Pengertian Standar Deviasi dan Cara Menghitung Simpangan Baku
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Pengertian Standar Deviasi dan Cara Menghitung Simpangan Baku

Jumat, 12 Juni 2020

Penggunaan istilah yang berbeda seringkali membingungkan, maka artikel ini mencoba untuk menjernihkan bahwa terdapat banyak istilah yang digunakan untuk mengatakan standar deviasi yaitu standard deviation, deviasi standar, standar deviasi, atau simpangan baku. Keempat istilah ini memiliki bentuk rumus yang serupa, jadi tidak perlu lagi bingung dan kita bebas untuk memilih istilah yang disukai.

 

Standar deviasi atau simpangan baku adalah akar pangkat dua dari varian yang dilambangkan dengan " S atau s ". Sehingga, untuk bisa mendapatkan besaran standar deviasi maka harus dihitung dulu variansnya, kedua ukuran variabilitas ini biasanya digunakan beriringan dan termasuk ukuran variabilitas yang populer dan banyak digunakan.

 

Pada artikel Pengertian dan Cara Menghitung Varians telah diketahui bahwa ada dua macam rumus varians, yaitu: biased estimate dan unbiased estimate. Dimana biased estimate dimaksudkan sebagai ukuran variabilitas pada sampel dan unbiased estimate sebagai ukuran variabilitas pada populasi.

 

Ternyata setelah dua macam rumus varian tersebut masih ada dua jenis lagi rumus lain, yaitu: data tunggal (tanpa kelas interval) dan data kelompok (dengan kelas interval). Sebenarnya nggak banyak beda sih, jadi kalau mau dihafalkan pun juga cukup mudah.

 

Rumus standar deviasi biased estimate

Rumus standar deviasi biased estimate baik data tunggal dan kelompok dapat pula ditulis dengan singkat seperti ini:

MathML (base64):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 

 

  • Data Tunggal

 

 MathML (base64):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

 

  • Data Kelompok

MathML (base64):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

 

Rumus standar deviasi unbiased estimate

Rumus standar deviasi unbiased estimate baik data tunggal dan kelompok dapat pula ditulis dengan singkat seperti ini:

MathML (base64):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

 

  • Data Tunggal

 

MathML (base64):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

 

  • Data Kelompok

MathML (base64):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

 

 

Keterangan:

MathML (base64):PG1hdGg+CiAgICA8bXJvdz4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICA8L21yb3c+CiAgICA8L21yb3c+CiAgICA8bXN1cD4KICAgICAgICA8bWkgbWF0aHNpemU9IjIwIj5TPC9taT4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICA8L21yb3c+CiAgICA8L21zdXA+CjwvbWF0aD4=  =  standar deviasi (biased estimate)

MathML (base64):PG1hdGg+CiAgICA8bXJvdz4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICA8L21yb3c+CiAgICA8L21yb3c+CiAgICA8bXN1cD4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3cgbWF0aHNpemU9IjIwIj4KICAgICAgICAgICAgICAgIDxtaT5zPC9taT4KICAgICAgICAgICAgPC9tcm93PgogICAgICAgIDwvbXJvdz4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICA8L21yb3c+CiAgICA8L21zdXA+CjwvbWF0aD4=   = standar deviasi (unbiased estimate)

MathML (base64):PG1hdGg+CiAgICA8bXJvdz4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICA8L21yb3c+CiAgICA8L21yb3c+CiAgICA8bXN1cD4KICAgICAgICA8bWkgbWF0aHNpemU9IjIwIj5TPC9taT4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1pIG1hdGhzaXplPSIxNSI+MjwvbWk+CiAgICAgICAgPC9tcm93PgogICAgPC9tc3VwPgo8L21hdGg+ = varians (biased estimate)

MathML (base64):PG1hdGg+CiAgICA8bXJvdz4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICA8L21yb3c+CiAgICA8L21yb3c+CiAgICA8bXN1cD4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1pIG1hdGhzaXplPSIyMCI+czwvbWk+CiAgICAgICAgPC9tcm93PgogICAgICAgIDxtcm93PgogICAgICAgICAgICA8bWkgbWF0aHNpemU9IjE1Ij4yPC9taT4KICAgICAgICA8L21yb3c+CiAgICA8L21zdXA+CjwvbWF0aD4=  = 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

 

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

Untuk bisa sampai pada perhitungan seperti tabel di atas, sebaiknya telaah dulu artikel Pengertian dan Cara Menghitung Varians. Perlu diketahui bahwa untuk bisa mendapatkan nilai varians sebesar 821,77 maka data pada tabel di atas peru diolah dengan  rumus varians unbiased estimate data kelompok, didapat:

 

MathML (base64):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

 

Setelah diketahui nilai varians = 821,77 selanjutnya diolah lagi dengan rumus standar deviasi unbiased estimate data kelompok, didapat:

MathML (base64):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

Maka diperoleh standar deviasi sebesar 28,67. Cukup mudah bukan untuk menghitung standar deviasi, namun yang perlu diperhatikan adalah langkah-langkah sebelumnya yang harus diikuti.

 

Pastikan setiap rumus pada artikel sebelumnya dibaca, jadi sebelum menghitung standar deviasi ada baiknya membaca dulu artikel cara menghitung varians, dan sebelum menghitung varians maka baca dulu artikel cara menghitung simpangan rata-rata. Setiap artikel selalu disertakan link ke artikel sebelumnya, jangan sampai terlewat lhoo yaah!

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