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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 :

table attributes columnalign right center left columnspacing 0px end attributes row cell D subscript i space end cell equals cell space desil space ke minus i comma space i equals 1 comma 2 comma space. space. space. space comma 9 space space end cell row cell L subscript i end cell equals cell space tepi space bawah space kelas space desil space ke minus i space space end cell row cell n space end cell equals cell space ukuran space data space left parenthesis jumlah space frekuensi right parenthesis space space end cell row cell c space end cell equals cell space interval space kelas space atau space panjang space kelas space space end cell row cell f subscript i space end cell equals cell space frekuensi space pada space interval space kelas space desil space ke minus i space space end cell row cell F subscript i space end cell equals cell space frekuensi space kumulatif space sebelum space interval space kelas space desil space ke minus straight i end cell end table 

Perhatikan tabel distribusi frekuensi kumulatif berikut untuk menghitung desil.

  • Desil 1

table attributes columnalign right center left columnspacing 0px end attributes row cell data space ke end cell equals cell straight i over 10. straight n end cell row blank equals cell 1 over 10.200 end cell row blank equals 20 row cell Kelas space end cell equals cell 11 minus 20 end cell end table 

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

table attributes columnalign right center left columnspacing 0px end attributes row cell data space ke end cell equals cell straight i over 10. straight n end cell row blank equals cell 4 over 10.200 end cell row blank equals 80 row cell Kelas space end cell equals cell 41 minus 50 end cell end table  

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

table attributes columnalign right center left columnspacing 0px end attributes row cell data space ke end cell equals cell straight i over 10. straight n end cell row blank equals cell 7 over 10.200 end cell row blank equals 140 row cell Kelas space end cell equals cell 61 minus 70 end cell end table  

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

table attributes columnalign right center left columnspacing 0px end attributes row cell data space ke end cell equals cell i over 10. straight n end cell row blank equals cell 8 over 10.200 end cell row blank equals 160 row cell Kelas space end cell equals cell 71 minus 80 end cell end table  

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 subscript 1 equals 15 comma 83 D subscript 4 equals 43 comma 5 D subscript 7 equals 65 comma 3 D subscript 8 equals 71 comma 61  

 

 

 

 

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