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Simpangan baku data  adalah

Pertanyaan

Simpangan baku data begin mathsize 14px style 50 comma 50 comma 60 comma 60 comma 70 comma 70 end style adalah .... space 

  1. begin mathsize 14px style 10 over 3 square root of 6 end style 

  2. size 14px 8 over size 14px 3 square root of size 14px 6 

  3. size 14px 10 over size 14px 3 square root of size 14px 3 

  4. size 14px 7 over size 14px 3 square root of size 14px 6 

  5. size 14px 8 over size 14px 3 square root of size 14px 3 

Pembahasan Video:

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose straight x end cell equals cell fraction numerator 50 plus 50 plus 60 plus 60 plus 70 plus 70 over denominator 6 end fraction end cell row blank equals cell 360 over 6 end cell row blank equals 60 end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell begin inline style sum for blank of end style open parentheses straight x subscript i minus top enclose straight x close parentheses squared end cell equals cell 2 left parenthesis 50 minus 60 right parenthesis squared plus 2 left parenthesis 60 minus 60 right parenthesis squared plus 2 left parenthesis 70 minus 60 right parenthesis squared space end cell row blank equals cell 2 cross times left parenthesis negative 10 right parenthesis squared plus 2 cross times 0 squared plus 2 cross times 10 squared end cell row blank equals cell 200 plus 0 plus 200 end cell row blank equals 400 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 1 over n begin inline style sum for blank of end style open parentheses x subscript i minus top enclose x close parentheses squared end root end cell row blank equals cell square root of 1 over 6 cross times 400 end root end cell row blank equals cell fraction numerator 20 over denominator square root of 6 end fraction end cell row blank equals cell fraction numerator 20 cross times square root of 6 over denominator square root of 6 cross times square root of 6 end fraction end cell row blank equals cell 20 over 6 square root of 6 end cell row blank equals cell 10 over 3 square root of 6 end cell end table end style 

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

D. Entry

Terakhir diupdate 07 Juni 2021

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Pertanyaan yang serupa

Simpangan baku dari data : adalah ...

Pembahasan Soal:

Nilai rata-rata data :

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

Simpangan baku :

table attributes columnalign right center left columnspacing 0px end attributes row S equals cell square root of fraction numerator sum for blank of open parentheses x minus x with bar on top close parentheses squared over denominator sum for blank of f end fraction end root end cell row blank equals cell square root of fraction numerator open curly brackets open parentheses 4 minus 5 close parentheses squared plus open parentheses 6 minus 5 close parentheses squared plus open parentheses 4 minus 5 close parentheses squared plus open parentheses 6 minus 5 close parentheses squared plus open parentheses 5 minus 5 close parentheses squared plus open parentheses 2 minus 5 close parentheses squared plus open parentheses 1 minus 5 close parentheses squared plus open parentheses 9 minus 5 close parentheses squared plus open parentheses 8 minus 5 close parentheses squared close curly brackets over denominator 9 end fraction end root end cell row blank equals cell square root of fraction numerator open curly brackets 1 plus 1 plus 1 plus 1 plus 0 plus 9 plus 16 plus 16 plus 9 close curly brackets over denominator 9 end fraction end root end cell row blank equals cell square root of 54 over 9 end root end cell row blank equals cell square root of 6 end cell end table

Maka, simpangan bakunya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 6 end cell end table

Oleh karena itu, jawaban yang benar adalah E

Roboguru

Simpangan baku dari data  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.

Roboguru

Simpangan baku dari data 4, 6, 7, 8, 6, 9, 8, 8 adalah...

Pembahasan Soal:

Simpangan baku ditentukan oleh rumus :

S equals square root of fraction numerator begin display style sum from i equals 1 to n of end style open parentheses x subscript i minus top enclose x close parentheses squared over denominator n end fraction end root

Pertama tentukan rata-rata open parentheses top enclose x close parentheses dari data tersebut, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose x end cell equals cell fraction numerator 4 plus 6 plus 7 plus 8 plus 6 plus 9 plus 8 plus 8 over denominator 8 end fraction end cell row blank equals 7 end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row S equals cell square root of fraction numerator open parentheses 4 minus 7 close parentheses squared plus open parentheses 6 minus 7 close parentheses squared plus open parentheses 7 minus 7 close parentheses squared plus open parentheses 8 minus 7 close parentheses squared plus... plus left parenthesis 8 minus 8 right parenthesis squared over denominator 8 end fraction end root end cell row blank equals cell square root of fraction numerator 9 plus 1 plus 0 plus 1 plus 1 plus 4 plus 1 plus 1 over denominator 8 end fraction end root end cell row blank equals cell square root of 9 over 4 end root end cell row blank equals cell 3 over 2 equals 1 comma 5 end cell end table

Jadi, jawaban yang tepat adalah D.

Roboguru

Diketahui data 6, 6, 5, 8, 7, 4, 5, 9, 3, 7, maka nilai simpangan bakunya adalah ....

Pembahasan Soal:

Menentukan nilai rata-rata

equals fraction numerator 6 plus 6 plus 5 plus 8 plus 7 plus 4 plus 5 plus 9 plus 3 plus 7 over denominator 10 end fraction equals 60 over 10 equals 6 

Menentukan nilai left parenthesis x subscript i minus top enclose x right parenthesis squared menggunakan tabel berikut

Menentukan simpangan baku

table attributes columnalign right center left columnspacing 0px end attributes row sigma equals cell square root of 1 over n begin inline style sum from i equals 1 to n of end style left parenthesis x subscript i minus top enclose x right parenthesis squared end root end cell row blank equals cell square root of 1 over 10 cross times 30 end root end cell row blank equals cell square root of 3 end cell end table 

Jadi, simpangan baku dari data tersebut adalah square root of 3.

Roboguru

Simpangan baku dari data: 6, 6, 5, 4, 4 adalah ...

Pembahasan Soal:

Diketahui data:

6 comma space 6 comma space 5 comma space 4 comma space 4

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose x end cell equals cell fraction numerator 6 plus 6 plus 5 plus 4 plus 4 over denominator 5 end fraction end cell row blank equals cell 25 over 5 end cell row blank equals 5 end table

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row S equals cell fraction numerator begin display style sum for blank of end style left parenthesis x subscript i minus top enclose x right parenthesis squared over denominator n end fraction end cell row blank equals cell fraction numerator left parenthesis 6 minus 5 right parenthesis squared plus left parenthesis 6 minus 5 right parenthesis squared plus left parenthesis 5 minus 5 right parenthesis squared plus left parenthesis 4 minus 5 right parenthesis squared plus left parenthesis 4 minus 5 right parenthesis squared over denominator 5 end fraction end cell row blank equals cell fraction numerator 1 squared plus 1 squared plus 0 squared plus left parenthesis negative 1 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared over denominator 5 end fraction end cell row blank equals cell 4 over 5 end cell end table 

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row S equals cell square root of S squared end root end cell row blank equals cell square root of 4 over 5 end root end cell row blank equals cell fraction numerator square root of 4 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell 2 over 5 square root of 5 end cell end table

Jadi, jawaban yang tepat adalah B

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