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Diketahui suatu kumpulan data sebagai berikut. (m + 1 ), (m − 1 ), (5m − 5), dan (m + 1) a. Nyatakanlah rataan dan simpangan baku data di atas dalam m. b. Tentukanlah nilai m jika rataan sama dengan simpangan baku

Pertanyaan

Diketahui suatu kumpulan data sebagai berikut.
left parenthesis m space plus space 1 space right parenthesis comma space left parenthesis m space minus space 1 space right parenthesis comma space left parenthesis 5 m space minus space 5 right parenthesis comma dan left parenthesis m space plus space 1 right parenthesis

a. Nyatakanlah rataan dan simpangan baku data di atas dalam m.

b. Tentukanlah nilai m jika rataan sama dengan simpangan baku

S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

rataan dan simpangan baku data tersebut adalah 2 m minus 1 dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of size 12px 3 size 12px m to the power of size 12px 2 size 12px minus size 12px 6 size 12px m size 12px plus size 12px 6 end root end cell end table sedangkan nilai m adalah m subscript 1 equals fraction numerator negative 2 plus 2 square root of 6 over denominator 8 end fraction space comma space m subscript 2 equals fraction numerator negative 2 minus 2 square root of 6 over denominator 8 end fraction.

Pembahasan

a. Suatu data: left parenthesis m space plus space 1 space right parenthesis comma space left parenthesis m space minus space 1 space right parenthesis comma space left parenthesis 5 m space minus space 5 right parenthesis comma dan left parenthesis m space plus space 1 right parenthesis

Rata-rata data tunggal dapat dihitung dengan rumus:

top enclose x equals fraction numerator Jumlah space data over denominator Banyak space data end fraction s equals square root of fraction numerator begin display style sum from i equals 1 to n of end style left parenthesis x subscript i minus top enclose x right parenthesis over denominator n minus 1 end fraction end root

Sehingga,

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose x end cell equals cell fraction numerator left parenthesis m plus 1 right parenthesis plus left parenthesis m minus 1 right parenthesis plus left parenthesis 5 m minus 5 right parenthesis plus left parenthesis m plus 1 right parenthesis over denominator 4 end fraction end cell row blank equals cell fraction numerator 8 m minus 4 over denominator 4 end fraction end cell row blank equals cell 2 m minus 1 end cell row blank blank blank row s equals cell square root of fraction numerator begin display style sum from i equals 1 to n of left parenthesis x subscript i minus top enclose x right parenthesis squared end style over denominator n end fraction end root end cell row blank equals cell square root of fraction numerator begin display style left parenthesis negative m plus 2 right parenthesis squared plus left parenthesis negative m right parenthesis squared plus left parenthesis 3 m minus 4 right parenthesis squared plus left parenthesis negative m plus 2 right parenthesis squared end style over denominator 4 end fraction end root end cell row blank equals cell square root of fraction numerator left parenthesis m squared minus 4 m plus 4 right parenthesis plus m squared plus left parenthesis 9 m squared minus 24 m plus 16 right parenthesis plus left parenthesis m squared plus 4 m plus 4 right parenthesis over denominator 4 end fraction end root end cell row blank equals cell square root of fraction numerator 12 m squared minus 24 m plus 24 over denominator 4 end fraction end root end cell row blank equals cell square root of 3 m squared minus 6 m plus 6 end root end cell end table end style

b. Rataan sama dengan simpangan baku:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 m minus 1 end cell equals cell square root of 3 m squared minus 6 m plus 6 end root end cell row cell open parentheses 2 m minus 1 close parentheses squared end cell equals cell open parentheses square root of 3 m squared minus 6 m plus 6 end root close parentheses squared end cell row cell 4 m squared minus 4 m plus 1 end cell equals cell 3 m squared minus 6 m plus 6 end cell row cell m squared plus 2 m minus 5 end cell equals 0 end table

m equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction equals fraction numerator negative 2 plus-or-minus square root of 2 squared minus 4 left parenthesis 1 right parenthesis left parenthesis negative 5 right parenthesis end root over denominator 2 left parenthesis 4 right parenthesis end fraction equals fraction numerator negative 2 plus-or-minus square root of 4 plus 20 end root over denominator 8 end fraction  equals fraction numerator negative 2 plus-or-minus square root of 24 over denominator 8 end fraction  equals fraction numerator negative 2 plus-or-minus 2 square root of 6 over denominator 8 end fraction  m subscript 1 equals fraction numerator negative 2 plus 2 square root of 6 over denominator 8 end fraction m subscript 2 equals fraction numerator negative 2 minus 2 square root of 6 over denominator 8 end fraction

Dengan demikian, rataan dan simpangan baku data tersebut adalah 2 m minus 1 dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of size 12px 3 size 12px m to the power of size 12px 2 size 12px minus size 12px 6 size 12px m size 12px plus size 12px 6 end root end cell end table sedangkan nilai m adalah m subscript 1 equals fraction numerator negative 2 plus 2 square root of 6 over denominator 8 end fraction space comma space m subscript 2 equals fraction numerator negative 2 minus 2 square root of 6 over denominator 8 end fraction.

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