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Nilai simpangan baku dari data :8,6,5,7,9 adalah...

Pertanyaan

Nilai simpangan baku dari data begin mathsize 14px style colon space 8 comma space 6 comma space 5 comma space 7 comma space 9 end style adalah...

Pembahasan Video:

Pembahasan Soal:

Rata-rata data di atas adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose x end cell equals cell fraction numerator 8 plus 6 plus 5 plus 7 plus 9 over denominator 5 end fraction end cell row blank equals cell 35 over 5 end cell row blank equals 7 end table end style

Simpangan baku

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row S equals cell square root of fraction numerator begin display style sum from i equals 1 to 5 of end style open parentheses x subscript i minus top enclose x close parentheses squared over denominator 5 end fraction end root end cell row blank equals cell square root of fraction numerator open parentheses 8 minus 7 close parentheses squared plus open parentheses 6 minus 7 close parentheses squared plus open parentheses 5 minus 7 close parentheses squared plus open parentheses 7 minus 7 close parentheses squared plus open parentheses 9 minus 7 close parentheses squared over denominator 5 end fraction end root end cell row blank equals cell square root of fraction numerator 1 plus 1 plus 4 plus 0 plus 4 over denominator 5 end fraction end root end cell row blank equals cell square root of 2 end cell end table end style

Dengan demikian simpangan baku data tersebut adalah begin mathsize 14px style square root of 2 end style.

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Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

Simpangan baku dari data 2,4,1,6,6,4,8,9,5 adalah ...

Pembahasan Soal:

Rumus dari simpangan baku data tunggal adalah:

ragam equals straight S squared equals fraction numerator sum from straight i equals 1 to straight n of left parenthesis straight x subscript straight i minus straight x with bar on top right parenthesis squared over denominator straight n end fraction

simpangan space baku equals straight S equals square root of straight S squared end root


Pertama kita urutkan datanya: 1 comma space 2 comma space 4 comma space 4 comma space 5 comma space 6 comma space 6 comma space 8 comma space 9.

Kita hitung rata-ratanya: 


table attributes columnalign right center left columnspacing 0px end attributes row cell straight x with bar on top end cell equals cell fraction numerator 1 plus 2 plus 4 plus 4 plus 5 plus 6 plus 6 plus 8 plus 9 over denominator 9 end fraction end cell row blank equals cell 45 over 9 end cell row blank equals 5 end table



table attributes columnalign right center left columnspacing 0px end attributes row cell straight S squared end cell equals cell 42 over 9 end cell row straight S equals cell square root of straight S squared end root end cell row blank equals cell square root of 42 over 9 end root end cell row straight S equals cell 1 third square root of 42 end cell end table


Jadi simpangan baku data tersebut adalah 1 third square root of 42.

0

Roboguru

Jika median dari data terurut 5, 6, 6, k, 10, 10, 11, 16 adalah 9, maka simpangan baku data tersebut adalah ....

Pembahasan Soal:

Diketahui ada 8 data dan mediannya adalah 9, maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell M e end cell equals cell fraction numerator x subscript 4 plus x subscript 5 over denominator 2 end fraction end cell row 9 equals cell fraction numerator k plus 10 over denominator 2 end fraction end cell row 18 equals cell k plus 10 end cell row cell 18 minus 10 end cell equals k row 8 equals k end table end style      

Selanjutnya, kita cari rata-ratanya terlebih dahulu.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x with minus on top end cell equals cell fraction numerator 5 plus 2 left parenthesis 6 right parenthesis plus 8 plus 2 left parenthesis 10 right parenthesis plus 11 plus 16 over denominator 8 end fraction end cell row blank equals cell 72 over 8 end cell row blank equals 9 end table end style      

