Pengertian dan Cara Menghitung Varians
centercoastrealty.com + intuitivejournal.com

Pengertian dan Cara Menghitung Varians

Rabu, 10 Juni 2020

Varians adalah rata-rata kuadrat dari tiap skor terhadap mean atau jumlah kuadrat deviasi rata-rata dibagi n-1. Sehingga dapat diketahui bahwa terdapat dua pengertian varian yang berbeda, oleh karena itu ada dua jenis pula rumus varian. Perbedaan lainnya ada pada lambang huruf kapital dan huruf kecil yang digunakan pada masing-masing rumus.


- Mean Squared Deviation (MSD) atau estimasi bias terhadap varian populasi (biased estimate) dilambangkan S2, dengan rumus :

MathML (base64):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

Beda lagi kalau menghitung varians dengan skor-skor kelas interval, maka rumus biased estimate menjadi:

MathML (base64):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


- Estimasi nirbias terhadap varian populasi (unbiased estimate) dilambangkan s2, dengan rumus:

MathML (base64):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

Sedangkan untuk menghitung varians dengan skor-skor kelas interval, maka rumus unbiased estimate menjadi:

MathML (base64):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


Keterangan untuk kedua rumus di atas:

MathML (base64):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 = varians (biased estimate)

MathML (base64):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 = varians (unbiased estimate)

fi = frekuensi suatu kelas interval

Xi  = anggota distribusi (tunggal) / titik tengah (kelompok)
n   = jumlah anggota distribusi

MathML (base64):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  = mean distribusi

 

Ukuran varians biased estimate merupakan perkiraan untuk ukuran variabilitas pada sampel, sedangkan varians unbiased estimate ialah perkiraan yang ditujukan untuk ukuran variabilitas pada populasi.

 

Yaps, sekarang menghitung varians menggunakan basis data dari tabel distribusi frekuensi pada artikel Cara Membuat Tabel Distribusi Frekuensi Kumulatif dan Relatif.

Bila ingin mengetahui asal usul angka-angka pada kolom warna hijau dan orange, detail penjelasannya ada pada artikel Pengertian, Rumus Simpangan Rata Rata, dan Contoh Menghitungnya. Sedangkan untuk kolom warna biru diperoleh dari kuadrat kolom orange, contoh: 12*27; 66*66. Kalau dilakukan di Ms Excel tentu akan lebih mudah lagi tinggal drag and drop aja!

 

Informasi dari tabel di atas bila diolah menggunakan rumus varians (unbiased estimate) dengan kelas interval, maka akan diperoleh hasil:

 

MathML (base64):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

Hasil perhitungan di atas menunjukkan bahwa varians dari distribusi skor pada tabel di atas adalah sebesar 821,77. Oh iya, huruf "x" itu untuk memberi tanda bahwa varians yang dihitung adalah dari tabel x dan bisa saja diganti dengan y dan lain sebagainya.

 

Setelah selesai menghitung varians, bisa dilanjutkan untuk menghitung standar deviasi atau simpangan baku pada artikel Pengertian Standar Deviasi dan Cara Menghitung Simpangan Baku

0 respon22 dilihat


Memuat Komentar