Tentukan simpangan kuartil, desil ke-, desil ke-, ...

Tentukan simpangan kuartil, desil ke- $begin mathsize 14px style 2 end style$ , desil ke- $begin mathsize 14px style 7 end style$ , persentil ke- $begin mathsize 14px style 45 end style$ , dan jangkauan persentil dari data pada tabel berikut.

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Jawaban:

Panjang kelas: $begin mathsize 14px style c equals 4 end style$

Banyak data: $begin mathsize 14px style n equals 40 end style$

Letak kelas $begin mathsize 14px style straight Q subscript 3 end style$

$begin mathsize 14px style equals 3 over 4 open parentheses 40 close parentheses equals 30 end style$

yaitu di kelas $begin mathsize 14px style 10 minus 13 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight Q subscript 3 end cell equals cell t subscript b plus open parentheses fraction numerator begin display style i over 4 end style open parentheses n close parentheses minus f subscript k over denominator f end fraction close parentheses c end cell row blank equals cell 9 comma 5 plus open parentheses fraction numerator begin display style 3 over 4 open parentheses 40 close parentheses minus 20 end style over denominator 10 end fraction close parentheses open parentheses 4 close parentheses end cell row blank equals cell 9 comma 5 plus 4 end cell row blank equals cell 13 comma 5 end cell end table end style$

Letak kelas $begin mathsize 14px style straight Q subscript 1 end style$

$begin mathsize 14px style equals 1 fourth left parenthesis 40 right parenthesis equals 10 end style$

yaitu di kelas $begin mathsize 14px style 6 minus 9 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight Q subscript 1 end cell equals cell t subscript b plus open parentheses fraction numerator begin display style i over 4 open parentheses n close parentheses minus f subscript k end style over denominator f end fraction close parentheses c end cell row blank equals cell 5 comma 5 plus open parentheses fraction numerator begin display style 1 fourth open parentheses 40 close parentheses minus 8 end style over denominator 12 end fraction close parentheses left parenthesis 4 right parenthesis end cell row blank equals cell 5 comma 5 plus 0 comma 6 end cell row blank equals cell 6 comma 1 end cell end table end style$

Simpangan kuartil

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell straight Q subscript 3 minus straight Q subscript 1 end cell row blank equals cell 13 comma 5 minus 6 comma 1 end cell row blank equals cell 7 comma 4 end cell end table end style$

Desil ke- $begin mathsize 14px style 2 end style$

Letaknya

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell 2 over 10 open parentheses 40 close parentheses end cell row blank equals 8 end table end style$

yaitu di kelas $begin mathsize 14px style 2 minus 5 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight D subscript 2 end cell equals cell t subscript b plus open parentheses fraction numerator begin display style i over 10 open parentheses n close parentheses minus f subscript k end style over denominator f end fraction close parentheses c end cell row blank equals cell 1 comma 5 plus open parentheses fraction numerator begin display style 2 over 10 open parentheses 40 close parentheses minus 0 end style over denominator 8 end fraction close parentheses left parenthesis 4 right parenthesis end cell row blank equals cell 1 comma 5 plus 4 end cell row blank equals cell 5 comma 5 end cell end table end style$

Desil ke- $begin mathsize 14px style 7 end style$

Letaknya

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell 8 over 10 left parenthesis 40 right parenthesis end cell row blank equals 28 end table end style$

yaitu di kelas $begin mathsize 14px style 10 minus 13 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight D subscript 7 end cell equals cell t subscript b plus open parentheses fraction numerator begin display style i over 10 open parentheses n close parentheses minus f subscript k end style over denominator f end fraction close parentheses c end cell row blank equals cell 9 comma 5 plus open parentheses fraction numerator begin display style 7 over 10 open parentheses 40 close parentheses minus 20 end style over denominator 10 end fraction close parentheses left parenthesis 4 right parenthesis end cell row blank equals cell 9 comma 5 plus 3 comma 2 end cell row blank equals cell 12 comma 7 end cell end table end style$

Persentil ke- $begin mathsize 14px style 45 end style$

letaknya

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell 45 over 100 left parenthesis 40 right parenthesis space end cell row blank equals 18 end table end style$

yaitu di kelas $begin mathsize 14px style 6 minus 9 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P subscript 45 end cell equals cell t subscript b plus open parentheses fraction numerator begin display style i over 100 open parentheses n close parentheses minus f subscript k end style over denominator f end fraction close parentheses c end cell row blank equals cell 5 comma 5 plus open parentheses fraction numerator begin display style 45 over 100 open parentheses 40 close parentheses minus 8 end style over denominator 12 end fraction close parentheses left parenthesis 4 right parenthesis end cell row blank equals cell 5 comma 5 plus 3 comma 3 end cell row blank equals cell 8 comma 8 end cell end table end style$

Jangkauan Persentil

Letak persentil ke- $begin mathsize 14px style 90 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell 90 over 100 left parenthesis 40 right parenthesis space end cell row blank equals 36 end table end style$

yaitu di kelas $begin mathsize 14px style 14 minus 17 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P subscript 90 end cell equals cell t subscript b plus open parentheses fraction numerator begin display style i over 100 open parentheses n close parentheses minus f subscript k end style over denominator f end fraction close parentheses c end cell row blank equals cell 13 comma 5 plus open parentheses fraction numerator begin display style 90 over 100 open parentheses 40 close parentheses minus 30 end style over denominator 6 end fraction close parentheses left parenthesis 4 right parenthesis end cell row blank equals cell 13 comma 5 plus 4 end cell row blank equals cell 17 comma 5 end cell end table end style$

Letak persentil ke- $begin mathsize 14px style 10 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 10 over 100 left parenthesis 40 right parenthesis space end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table end style$

yaitu di kelas $begin mathsize 14px style 2 minus 5 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P subscript 10 end cell equals cell t subscript b plus open parentheses fraction numerator begin display style i over 100 open parentheses n close parentheses minus f subscript k end style over denominator f end fraction close parentheses c end cell row blank equals cell 1 comma 5 plus open parentheses fraction numerator begin display style 10 over 100 open parentheses 40 close parentheses minus 0 end style over denominator 8 end fraction close parentheses left parenthesis 4 right parenthesis end cell row blank equals cell 1 comma 5 plus 2 end cell row blank equals cell 3 comma 5 end cell end table end style$

Jangkauan Persentil

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell straight P subscript 3 minus straight P subscript 1 end cell row blank equals cell 17 comma 5 minus 3 comma 5 end cell row blank equals cell 14 comma 5 end cell end table end style$

Dengan demikian nilai dari simpangan kuartil, desil ke- $begin mathsize 14px style 2 end style$ , desil ke- $begin mathsize 14px style 7 end style$ , persentil ke- $undefined$ , dan jangkauan persentil adalah $begin mathsize 14px style 7 comma 4 semicolon space 5 comma 5 semicolon space 12 comma 7 semicolon space 8 comma 8 end style$ dan $begin mathsize 14px style 14 comma 5 end style$ .

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