Tentukan D1, D4, D7, dan D8 dari data yang dinyatakan dalam distribusi frekuensi berikut.

Pertanyaan

Tentukan D₁, D₄, D₇, dan D₈ dari data yang dinyatakan dalam distribusi frekuensi berikut.

A. Septianingsih

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

Gunakan rumus desil berikut :

$Desil space left parenthesis D subscript i right parenthesis equals L subscript i plus open parentheses fraction numerator begin display style i over 10 end style n minus F subscript i over denominator f subscript i end fraction close parentheses. c$

dengan :

$\begin{array}{rcl}D_i\;&=&\;\mathrm{desil}\;\mathrm{ke}-i,\;i=1,2,\;.\;.\;.\;,9\;\;\\L_i&=&\;\mathrm{tepi}\;\mathrm{bawah}\;\mathrm{kelas}\;\mathrm{desil}\;\mathrm{ke}-i\;\;\\n\;&=&\;\mathrm{ukuran}\;\mathrm{data}\;(\mathrm{jumlah}\;\mathrm{frekuensi})\;\;\\c\;&=&\;\mathrm{interval}\;\mathrm{kelas}\;\mathrm{atau}\;\mathrm{panjang}\;\mathrm{kelas}\;\;\\f_i\;&=&\;\mathrm{frekuensi}\;\mathrm{pada}\;\mathrm{interval}\;\mathrm{kelas}\;\mathrm{desil}\;\mathrm{ke}-i\;\;\\F_i\;&=&\;\mathrm{frekuensi}\;\mathrm{kumulatif}\;\mathrm{sebelum}\;\mathrm{interval}\;\mathrm{kelas}\;\mathrm{desil}\;\mathrm{ke}-\mathrm i\end{array}$

Perhatikan tabel distribusi frekuensi kumulatif berikut untuk menghitung desil.

Desil 1

$\begin{array}{rcl}\mathrm{data}\;\mathrm{ke}&=&\frac{\mathrm i}{10}.\mathrm n\\&=&\frac1{10}.200\\&=&20\\\mathrm{Kelas}\;&=&11-20\end{array}$

maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell Desil space space left parenthesis D subscript i right parenthesis end cell equals cell L subscript i plus open parentheses fraction numerator begin display style i over 10 end style n minus F subscript i over denominator f subscript i end fraction close parentheses. c end cell row cell D subscript 1 end cell equals cell 10 comma 5 plus open parentheses fraction numerator 20 minus 12 over denominator 15 end fraction close parentheses.10 end cell row blank equals cell 10 comma 5 plus 5 comma 33 end cell row blank equals cell 15 comma 833 end cell row blank blank blank end table$

Desil 4

$\begin{array}{rcl}\mathrm{data}\;\mathrm{ke}&=&\frac{\mathrm i}{10}.\mathrm n\\&=&\frac4{10}.200\\&=&80\\\mathrm{Kelas}\;&=&41-50\end{array}$

maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell Desil space space left parenthesis D subscript i right parenthesis end cell equals cell L subscript i plus open parentheses fraction numerator begin display style i over 10 end style n minus F subscript i over denominator f subscript i end fraction close parentheses. c end cell row cell D subscript 4 end cell equals cell 40 comma 5 plus open parentheses fraction numerator 80 minus 71 over denominator 30 end fraction close parentheses.10 end cell row blank equals cell 40 comma 5 plus 3 end cell row blank equals cell 43 comma 5 end cell row blank blank blank end table$

Desil 7

$\begin{array}{rcl}\mathrm{data}\;\mathrm{ke}&=&\frac{\mathrm i}{10}.\mathrm n\\&=&\frac7{10}.200\\&=&140\\\mathrm{Kelas}\;&=&61-70\end{array}$

maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell Desil space space left parenthesis D subscript i right parenthesis end cell equals cell L subscript i plus open parentheses fraction numerator begin display style i over 10 end style n minus F subscript i over denominator f subscript i end fraction close parentheses. c end cell row cell D subscript 7 end cell equals cell 60 comma 5 plus open parentheses fraction numerator 140 minus 128 over denominator 25 end fraction close parentheses.10 end cell row blank equals cell 60 comma 5 plus 4 comma 8 end cell row blank equals cell 65 comma 3 end cell row blank blank blank end table$

Desil 8

$\begin{array}{rcl}\mathrm{data}\;\mathrm{ke}&=&\frac i{10}.\mathrm n\\&=&\frac8{10}.200\\&=&160\\\mathrm{Kelas}\;&=&71-80\end{array}$

maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell Desil space space left parenthesis D subscript i right parenthesis end cell equals cell L subscript i plus open parentheses fraction numerator begin display style i over 10 end style n minus F subscript i over denominator f subscript i end fraction close parentheses. c end cell row cell D subscript 8 end cell equals cell 70 comma 5 plus open parentheses fraction numerator 160 minus 158 over denominator 18 end fraction close parentheses.10 end cell row blank equals cell 70 comma 5 plus 1 comma 11 end cell row blank equals cell 71 comma 61 end cell row blank blank blank end table$

Dengan demikian hasil dari

$D_1=15,83\\D_4=43,5\\D_7=65,3\\D_8=71,61$