Pengertian dan Rumus Distribusi Normal
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Pengertian dan Rumus Distribusi Normal

Senin, 10 Agustus 2020

Distribusi normal adalah persebaran skor yang digambarkan dengan kurva berbentuk lonceng simetrik yang memiliki nilai mean, median, modus, dan titik tengah yang sama, sehingga memisahkan kurva menjadi dua bagian sama besar.

 

Konsep distribusi normal dalam rumus

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Keterangan:
X = besaran yang diukur dari percobaan
Y = besaran yang berkaitan dengan X
MathML (base64):PG1hdGg+CiAgICA8bXN1Yj4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICAgICAgPG1pIG1hdGhzaXplPSIyMCI+JiN4M0JDOzwvbWk+CiAgICAgICAgPC9tcm93PgogICAgICAgIDxtcm93PgogICAgICAgIDwvbXJvdz4KICAgIDwvbXN1Yj4KPC9tYXRoPg=== rerata X pada populasi / expected values of X
MathML (base64):PG1hdGg+CiAgICA8bXN1Yj4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICAgICAgPG1pIG1hdGhzaXplPSIyMCI+JiN4M0MzOzwvbWk+CiAgICAgICAgPC9tcm93PgogICAgICAgIDxtcm93PgogICAgICAgIDwvbXJvdz4KICAgIDwvbXN1Yj4KPC9tYXRoPg=== simpangan baku populasi X
MathML (base64):PG1hdGg+CiAgICA8bXN1Yj4KICAgICAgICA8bXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICAgICAgPG1yb3c+CiAgICAgICAgICAgIDwvbXJvdz4KICAgICAgICAgICAgPG1pIG1hdGhzaXplPSIyMCI+JiN4M0MwOzwvbWk+CiAgICAgICAgPC9tcm93PgogICAgICAgIDxtcm93PgogICAgICAgIDwvbXJvdz4KICAgIDwvbXN1Yj4KPC9tYXRoPg=== 3,14
e = besaran konstan logaritma navier bernilai 2,7183


Sedangkan, bentuk distribusi normal dapat digambarkan sebagai berikut:

*Buku Research in Education, Best dan Kahn, Edisi 10, Halaman 370

 

Gambar di atas menunjukkan beberapa karakteristik distribusi normal, yaitu:

  1. Luas daerah dibawah kurva distribusi normal atau f(x) dan diatas sumbu X selalu samadengan satu, yaitu P(-...
  2. Distribusi normal berkaitan dengan hasil transformasi linear dari suatu skor menjadi skor standar z, karena setiap skor z dapat diperoleh kesamaan titik skornya pada distribusi normal.
  3. Distribusi normal hanya memilikisatu modul (unimodal), simetris, berbentuk genta, dan tinggi maksimum ada pada mean.
  4. Kurva berfungsi kontinuitas dengan rerata nilai y selalu memiliki persentase yang sama dengan tinggi puncak.
  5. Kurva asimtotik, artinya kurva distribusi normal tidak akan berpotongan dengan sumu X kecuali daerah tak terhingga. Bila X atau Z makin jauh dari rerata maka peluang munculnya nilai ekstrim makin kecil.
  6. Kurva yang tergantung pada nilai rerata dan simpangan baku tidak dapat mempengaruhi bentuk kurva, kecuali kalau mengumpul atau tersebar.
  7. Sifat simetris distribusi normal memberikan kesempatan untuk melakukan observasi pada besaran dan jarak tertentu dari rerata akan selalu sama, arah positifmaupun negatif.
  8. Distribusi normal standar dimaknai sebagai nilai dengan rerata samadengan nol dan simpangan baku samadengan satu.

Karakter yang khas dari kurva distribusi normal ialah asimtotik yang dapat dimaknai sebagai kurva yang memiliki puncak sebagai titik frekuensi tertinggi yang terletak pada nilai mean dan memiliki bentuk kurva yang menjauh dari titik puncaknya namun semakin rendah kurva akan semakin mendekati sumbu X atau garis horizontal tanpa sedikitpun menyentuh garis tersebut. 

 

Meskipun distribusi frekuensi digambarkan dengan kurva simetrik, tetapi lebar dan tinggi rendah kurvanya akan terlihat berbeda ketika melihat nilai mean dan variannya. Keduanya akan menjadikan bentuk kurva berbeda-beda, sehingga ada beberapa kurva distribusi normal yang dikenal.

 

Seperti kurva platykurtic dengan bentuk melebar ke samping namun tidak meruncing ke atas karena bagian puncaknya lebih datar, ada pula kurva leptokurtic yang menyempit ke tengah namun puncaknya meruncing ke atas, dan kurva mesokurtic yang puncak kurvanya berada ditengah-tengah antara platykurtic dan mesokurtic.

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