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Tentukan kuartil 1, kuartil 2, dan kuartil 3 dari ...

Tentukan kuartil 1, kuartil 2, dan kuartil 3 dari data berikut.

Jawaban:

Rumus Kuartil Data Kelompok

begin mathsize 14px style Q subscript i equals T b plus open parentheses fraction numerator begin display style i over 4 end style n minus f subscript k over denominator f subscript i end fraction close parentheses end style

dengan

  • begin mathsize 14px style i equals 1 end style untuk kuartil bawah atau kuartil 1 begin mathsize 14px style open parentheses Q subscript 1 close parentheses end style 
  • begin mathsize 14px style i equals 2 end style untuk kuartil tengah atau kuartil 2 begin mathsize 14px style open parentheses Q subscript 2 close parentheses end style 
  • begin mathsize 14px style i equals 3 end style untuk kuartil atas atau kuartil 3 begin mathsize 14px style open parentheses Q subscript 3 close parentheses end style 
  • begin mathsize 14px style T subscript b end style adalah tepi bawah kelas kuartil
  • begin mathsize 14px style f subscript k end style adalah jumlah frekuensi sebelum kelas kuartil
  • begin mathsize 14px style f subscript i end style adalah frekuensi kelas kuartil
  • begin mathsize 14px style p end style adalah panjang kelas interval

Perhatikan data berikut.

Diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Q subscript 1 end cell equals cell T b plus open parentheses fraction numerator begin display style i over 4 n minus f subscript k end style over denominator f subscript i end fraction close parentheses end cell row blank equals cell 20 comma 5 plus open parentheses fraction numerator begin display style 1 fourth times 60 minus 9 end style over denominator 16 end fraction close parentheses end cell row blank equals cell 20 comma 5 plus 6 over 16 end cell row blank equals cell 20 comma 5 plus 0 comma 375 end cell row blank equals cell 20 comma 875 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Q subscript 2 end cell equals cell T b plus open parentheses fraction numerator begin display style i over 4 n minus f subscript k end style over denominator f subscript i end fraction close parentheses end cell row blank equals cell 40 comma 5 plus open parentheses fraction numerator begin display style 2 over 4 times 60 minus 16 end style over denominator 25 end fraction close parentheses end cell row blank equals cell 40 comma 5 plus 14 over 25 end cell row blank equals cell 40 comma 5 plus 0 comma 56 end cell row blank equals cell 41 comma 06 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Q subscript 3 end cell equals cell T b plus open parentheses fraction numerator begin display style i over 4 n minus f subscript k end style over denominator f subscript i end fraction close parentheses end cell row blank equals cell 40 comma 5 plus open parentheses fraction numerator begin display style 3 over 4 times 60 minus 16 end style over denominator 25 end fraction close parentheses end cell row blank equals cell 40 comma 5 plus 29 over 25 end cell row blank equals cell 40 comma 5 plus 1 comma 16 end cell row blank equals cell 41 comma 66 end cell end table end style  

Jadi, begin mathsize 14px style text kuartil end text space 1 equals 20 comma 875 comma space text kuartil  end text 2 equals 41 comma 06 end style, dan begin mathsize 14px style text kuartil end text space 3 equals 41 comma 66 end style.

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