Pengertian, Rumus Simpangan Rata Rata, dan Contoh Menghitungnya
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Pengertian, Rumus Simpangan Rata Rata, dan Contoh Menghitungnya

Selasa, 09 Juni 2020

Terdapat beda istilah antara penulis buku satu dengan penulis lainnya, sehingga seringkali kita menjumpai istilah yang berbeda padahal bentuk rumus atau formula yang digunakan untuk mengolah data ternyata sama.

 

Sebelum membaca pembahasan pada artikel ini, ada baiknya sudah membaca mengenai karakter teman-teman simpangan baku yang lain pada artikel Pengertian, Jenis, dan Karakteristik Ukuran Variabilitas.

 

Deviasi berasal dari kata deviation yang diartikan sebagai penyimpangan atau simpangan, akibatnya istilah simpangan atau penyimpangan banyak digunakan. Tapi ada juga penulis buku lain yang tetap mengartikan deviation sebagai deviasi.

 

Oleh karena itu, artikel ini sekaligus mencantumkan istilah-istilah tersebut agar nantinya dapat dipahami dan tidak perlu mengundang perdebatan lebih panjang lagi. Pengertian mean deviation/ deviasi rata-rata/ simpangan absolut/ simpangan rata-rata adalah nilai rata-rata penyimpangan skor dari mean distribusi atau rata-rata jarak mutlak skor terhadap titik tengah (median).

 

Dua pengertian di atas menunjukkan bahwa ada yang menggunakan mean dan ada pula yang menggunakan median dalam formula tersebut. Sehingga dapat diketahui bahwa rumus yang digunakan sebagai berikut.

 

- menggunakan median, tanpa kelas interval

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- menggunakan mean, tanpa kelas interval

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- menggunakan mean dengan kelas interval data kelompok

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keterangan untuk ketiga rumus di atas:
SR = simpangan rata-rata
|...| = skor mutlak (hanya nilai positif saja, jika ada -5 maka menjadi 5)
Xi = anggota distribusi
n = jumlah anggota distribusi
Me = median distribusi

MathML (base64):PG1hdGggbWF0aHNpemU9IjIwIj4KICAgIDxtb3Zlcj4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1pIG1hdGhzaXplPSIxNSI+WDwvbWk+CiAgICAgICAgPC9tcm93PgogICAgICAgIDxtbz4mI3gyMDNFOzwvbW8+CiAgICA8L21vdmVyPgo8L21hdGg+ = mean distribusi
fi = frekuensi suatu kelas interval
Xt = titik tengah kelas interval


Okey, sekarang kita coba menghitung simpangan rata-rata menggunakan tabel distribusi frekuensi sesuai dengan basis data dari Cara Membuat Tabel Distribusi Frekuensi Kumulatif dan Relatif.

Data pada tabel di atas selanjutnya diolah sesuai dengan rumus simpangan rata-rata yang dihitung menggunakan mean dengan kelas interval data kelompok, sebagai berikut:

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sehingga memperoleh hasil:

MathML (base64):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

Untuk bisa sampai seperti hasil di atas maka perhatikan beberapa hal berikut:

  • mean distribusi sebesar 73 diperoleh dari nilai perhitungan 73,15 pada artikel Pengertian dan Cara Menghitung Mean Data Kelompok
  • rumus pada kolom warna hijau didapat dengan: kolom titik tengah frekuensi dikurangi mean distribusi; contoh: 46-73, 51, 73, dst.
  • rumus pada kolom orange didapat dengan: kolom frekuensi dikali dengan nilai mutlak kolom hijau, nilai mutlak artinya semua yang negatif menjadi positifkalau di excel pakai formula =ABS; contoh: 1*27, 3*22, dst.

Simpangan rata-rata memberikan informasi mengenai besarnya rata-rata penyimpangan yang ada didalam variasi skor. Angka penyimpangan yang makin besar menggambarkan skor-skor yang lebih heterogen dalam distribusi, sedangkan angka penyimpangan yang makin kecil menunjukkan bahwa skor-skor didalam distribusi lebih homogen. Kalau ada yang kurang dipahami mari kita diskusikan lewat komentar di bawah.

 

Nah, setelah mendapatkan nilai simpangan rata-rata kemudian lanjutkan untuk memahami dan menghitung varians pada artikel Pengertian dan Cara Menghitung Varians

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