{"id":313915,"date":"2023-02-28T13:19:00","date_gmt":"2023-02-28T06:19:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=313915"},"modified":"2023-03-01T09:25:37","modified_gmt":"2023-03-01T02:25:37","slug":"simpangan-rata-rata","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/simpangan-rata-rata\/","title":{"rendered":"Materi Simpangan Rata-rata Lengkap dengan Rumus, Penerapan dan Contohnya"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

Hai Quipperian, apakah kamu masih ingat pembahasan Quipper Blog sebelumnya tentang simpangan baku? Simpangan baku baku termasuk salah satu bentuk ukuran penyebaran data, kan? Memangnya, ada berapa sih bentuk penyebaran data itu? Kalau lupa, buka lagi materinya, ya.<\/p>\n\n\n\n

Di pembahasan ini, Quipper Blog akan membahas bentuk penyebaran data yang lain, yaitu simpangan rata-rata. Apa yang dimaksud dengan simpangan rata-rata? Daripada penasaran, yuk simak selengkapnya!<\/p>\n\n\n\n

Pengertian Simpangan Rata-Rata<\/strong><\/h2>\n\n\n\n

Simpangan rata-rata adalah bentuk penyebaran data yang menunjukkan selisih suatu data terhadap nilai rata-ratanya. Dengan adanya simpangan rata-rata kamu bisa tahu sejauh mana data-data itu menyimpang dari nilai pusatnya. Suatu data dikatakan konsisten jika simpangan rata-ratanya cukup kecil, sehingga selisih antara data tersebut dan rata-ratanya tidak terlalu besar. Artinya, datanya cukup seragam. Perhatikan contoh berikut.<\/p>\n\n\n\n

Data 1: 23, 22, 22, 21, 25 \u2192 rata-rata = 23<\/p>\n\n\n\n

Data 2: 32, 24, 18, 19, 20 \u2192 rata-rata = 23<\/p>\n\n\n\n

Kedua data di atas memiliki rata-rata yang sama, yaitu 23. Menurutmu, data mana yang lebih terpusat atau konsisten? Tentu data 1, ya. Hal itu karena selisih antara data dan nilai rata-ratanya tidak terlalu jauh.<\/p>\n\n\n\n

Rumus Simpangan Rata-Rata<\/strong><\/h2>\n\n\n\n

Secara umum, data dibagi menjadi dua, yaitu data tunggal dan data berkelompok. Rumus simpangan rata-rata kedua jenis data juga berbeda. Ingin tahu perbedaannya?<\/p>\n\n\n\n

\n

Baca Juga: <\/span> Komplemen Himpunan: Pegertian dan Cara Menentukan Komplemennya<\/a><\/p>\n<\/div>\n\n\n\n

Rumus Simpangan Rata-Rata Data Tunggal<\/strong><\/h3>\n\n\n\n

Data tunggal adalah data yang tidak disusun secara interval. Secara matematis, rumus simpangan rata-rata data tunggal adalah:<\/p>\n\n\n\n

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

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

SR <\/em>= simpangan rata-rata;<\/p>\n\n\n\n

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

x=rata-rata; dan<\/p>\n\n\n\n

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

Lalu, bagaimana jika ada data tunggal yang disusun dalam bentuk tabel dengan jumlah n<\/em> cukup banyak? Apabila kamu menjumpai soal-soal demikian, gunakan persamaan berikut.<\/p>\n\n\n\n

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

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

SR <\/em>= simpangan rata-rata;<\/p>\n\n\n\n

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

x=rata-rata; dan<\/p>\n\n\n\n

f<\/em>1<\/sub><\/em> = frekuensi data ke-i<\/em>.<\/p>\n\n\n\n

Agar kamu semakin paham, simak contoh berikut ini.<\/p>\n\n\n\n

Pada suatu percobaan, diperoleh 10 data berikut ini.<\/p>\n\n\n\n

45, 44, 46, 47, 44, 43, 42, 41, 40, 44<\/p>\n\n\n\n

Tentukan simpangan rata-rata data di atas!<\/p>\n\n\n\n

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

Dari data di atas, n<\/em> = 10.<\/p>\n\n\n\n

Mula-mula, tentukan dahulu rata-rata (mean<\/em>) data pada soal.<\/p>\n\n\n\n

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

Lalu, tentukan selisih antara setiap data dan rata-ratanya. Untuk memudahkanmu, buatlah tabel seperti di bawah ini.<\/p>\n\n\n\n

