-9417Tentukan D1, D3, D6, dan D9 dari data yang dinyatakan dalam poligon frekuensi berikut.

Pertanyaan

-9417Tentukan D1, D3, D6, dan D9 dari data yang dinyatakan dalam poligon 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 10.100 end cell row blank equals 10 row cell Kelas space end cell equals cell 60 minus 64 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 59 comma 5 plus open parentheses fraction numerator 10 minus 7 over denominator 12 end fraction close parentheses.5 end cell row blank equals cell 59 comma 5 plus 1 comma 25 end cell row blank equals cell 60 comma 75 end cell row blank blank blank end table   

 

  • Desil 3

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 3 over 10.100 end cell row blank equals 30 row cell Kelas space end cell equals cell 65 minus 69 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 3 end cell equals cell 64 comma 5 plus open parentheses fraction numerator 30 minus 19 over denominator 23 end fraction close parentheses.5 end cell row blank equals cell 64 comma 5 plus 2 comma 39 end cell row blank equals cell 66 comma 89 end cell row blank blank blank end table   

 

  • Desil 6

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 6 over 10.100 end cell row blank equals 60 row cell Kelas space end cell equals cell 70 minus 74 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 6 end cell equals cell 69 comma 5 plus open parentheses fraction numerator 60 minus 42 over denominator 21 end fraction close parentheses.5 end cell row blank equals cell 69 comma 5 plus 4 comma 28 end cell row blank equals cell 73 comma 78 end cell row blank blank blank end table    

 

  • Desil 9

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 9 over 10.100 end cell row blank equals 90 row cell Kelas space end cell equals cell 80 minus 84 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 9 end cell equals cell 79 comma 5 plus open parentheses fraction numerator 90 minus 81 over denominator 10 end fraction close parentheses.5 end cell row blank equals cell 79 comma 5 plus 4 comma 5 end cell row blank equals 84 row blank blank blank end table     

Dengan demikian hasil dari 

D subscript 1 equals 60 comma 75 D subscript 3 equals 66 comma 89 D subscript 6 equals 73 comma 78 D subscript 9 equals 84     

 

 

 

 

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