Sehingga kita peroleh simpangan bakunya adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sigma squared end cell equals cell fraction numerator sum from i equals 1 to n of open parentheses x subscript i minus x with minus on top close parentheses squared over denominator n end fraction end cell row cell sigma squared end cell equals cell fraction numerator open parentheses 5 minus 9 close parentheses squared plus 2 open parentheses 6 minus 9 close parentheses squared plus open parentheses 8 minus 9 close parentheses squared over denominator 8 end fraction end cell row blank blank cell blank plus fraction numerator 2 open parentheses 10 minus 9 close parentheses squared plus open parentheses 11 minus 9 close parentheses squared plus open parentheses 16 minus 9 close parentheses squared over denominator 8 end fraction end cell row cell sigma squared end cell equals cell fraction numerator 16 plus 18 plus 1 plus 2 plus 4 plus 49 over denominator 8 end fraction end cell row cell sigma squared end cell equals cell 90 over 8 end cell row cell sigma squared end cell equals cell 45 over 4 end cell row sigma equals cell 3 over 2 square root of 5 end cell end table end style 

Jadi, jawaban yang tepat adalah A.

0

Roboguru

Tentukan simpangan rata-rata, ragam, dan simpangan baku dari data berikut ini! a. 4,6,7,8,9,10,12

Pembahasan Soal:

Ingat kembali:

-rumus rata-rata:

x=banyaknyadatajumlahdata

-simpangan rata-rata

simpanganratarata=nxix¯ 

-rumus ragam

ragam=n(xix¯)2

-simpangan baku

s=ragam

Pertama kita tentukan rata-rata dari data tersebut:

x===74+6+7+8+9+10+127568

Kemudian, kita tentukan simpangan rata-rata:

SR=====nxix¯748+68+78+88+98+108+12874+2+1+0+1+2+47142

Selanjutnya mennetukan ragam

ragam=====n(xix¯)27(48)2+(68)2+(78)2+(88)2+(98)2+(108)2+(128)2716+4+1+0+1+4+167426  

Selanjutnya, kita tenatukan simpangan baku:

s==ragam6

Dengan demikian, simpangan rata-rata, ragam, dan simpangan baku dari data tersebut masing-masing adalah 3,6dan6.

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Roboguru

Dari setiap data berikut, tentukan simpangan rata-rata, ragam dan simpangan baku.  4,5,3,6,7,5

Pembahasan Soal:

begin mathsize 14px style x with minus on top equals 1 over 6 cross times open parentheses 4 plus 5 plus 3 plus 6 plus 7 plus 5 close parentheses equals 5 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S R end cell equals cell fraction numerator open vertical bar 4 minus 5 close vertical bar plus open vertical bar 5 minus 5 close vertical bar plus open vertical bar 3 minus 5 close vertical bar plus open vertical bar 6 minus 5 close vertical bar plus open vertical bar 7 minus 5 close vertical bar plus open vertical bar 5 minus 5 close vertical bar over denominator 6 end fraction end cell row cell S R end cell equals cell 6 over 6 equals 1 end cell end table end style 

begin mathsize 14px style s squared equals fraction numerator open parentheses 4 minus 5 close parentheses squared plus open parentheses 5 minus 5 close parentheses squared plus open parentheses 3 minus 5 close parentheses squared plus open parentheses 6 minus 5 close parentheses squared plus open parentheses 7 minus 5 close parentheses squared plus open parentheses 5 minus 5 close parentheses squared over denominator 6 end fraction s squared equals 10 over 6 equals 1 , 67 end style 

begin mathsize 14px style s equals square root of 1 , 67 end root equals 1 , 291 end style 

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Roboguru

Simpangan baku dari data 5,4,6,6,8,7,6 adalah ...

Pembahasan Soal:

Rumus simpangan baku data tunggal yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank s 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 cell square root of fraction numerator begin display style sum from i equals 1 to n of space open parentheses x subscript i minus top enclose x close parentheses squared end style over denominator n end fraction end root end cell end table

Tentukan terlebih dahulu rata-rata data.