xi<\/sub><\/em><\/th>x<\/th>xi-x<\/th><\/tr><\/thead>
45<\/td>43,6<\/td>1,4<\/td><\/tr>
44<\/td>43,6<\/td>0,4<\/td><\/tr>
46<\/td>43,6<\/td>2,4<\/td><\/tr>
47<\/td>43,6<\/td>3,4<\/td><\/tr>
44<\/td>43,6<\/td>0,4<\/td><\/tr>
43<\/td>43,6<\/td>0,6<\/td><\/tr>
42<\/td>43,6<\/td>1,6<\/td><\/tr>
41<\/td>43,6<\/td>2,6<\/td><\/tr>
40<\/td>43,6<\/td>3,6<\/td><\/tr>
44<\/td>43,6<\/td>0,4<\/td><\/tr>
<\/sub><\/td>16,8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Terakhir, substitusikan nilai 16,8 pada persamaan simpangan rata-rata.<\/p>\n\n\n\n

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

Jadi, simpangan rata-rata data pada soal adalah 1,68.<\/p>\n\n\n\n

Rumus Simpangan Rata-Rata Data Berkelompok<\/strong><\/h3>\n\n\n\n

Data berkelompok adalah data yang disajikan dalam bentuk tabel dengan interval kelas tertentu. Secara matematis, rumus simpangan rata-rata data berkelompok adalah sebagai berikut.<\/p>\n\n\n\n

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

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

SR <\/em>= simpangan rata-rata;<\/p>\n\n\n\n

f<\/em>i<\/sub> = frekuensi data ke-I<\/em>;<\/p>\n\n\n\n

x<\/em>i<\/sub> = data tengah di setiap interval;<\/p>\n\n\n\n

x=rata-rata; dan<\/p>\n\n\n\n

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

Penerapan Simpangan Rata-Rata<\/strong><\/h2>\n\n\n\n

Sebagai salah satu bentuk ukuran penyebaran data, simpangan rata-rata berfungsi untuk menganalisis seberapa jauh suatu data menyimpang dari rata-ratanya. Perhatikan tabel pengamatan pada pertumbuhan akar Vigna radiata<\/em> L<\/em> berikut ini.<\/p>\n\n\n\n

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

Sumber: https:\/\/semnas.biologi.fmipa.unp.ac.id\/index.php\/prosiding\/article\/download\/72\/61\/210&nbsp<\/a>;<\/p>\n\n\n\n

Apa yang bisa kamu simpulkan dari kedua data tersebut? Eitss <\/em>tunggu dulu. Sebelum membuat kesimpulan, kamu harus hitung dulu simpangan rata-ratanya, ya. Simpangan ini kamu tentukan dari keenam data, yaitu mulai hari ke-0 sampai ke-5.<\/p>\n\n\n\n

Simpangan rata-rata pada perlakuan gelap<\/strong><\/p>\n\n\n\n

Data yang diperoleh dari perlakukan gelap adalah 0; 0; 1,0; 1,5; 7,0; 7,5. Dengan demikian, rata-rata pertumbuhannya adalah:<\/p>\n\n\n\n

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

Lalu, tentukan selisih antara setiap data dan rata-ratanya. Untuk memudahkanmu, buatlah tabel seperti di bawah ini.<\/p>\n\n\n\n

x<\/em>i<\/sub><\/em><\/td>x<\/td>xi-x<\/td><\/tr>
0<\/td>2,83<\/td>2,83<\/td><\/tr>
0<\/td>2,83<\/td>2,83<\/td><\/tr>
1<\/td>2,83<\/td>1,83<\/td><\/tr>
1,5<\/td>2,83<\/td>1,33<\/td><\/tr>
7<\/td>2,83<\/td>4,17<\/td><\/tr>
7,5<\/td>2,83<\/td>4,67<\/td><\/tr>
<\/sub><\/td>17,66<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Terakhir, substitusikan nilai 17,66 pada persamaan simpangan rata-rata.<\/p>\n\n\n\n

