<\/td>3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Berapakah simpangan baku dari usia pesertanya?<\/p>\n\n\n\n

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

      Untuk memudahkanmu dalam menentukan simpangan baku, mula-mula tentukan dahulu nilai rata-ratanya menggunakan tabel seperti berikut.<\/p>\n\n\n\n

      Usia<\/th>xi<\/sub><\/em><\/th>fi<\/sub><\/em><\/th>xi<\/sub> <\/em>. fi<\/sub><\/em><\/th><\/tr><\/thead>
      16 \u2013 20<\/td>18<\/td>4<\/td>72<\/td><\/tr>
      21 \u2013 25<\/td>23<\/td>10<\/td>230<\/td><\/tr>
      26 \u2013 30<\/td>28<\/td>6<\/td>168<\/td><\/tr>
      31 \u2013 35<\/td>33<\/td>15<\/td>495<\/td><\/tr>
      36 \u2013 40<\/td>38<\/td>8<\/td>304<\/td><\/tr>
      41 \u2013 45<\/td>43<\/td>14<\/td>602<\/td><\/tr>
      46 \u2013 50<\/td>48<\/td>3<\/td>144<\/td><\/tr>
      Jumlah <\/td>60<\/td>2.015<\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Secara matematis, nilai rata-ratanya dirumuskan sebagai berikut.<\/p>\n\n\n\n

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

      Lalu, buat lanjutan tabelnya seperti berikut.<\/p>\n\n\n\n

      Usia<\/th>xi<\/sub><\/em><\/th>fi<\/sub><\/em><\/th>xi<\/sub> <\/em>. fi<\/sub><\/em><\/th>x<\/th>xi<\/sub> <\/em>– x<\/th>(xi<\/sub> <\/em>– x)2<\/sup><\/th>fi<\/sub> . <\/em>(xi<\/sub> <\/em>– x)2<\/sup><\/th><\/tr><\/thead>
      16 \u2013 20<\/td>18<\/td>4<\/td>72<\/td>33,58<\/td>-15,58<\/td>242,7364<\/td>970,9456<\/td><\/tr>
      21 \u2013 25<\/td>23<\/td>10<\/td>230<\/td>33,58<\/td>-10,58<\/td>111,9364<\/td>1.119,364<\/td><\/tr>
      26 \u2013 30<\/td>28<\/td>6<\/td>168<\/td>33,58<\/td>-5,58<\/td>31,1364<\/td>186,8184<\/td><\/tr>
      31 \u2013 35<\/td>33<\/td>15<\/td>495<\/td>33,58<\/td>-0,58<\/td>31,1364<\/td>5,046<\/td><\/tr>
      36 \u2013 40<\/td>38<\/td>8<\/td>304<\/td>33,58<\/td>4,42<\/td>0,3364<\/td>156,2912<\/td><\/tr>
      41 \u2013 45<\/td>43<\/td>14<\/td>602<\/td>33,58<\/td>9,42<\/td>19,5364<\/td>1.242,3096<\/td><\/tr>
      46 \u2013 50<\/td>48<\/td>3<\/td>144<\/td>33,58<\/td>14,42<\/td>207,9364<\/td>623,8092<\/td><\/tr>
      Jumlah<\/td>60<\/td>3<\/td><\/td><\/td><\/td>4.304,584<\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Dengan demikian, simpangan baku atau standar deviasinya adalah sebagai berikut.<\/p>\n\n\n\n

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

      Dari perhitungan di atas, diperoleh bahwa standar deviasinya lebih kecil dari mean atau rata-rata. Bagaimana jika standar deviasi lebih kecil dari mean? Hal itu menunjukkan bahwa data kurang bervariatif.<\/p>\n\n\n\n

      Jadi, simpangan baku dari usia pesertanya adalah 8,47 tahun.<\/p>\n\n\n\n

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

      Hai Quipperian, mungkin kamu sudah tak asing lagi dengan istilah penelitian ilmiah. Tanpa adanya penelitian ilmiah, ilmu pengetahuan tidak akan berkembang. Saat melakukan penelitian,…<\/p>\n","protected":false},"author":156447303,"featured_media":308695,"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-308686","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-materi-matematika-kelas-12"],"acf":[],"yoast_head":"\nPengertian Standar Deviasi, Fungsi, Rumus dan Cara Menghitungnya - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Standar deviasi adalah suatu nilai yang menunjukkan tingkat penyebaran data terhadap nilai rata-rata data tersebut. 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