The mean and variance of seven observations a | vedclass

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Question

Let $7$ observation be ${x_1},{x_2},{x_3},{x_4},{x_5},{x_6},{x_7}$

$\bar x = 8 \Rightarrow \sum\limits_{i = 1}^7 {{x_i}}  = 56\,\,\,\,\,\

Vedclass · Accepted Answer

$48$

Vedclass · Answer

Let $7$ observation be ${x_1},{x_2},{x_3},{x_4},{x_5},{x_6},{x_7}$

$\bar x = 8 \Rightarrow \sum\limits_{i = 1}^7 {{x_i}}  = 56\,\,\,\,\,\,.......\left( 1 ight)$

Also ${\sigma ^2} = 16$

$ \Rightarrow 16 = \frac{1}{7}\left( {\sum\limits_{i = 1}^7 {x_i^2} } ight) - {\left( {\bar x} ight)^2}$

$ \Rightarrow 16 = \frac{1}{7}\left( {\sum\limits_{i = 1}^7 {x_i^2} } ight) - 64$

$ \Rightarrow \left( {\sum\limits_{i = 1}^7 {x_i^2} } ight) = 560\,\,\,\,\,\,\,\,\,.......\left( 2 ight)$

Now, ${x_1} = 2,{x_2} = 4,{x_3} = 10,{x_4} = 12,{x_5} = 14$

$ \Rightarrow {x_6} + {x_7} = 14$ (from $(1)$) and $x_6^2 + x_7^2 = 100$ (from$(2)$)

$	herefore x_6^2 + x_7^2 = {\left( {{x_6} + {x_7}} ight)^2} - 2{x_6}{x_7} \Rightarrow {x_6}{x_7} = 48$

class	$0-10$	$10-20$	$20-30$	$30-40$
Freq	$1$	$3$	$4$	$2$

The mean and variance of seven observations are $8$ and $16$, respectively. If $5$ of the observations are $2, 4, 10, 12, 14,$ then the product of the remaining two observations is

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class $0-10$ $10-20$ $20-30$ $30-40$

Freq $1$ $3$ $4$ $2$

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