Pertanyaan

Berapakah standar deviasi pada sampel data di bawah ini?

$1, 77$
$1, 7$
$1, 66$
$1, 6$
$1, 78$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Ingat kembali konsep standar deviasi pada data tunggal: S = n − 1 ∑ i = 1 n ( x i − x ) 2 Ingat kembali nilai rata-rata atau mean pada data tunggal: x = n x 1 + x 2 + ... + x n -Menentukan nilai rata-rata x : x = = = = n x 1 + x 2 + ... + x n 7 15 + 16 + 14 + 15 + 14 + 12 + 11 7 97 13 , 9 -Menentukan i = 1 ∑ n ( x i − x ) 2 : ∑ i = 1 7 ( x i − x ) 2 = ( 15 − 13 , 9 ) 2 + ( 16 − 13 , 9 ) 2 + ( 14 − 13 , 9 ) 2 + ( 15 − 13 , 9 ) 2 + ( 14 − 13 , 9 ) 2 + ( 12 − 13 , 9 ) 2 + ( 11 − 13 , 9 ) 2 = ( 1 , 1 ) 2 + ( 2 , 1 ) 2 + ( 0 , 1 ) 2 + ( 1 , 1 ) 2 + ( 0 , 1 ) 2 + ( − 1 , 9 ) 2 + ( 2 , 9 ) 2 = 1 , 21 + 4 , 41 + 0 , 01 + 1 , 21 + 0 , 01 + 3 , 61 + 8 , 41 = 18 , 87 -Menentukan standar deviasi Oleh karena itu, jawaban yang benar adalah A.

Ingat kembali konsep standar deviasi pada data tunggal:

$S = \frac{\sum _{i = 1}^{n} ( x _{i} - x ) ^{2}}{n - 1}$

Ingat kembali nilai rata-rata atau mean pada data tunggal:

$\overline{x} = \frac{x _{1} + x _{2} + ... + x _{n}}{n}$

-Menentukan nilai rata-rata $\overline{x}$ :

$\overline{x} = = = = \frac{x _{1} + x _{2} + ... + x _{n}}{n} \frac{15 + 16 + 14 + 15 + 14 + 12 + 11}{7} \frac{97}{7} 13, 9$

-Menentukan $i = 1 \sum n (x_{i} - \overline{x})^{2}$ :

$\sum_{i = 1}^{7} (x_{i} - \overline{x})^{2} = (15 - 13, 9)^{2} + (16 - 13, 9)^{2} + (14 - 13, 9)^{2} + (15 - 13, 9)^{2} + (14 - 13, 9)^{2} + (12 - 13, 9)^{2} + (11 - 13, 9)^{2} = (1, 1)^{2} + (2, 1)^{2} + (0, 1)^{2} + (1, 1)^{2} + (0, 1)^{2} + (- 1, 9)^{2} + (2, 9)^{2} = 1, 21 + 4, 41 + 0, 01 + 1, 21 + 0, 01 + 3, 61 + 8, 41 = 18, 87$

-Menentukan standar deviasi

$table attributes columnalign right center left columnspacing 0px end attributes row straight S equals cell square root of fraction numerator sum from i equals 1 to 7 of space open parentheses x subscript i minus x with bar on top close parentheses squared over denominator n minus 1 end fraction end root end cell row blank equals cell square root of fraction numerator open parentheses x subscript 1 minus x with bar on top close parentheses squared plus open parentheses x subscript 2 minus x with bar on top close parentheses squared plus open parentheses x subscript 3 minus x with bar on top close parentheses squared plus... plus open parentheses x subscript 7 minus x with bar on top close parentheses squared over denominator 7 minus 1 end fraction end root end cell row blank equals cell square root of fraction numerator size 12px left parenthesis size 12px 15 size 12px minus size 12px 13 size 12px comma size 12px 9 size 12px right parenthesis to the power of size 12px 2 size 12px plus begin mathsize 12px style left parenthesis 16 minus 13 comma 9 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis 14 minus 13 comma 9 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis 15 minus 13 comma 9 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis 14 minus 13 comma 9 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis 12 minus 13 comma 9 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis 11 minus 13 comma 9 right parenthesis squared end style over denominator 6 end fraction end root end cell row blank equals cell square root of fraction numerator size 12px left parenthesis size 12px 1 size 12px comma size 12px 1 size 12px right parenthesis to the power of size 12px 2 size 12px plus begin mathsize 12px style left parenthesis 2 comma 1 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis 0 comma 1 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis 1 comma 1 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis 0 comma 1 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis negative 1 comma 9 right parenthesis squared end style size 12px plus begin mathsize 12px style left parenthesis 2 comma 9 right parenthesis squared end style over denominator 6 end fraction end root end cell row blank equals cell square root of fraction numerator size 12px 1 size 12px comma size 12px 21 size 12px plus size 12px 4 size 12px comma size 12px 41 size 12px plus size 12px 0 size 12px comma size 12px 01 size 12px plus size 12px 1 size 12px comma size 12px 21 size 12px plus size 12px 0 size 12px comma size 12px 01 size 12px plus size 12px 3 size 12px comma size 12px 61 size 12px plus size 12px 8 size 12px comma size 12px 41 over denominator 6 end fraction end root end cell row blank equals cell square root of fraction numerator 18 comma 87 over denominator 6 end fraction end root end cell row blank equals cell square root of 3 comma 145 end root end cell row blank equals cell 1 comma 77 end cell end table$

Oleh karena itu, jawaban yang benar adalah A.

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