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

Simpangan rata-rata pada perlakuan terang<\/strong><\/p>\n\n\n\n

Data yang diperoleh dari perlakukan gelap adalah 0; 0; 0,5; 1,2; 3,7; 4,3. Dengan demikian, rata-rata pertumbuhannya adalah:<\/p>\n\n\n\n

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

Lalu, tentukan selisih antara setiap data dan rata-ratanya. Untuk memudahkanmu, buatlah tabel seperti di bawah ini.<\/p>\n\n\n\n

xi<\/sub><\/em><\/th>x<\/th>xi-x<\/th><\/tr><\/thead>
<\/td><\/td><\/td><\/tr>
0<\/td>1,62<\/td>1,62<\/td><\/tr>
0<\/td>1,62<\/td>1,62<\/td><\/tr>
0,5<\/td>1,62<\/td>1,12<\/td><\/tr>
1,2<\/td>1,62<\/td>0,42<\/td><\/tr>
3,7<\/td>1,62<\/td>2,08<\/td><\/tr>
4,3<\/td>1,62<\/td>2,68<\/td><\/tr>
<\/sub><\/td>9,54<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Terakhir, substitusikan nilai 9,54 pada persamaan simpangan rata-rata.<\/p>\n\n\n\n

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

Dari perhitungan diperoleh SR pertumbuhan akar Vigna radiata<\/em> L<\/em> di kondisi gelap adalah 2,94. Sementara itu, SR pertumbuhan akar Vigna radiata<\/em> L <\/em>di kondisi terang adalah 1,59. Oleh karena SR pertumbuhan akar di tempat terang lebih kecil dari SR di tempat gelap, maka bisa disimpulkan bahwa pertumbuhan akar di kondisi terang lebih konsisten dan menghasilkan data yang lebih seragam.<\/p>\n\n\n\n

Jika ditinjau dari sisi Biologi, data itu sangat relevan. Mengingat, pertumbuhan akar tanaman bisa berjalan optimal di tempat terang. Sebaliknya, pertumbuhan akan berjalan lebih cepat di tempat gelap atau kurang cahaya.<\/p>\n\n\n\n

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

Agar semakin paham, kamu bisa ikutan Quipper Blog ngerjain<\/em> contoh soal berikut ini.<\/p>\n\n\n\n

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

Berikut ini data tinggi badan siswa laki-laki SMA Harapan Bangsa Kelas XII.<\/p>\n\n\n\n

Tinggi badan (cm)<\/th>Frekuensi<\/th><\/tr><\/thead>
165<\/td>20<\/td><\/tr>
168<\/td>24<\/td><\/tr>
170<\/td>15<\/td><\/tr>
172<\/td>30<\/td><\/tr>
173<\/td>22<\/td><\/tr>
174<\/td>19<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Tentukan simpangan rata-rata tinggi badan siswa laki-laki tersebut!<\/p>\n\n\n\n

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

Mula-mula, tentukan dahulu rata-ratanya. Oyya, data di atas termasuk data tunggal karena tidak ditulis dalam bentuk interval kelas.<\/p>\n\n\n\n

Tinggi badan (cm)<\/th>Frekuensi<\/th><\/tr><\/thead>
165<\/td>20<\/td><\/tr>
168<\/td>24<\/td><\/tr>
170<\/td>15<\/td><\/tr>
172<\/td>30<\/td><\/tr>
173<\/td>22<\/td><\/tr>
174<\/td>19<\/td><\/tr>
Jumlah:<\/td>130<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Rata-ratanya adalah:<\/p>\n\n\n\n

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

Lalu, tentukan selisih setiap data dengan rata-ratanya.<\/p>\n\n\n\n

xi<\/sub><\/em><\/th>fi<\/sub><\/em><\/th>x<\/th>fixi-x<\/th><\/tr><\/thead>
165<\/td>20<\/td>170,41<\/td>108,2<\/td><\/tr>
168<\/td>24<\/td>170,41<\/td>57,84<\/td><\/tr>
170<\/td>15<\/td>170,41<\/td>6,15<\/td><\/tr>
172<\/td>30<\/td>170,41<\/td>47,7<\/td><\/tr>
173<\/td>22<\/td>170,41<\/td>56,98<\/td><\/tr>
174<\/td>19<\/td>170,41<\/td>68,21<\/td><\/tr>
Jumlah:<\/td>130<\/td><\/td>345,08<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Dengan demikian, diperoleh simpangan rata-ratanya sebagai berikut.<\/p>\n\n\n\n

