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Pertanyaan

Perhatikan data berikut!

2 5 1 4 3 4 8 4 1 7 0 7

Berdasarkan data di atas, tentukan

d. kuartil bawah, kuartil tengah, dan kuartil atasnya!undefined 

K. Prameswari

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

diperoleh kuartil bawah = 1,5; kuartil tengah = 4 dan kuartil atas = 6.undefined 

Pembahasan

Akan diurutkan terlebih dahulu data di atas dari yang terkecil ke yang terbesar sebagai berikut:

0 1 1 2 3 4 4 4 5 7 7 8

Jumlah data di atas adalah undefined (berjumlah genap). Maka diperoleh

1. Kuartil bawah atau begin mathsize 14px style Q subscript 1 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Q subscript 1 end cell equals cell fraction numerator x subscript open parentheses n over 4 close parentheses end subscript plus x subscript open parentheses n over 4 plus 1 close parentheses end subscript over denominator 2 end fraction end cell row blank equals cell fraction numerator x subscript open parentheses 12 over 4 close parentheses end subscript plus x subscript open parentheses 12 over 4 plus 1 close parentheses end subscript over denominator 2 end fraction end cell row blank equals cell fraction numerator x subscript 3 plus x subscript 4 over denominator 2 end fraction end cell row blank equals cell fraction numerator 1 plus 2 over denominator 2 end fraction end cell row blank equals cell 1 comma 5 end cell end table end style

2. Kuartil tengah atau begin mathsize 14px style Q subscript 2 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 fraction numerator x subscript open parentheses n over 2 close parentheses end subscript plus x subscript open parentheses n over 2 plus 1 close parentheses end subscript over denominator 2 end fraction end cell row blank equals cell fraction numerator x subscript open parentheses begin display style 12 over 2 end style close parentheses end subscript plus x subscript open parentheses begin display style 12 over 2 end style plus 1 close parentheses end subscript over denominator 2 end fraction end cell row blank equals cell fraction numerator x subscript 6 plus x subscript 7 over denominator 2 end fraction end cell row blank equals cell fraction numerator 4 plus 4 over denominator 2 end fraction end cell row blank equals 4 end table end style 

3. Kuartil atas atau begin mathsize 14px style Q subscript 3 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 fraction numerator x subscript open parentheses fraction numerator 3 n over denominator 4 end fraction close parentheses end subscript plus x subscript open parentheses fraction numerator 3 n over denominator 4 end fraction plus 1 close parentheses end subscript over denominator 2 end fraction end cell row blank equals cell fraction numerator x subscript begin display style open parentheses fraction numerator 3 cross times 12 over denominator 4 end fraction close parentheses end style end subscript plus x subscript begin display style open parentheses fraction numerator 3 cross times 12 over denominator 4 end fraction plus 1 close parentheses end style end subscript over denominator 2 end fraction end cell row blank equals cell fraction numerator x subscript 9 plus x subscript 10 over denominator 2 end fraction end cell row blank equals cell fraction numerator 5 plus 7 over denominator 2 end fraction end cell row blank equals 6 end table end style

Jadi diperoleh kuartil bawah = 1,5; kuartil tengah = 4 dan kuartil atas = 6.undefined 

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