Question

answer is ( 2 ) . 29/3

need explanation​

Answer 1

Mean of the 6 numbers,

$\longrightarrow\bar x=\dfrac{(x+1)+(x+2)+(x+3)+(x+7)+(x+8)+(x+9)}{6}$

$\longrightarrow\bar x=\dfrac{6x+30}{6}$

$\longrightarrow\bar x=x+5$

Square deviation of each term,

$\longrightarrow (x_1-\bar x)^2=((x+1)-(x+5))^2=16$

$\longrightarrow (x_2-\bar x)^2=((x+2)-(x+5))^2=9$

$\longrightarrow (x_3-\bar x)^2=((x+3)-(x+5))^2=4$

$\longrightarrow (x_4-\bar x)^2=((x+7)-(x+5))^2=4$

$\longrightarrow (x_5-\bar x)^2=((x+8)-(x+5))^2=9$

$\longrightarrow (x_6-\bar x)^2=((x+9)-(x+5))^2=16$

Then, variance,

$\longrightarrow \sigma^2=\dfrac{16+9+4+4+9+16}{6}$

$\longrightarrow\underline{\underline{\sigma^2=\dfrac{29}{3}}}$

Hence (2) is the answer.

Answer 2

Answer:

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