Tentukan simpangan rata-rata, ragam, dan simpangan baku dari data berikut ini! c. 9,3,8,8,9,8,9,18

Pertanyaan

Tentukan simpangan rata-rata, ragam, dan simpangan baku dari data berikut ini!

c. 9,3,8,8,9,8,9,18 $\;$

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

simpangan rata-rata, ragam, dan simpangan baku dari data tersebut masing-masing adalah $2,25,\;15\;\mathrm{dan}\;3,87$ .

Pembahasan

Ingat kembali:

-rumus rata-rata:

$x with bar on top equals fraction numerator jumlah space data over denominator banyaknya space data end fraction$

-simpangan rata-rata

$simpangan space rata minus rata equals fraction numerator begin display style sum from blank to blank of vertical line x subscript i italic minus x with italic bar on top vertical line end style over denominator n end fraction$

-rumus ragam

$ragam equals fraction numerator begin display style sum from blank to blank of end style left parenthesis x subscript i italic minus x with italic bar on top right parenthesis squared over denominator straight n end fraction$

-simpangan baku

$s=\sqrt{\mathrm{ragam}}$

Pertama kita tentukan rata-rata dari data tersebut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell x with bar on top end cell equals cell fraction numerator 9 plus 3 plus 8 plus 8 plus 9 plus 8 plus 9 plus 18 over denominator 8 end fraction end cell row blank equals cell 72 over 8 end cell row blank equals 9 end table$

Kemudian, kita tentukan simpangan rata-rata:

$table attributes columnalign right center left columnspacing 0px end attributes row SR equals cell fraction numerator begin display style sum from blank to blank of vertical line x subscript i italic minus x with italic bar on top vertical line end style over denominator n end fraction end cell row blank equals cell fraction numerator vertical line 9 minus 9 vertical line plus vertical line 3 minus 9 vertical line plus vertical line 8 minus 9 vertical line plus vertical line 8 minus 9 vertical line plus vertical line 9 minus 9 vertical line plus vertical line 8 minus 9 vertical line plus vertical line 9 minus 9 vertical line plus vertical line 18 minus 9 vertical line over denominator 8 end fraction end cell row blank equals cell 18 over 8 end cell row blank equals cell 2 comma 25 end cell row blank blank blank end table$

Selanjutnya mennetukan ragam

$table attributes columnalign right center left columnspacing 0px end attributes row SR equals cell fraction numerator begin display style sum from blank to blank of begin italic style left parenthesis x subscript i minus x with bar on top right parenthesis end style squared end style over denominator n end fraction end cell row blank equals cell fraction numerator open parentheses 9 minus 9 close parentheses squared plus open parentheses 3 minus 9 close parentheses squared plus open parentheses 8 minus 9 close parentheses squared plus open parentheses 8 minus 9 close parentheses squared plus open parentheses 9 minus 9 close parentheses squared plus open parentheses 8 minus 9 close parentheses squared plus open parentheses 9 minus 9 close parentheses squared plus open parentheses 18 minus 9 close parentheses squared over denominator 8 end fraction end cell row blank equals cell 120 over 8 end cell row blank equals 15 end table$

Selanjutnya, kita tenatukan simpangan baku:

$\begin{array}{rcl}s&=&\sqrt{\mathrm{ragam}}\\&=&\sqrt{15}\\&=&3,87\end{array}$

Dengan demikian, simpangan rata-rata, ragam, dan simpangan baku dari data tersebut masing-masing adalah $2,25,\;15\;\mathrm{dan}\;3,87$ .

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