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose x end cell equals cell fraction numerator Jumlah space nilai over denominator Banyak space data end fraction end cell row blank equals cell fraction numerator 5 plus 4 plus 6 open parentheses 3 close parentheses plus 8 plus 7 over denominator 7 end fraction end cell row blank equals cell fraction numerator 9 plus 18 plus 15 over denominator 7 end fraction end cell row blank equals cell 42 over 7 end cell row blank equals 6 end table

Kemudian tentukan selisih data dengan nilai rata-rata.

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 end cell equals 5 row cell open parentheses x subscript 1 minus top enclose x close parentheses squared end cell equals cell open parentheses 5 minus 6 close parentheses squared end cell row blank equals cell open parentheses negative 1 close parentheses squared end cell row blank blank blank row cell x subscript 2 end cell equals 4 row cell open parentheses x subscript 2 minus top enclose x close parentheses squared end cell equals cell open parentheses 4 minus 6 close parentheses squared end cell row blank equals cell open parentheses negative 2 close parentheses squared end cell row blank blank blank row cell x subscript 3 end cell equals 6 row cell open parentheses x subscript 3 minus top enclose x close parentheses squared end cell equals cell open parentheses 6 minus 6 close parentheses squared end cell row blank equals cell open parentheses 0 close parentheses squared end cell row blank blank blank row cell x subscript 4 end cell equals 6 row cell open parentheses x subscript 4 minus top enclose x close parentheses squared end cell equals cell open parentheses 6 minus 6 close parentheses squared end cell row blank equals cell open parentheses 0 close parentheses squared end cell row blank blank blank row cell x subscript 5 end cell equals 8 row cell open parentheses x subscript 5 minus top enclose x close parentheses squared end cell equals cell open parentheses 8 minus 6 close parentheses squared end cell row blank equals cell open parentheses 2 close parentheses squared end cell row blank blank blank row cell x subscript 6 end cell equals 7 row cell open parentheses x subscript 6 minus top enclose x close parentheses squared end cell equals cell open parentheses 7 minus 6 close parentheses squared end cell row blank equals cell open parentheses 1 close parentheses squared end cell row blank blank blank row cell x subscript 7 end cell equals 6 row cell open parentheses x subscript 7 minus top enclose x close parentheses squared end cell equals cell open parentheses 6 minus 6 close parentheses squared end cell row blank equals cell open parentheses 0 close parentheses squared end cell end table

Sehingga diperoleh simpangan bakunya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row s equals cell square root of fraction numerator begin display style sum from i equals 1 to n of end style space open parentheses x subscript i minus top enclose x close parentheses squared over denominator n end fraction end root end cell row blank equals cell square root of fraction numerator begin display style sum from i equals 1 to 7 of space open parentheses x subscript i minus top enclose x close parentheses squared end style over denominator 7 end fraction end root end cell row blank equals cell square root of fraction numerator open parentheses negative 1 close parentheses squared plus open parentheses negative 2 close parentheses squared plus open parentheses 0 close parentheses squared plus open parentheses 0 close parentheses squared plus open parentheses 2 close parentheses squared plus open parentheses 1 close parentheses squared plus open parentheses 0 close parentheses squared over denominator 7 end fraction end root end cell row blank equals cell square root of fraction numerator 1 plus 4 plus 0 plus 0 plus 4 plus 1 plus 0 over denominator 7 end fraction end root end cell row blank equals cell square root of 10 over 7 end root end cell row blank equals cell fraction numerator square root of 10 over denominator square root of 7 end fraction cross times fraction numerator square root of 7 over denominator square root of 7 end fraction end cell row blank equals cell fraction numerator square root of 70 over denominator 7 end fraction end cell row blank equals cell 1 comma 19 end cell end table

Maka, simpangan baku dari data 5 comma space 4 comma space 6 comma space 6 comma space 8 comma space 7 comma space 6 adalah 1 comma 19.

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