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

Jadi, simpangan rata-rata tinggi badan siswa laki-laki SMA Harapan Bangsa kelas XII adalah 2,65.<\/p>\n\n\n\n

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

Dalam rangka dies natalis, suatu sekolah mengadakan olimpiade Matematika. Kegiatan itu diikuti oleh 100 peserta dari berbagai sekolah. Adapun tabel perolehan nilai para peserta dinyatakan sebagai berikut.<\/p>\n\n\n\n

Interval Nilai<\/th>Frekuensi<\/th><\/tr><\/thead>
41 \u2013 45 <\/td>30<\/td><\/tr>
46 \u2013 50 <\/td>8<\/td><\/tr>
51 \u2013 55 <\/td>12<\/td><\/tr>
56 \u2013 60 <\/td>32<\/td><\/tr>
61 \u2013 65 <\/td>18<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Tentukan simpangan rata-rata nilai olimpiade tersebut!<\/p>\n\n\n\n

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

Oleh karena penulisan kelasnya dijadikan interval, maka data di atas termasuk data berkelompok.<\/p>\n\n\n\n

Pertama, tentukan dahulu rata-ratanya.<\/p>\n\n\n\n

Interval Nilai<\/th>Frekuensi (f<\/em>i<\/sub>)<\/th>x<\/em>i<\/sub> (nilai tengah data)<\/th>xi<\/sub><\/em>.fi<\/sub><\/em><\/th><\/tr><\/thead>
41 \u2013 45 <\/td>30<\/td>43<\/td>1.290<\/td><\/tr>
46 \u2013 50 <\/td>8<\/td>48<\/td>384<\/td><\/tr>
51 \u2013 55 <\/td>12<\/td>53<\/td>636<\/td><\/tr>
56 \u2013 60 <\/td>32<\/td>58<\/td>1.856<\/td><\/tr>
61 \u2013 65 <\/td>18<\/td>63<\/td>1.134<\/td><\/tr>
Jumlah<\/td>100<\/td><\/td>5.300<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Nilai rata-ratanya adalah:<\/p>\n\n\n\n

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

Selanjutnya, tentukan simpangan rata-ratanya.<\/p>\n\n\n\n

Interval Nilai<\/th>Frekuensi (f<\/em>i<\/sub>)<\/th>x<\/em>i<\/sub> (nilai tengah data)<\/th>x<\/th>fixi-x<\/th><\/tr><\/thead>
41 \u2013 45 <\/td>30<\/td>43<\/td>53<\/td>300<\/td><\/tr>
46 \u2013 50 <\/td>8<\/td>48<\/td>53<\/td>40<\/td><\/tr>
51 \u2013 55 <\/td>12<\/td>53<\/td>53<\/td>0<\/td><\/tr>
56 \u2013 60 <\/td>32<\/td>58<\/td>53<\/td>160<\/td><\/tr>
61 \u2013 65 <\/td>18<\/td>63<\/td>53<\/td>180<\/td><\/tr>
Jumlah<\/td>100<\/td><\/td><\/td>680<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Substitusikan nilai total fixi-x pada persamaan berikut.<\/p>\n\n\n\n

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

Itulah pembahasan Quipper Blog kali ini. Semoga bisa bermanfaat buat Quipperian. Materi lengkapnya bisa kamu unduh di Quipper Video, ya. Jika belum berlangganan, yuks buruan. Salam Quipper<\/p>\n","protected":false},"excerpt":{"rendered":"

Hai Quipperian, apakah kamu masih ingat pembahasan Quipper Blog sebelumnya tentang simpangan baku? Simpangan baku baku termasuk salah satu bentuk ukuran penyebaran data, kan?…<\/p>\n","protected":false},"author":156447303,"featured_media":313931,"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-313915","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-materi-matematika-kelas-12"],"acf":[],"yoast_head":"\nMateri Simpangan Rata-rata Lengkap dengan Rumus, Penerapan dan Contohnya - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Simpangan rata-rata adalah bentuk penyebaran data yang menunjukkan selisih suatu data terhadap nilai rata-ratanya. 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