The mean and variance of the data 4, 5,6,6,7,8, x, y where x < y … - Vidyadip

MCQ

The mean and variance of the data $4, 5,6,6,7,8, x$, $y$ where $x < y$ are $6$ , and $\frac{9}{4}$ respectively. Then $x^{4}+y^{2}$ is equal to

A
$162$
✓
$320$
C
$674$
D
$420$

✓

Answer

Correct option: B.

$320$

b
mean $\bar{x}=\frac{4+5+6+6+7+8+x+y}{8}=6$

$\Rightarrow x+y=48-36=12$

Variance

$=\frac{1}{8}\left(16+25+36+36+49+64+x^{2}+y^{2}\right)-36=\frac{9}{4}$

$\Rightarrow x^{2}+y^{2}=80$

$\therefore x=4 ; y=8$

$x^{4}+y^{2}=256+64=320$

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