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Jika rata-rata dari dan berturut-turut adalah dan , maka rata-rata dari adalah ...

Jika rata-rata dari begin mathsize 14px style a comma space b comma space c end style dan begin mathsize 14px style a squared comma space b squared comma space c squared end style berturut-turut adalah begin mathsize 14px style 2 end style dan begin mathsize 14px style 4 end style, maka rata-rata dari begin mathsize 14px style ab comma space bc comma space ac end style adalah ...

Jawaban:

Diketahui:

Rata-rata begin mathsize 14px style a comma space b comma space c end style adalah begin mathsize 14px style 2 end style.

Rata-rata begin mathsize 14px style a squared comma space b squared comma space c squared end style adalah begin mathsize 14px style 4 end style.

Banyak data masing-masing adalah begin mathsize 14px style 3 end style.

Rata-rata adalah nilai perbandingan antara jumlah nilai data dengan banyaknya data.

Sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose straight x subscript 1 end enclose end cell equals 2 row cell fraction numerator straight a plus straight b plus straight c over denominator 3 end fraction end cell equals 2 row cell straight a plus straight b plus straight c end cell equals cell 3 cross times 2 end cell row cell straight a plus straight b plus straight c end cell equals cell 6 space space space space space space space space... left parenthesis 1 right parenthesis end cell end table end style

Dan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose straight x subscript 2 end enclose end cell equals 4 row cell fraction numerator straight a squared plus straight b squared plus straight c squared over denominator 3 end fraction end cell equals 4 row cell straight a squared plus straight b squared plus straight c squared end cell equals cell 4 cross times 3 end cell row cell straight a squared plus straight b squared plus straight c squared end cell equals cell 12 space space space space space space... space left parenthesis 2 right parenthesis end cell end table end style

Substitusi kedua persamaan untuk memperoleh jumlah nilai data dari begin mathsize 14px style ab comma space bc comma space ac end style seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a plus straight b plus straight c end cell equals 6 row cell open parentheses straight a plus straight b plus straight c close parentheses squared end cell equals cell 6 squared end cell row cell straight a squared plus straight b squared plus straight c squared plus 2 ab plus 2 ac plus 2 bc end cell equals 36 row cell open parentheses straight a squared plus straight b squared plus straight c squared close parentheses plus 2 open parentheses ab plus bc plus ca close parentheses end cell equals 36 row cell 12 plus 2 open parentheses ab plus bc plus ca close parentheses end cell equals 36 row cell 2 open parentheses ab plus bc plus ca close parentheses end cell equals cell 36 minus 12 end cell row cell 2 open parentheses ab plus bc plus ca close parentheses end cell equals 24 row cell ab plus bc plus ca end cell equals cell 24 over 2 end cell row cell ab plus bc plus ca end cell equals 12 end table end style

Sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose straight x subscript 3 end enclose end cell equals cell fraction numerator ab plus bc plus ac over denominator 3 end fraction end cell row blank equals cell 12 over 3 end cell row blank equals 4 end table end style

Maka rata-rata dari begin mathsize 14px style ab comma space bc comma space ac end style adalah begin mathsize 14px style 4 end style.

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