Jawaban:

Simpangan rata-rata dari data 8, 10, 7, 10, 7, 5, 8, 6, 10, 9 adalah 1,4

Rata-rata

\begin{gathered}\overline {x} = \frac{x_1~+~ x_2~ +~ x_3~ +~ ...~ +~ x_n}{n} \\ \overline {x} = \frac{\sum x_{i} }{n}\end{gathered}

x

=

n

x

1

+ x

2

+ x

3

+ ... + x

n

x

=

n

∑x

i

Simpangan rata-rata atau deviasi rata-rata (mean devation) merupakan selisih tiap datum terhadap mean (rata-rata).

\begin{gathered}SR = \frac{|x_1~ -~\overline {x}|~ +~ |x_2~ -~ \overline {x}|~ +~ |x_3~ -~ \overline {x}|~ +~ ...~ +~ |x_n~ -~ \overline {x}|}{n} \\ SR = \frac{\sum | x_{i} ~-~\overline {x}|}{n}\end{gathered}

SR=

n

∣x

1

−

x

∣ + ∣x

2

−

x

∣ + ∣x

3

−

x

∣ + ... + ∣x

n

−

x

∣

SR=

n

∑∣x

i

−

x

∣

Dalam hal ini, \overline {x}

x

adalah mean dan lambang |x - \overline {x}

x

| menyatakan harga mutlak dari x_{i} ~ - ~\overline {x}x

i

−

x

, yg membuat | x_{i} ~ - ~\overline {x}x

i

−

x

| selalu positif.

Pembahasan

Diketahui :

data 8, 10, 7, 10, 7, 5, 8, 6, 10, 9

n = 10

Ditanya :

simpangan rata-rata ?

Jawab :

Rata-rata

\begin{gathered}\overline {x} = \frac{x_1~+~ x_2~ +~ x_3~ +~ ...~ +~ x_n}{n} \\ \overline {x} = \frac{8~+ ~10~ +~ 7~ + ~10~+ ~7~ + ~5~ + ~8~ + ~6~ + ~10~ + ~9}{10} \\ \overline {x} = \frac{80}{10} \\ \overline {x} = 8\end{gathered}

x

=

n

x

1

+ x

2

+ x

3

+ ... + x

n

x

=

10

8 + 10 + 7 + 10 + 7 + 5 + 8 + 6 + 10 + 9

x

=

10

80

x

=8

Simpangan rata-rata

\begin{gathered}SR = \frac{|x_1~ -~ \overline {x}|~ +~ |x_2~ -~ \overline {x}|~ +~ |x_3~ -~ \overline {x}|~ +~ ...~ +~ |x_n~ -~ \overline {x}|}{n} \\ SR = \frac{|8 - 8| + |10 - 8| +|7 - 8|+ |10 - 8|+ |7 - 8| + |5 - 8| + |8 - 8| + |6 - 8| + |10 - 8| + |9 - 8|}{10} \\ SR = \frac{|0|~ + ~|2|~ +~ |-1|~ +~ |2| ~+ |-1| ~+ |-3|~+ ~|0|~ + ~|-2|~ + ~|2|~ + ~|1|}{10} \\ SR = \frac{0~ +~ 2~ +~ 1~+ ~2~ +~1~ + ~3~ + ~0~ + ~2~ + ~2~ + ~1 }{10} \\ SR = \frac{14}{10} \\ SR = 1,4\end{gathered}

SR=

n

∣x

1

−

x

∣ + ∣x

2

−

x

∣ + ∣x

3

−

x

∣ + ... + ∣x

n

−

x

∣

SR=

10

∣8−8∣+∣10− 8∣+∣7 −8∣+∣10−8∣+∣7−8∣+∣5−8∣+∣8−8∣+∣6−8∣+∣10−8∣+∣9−8∣

SR=

10

∣0∣ + ∣2∣ + ∣−1∣ + ∣2∣ +∣−1∣ +∣−3∣ + ∣0∣ + ∣−2∣ + ∣2∣ + ∣1∣

SR=

10

0 + 2 + 1 + 2 + 1 + 3 + 0 + 2 + 2 + 1

SR=

10

14

SR=1,4

Jadi simpangan rata-rata dari data 8, 10, 7, 10, 7, 5, 8, 6, 10, 9 adalah 1,4

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