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13. statistics — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS13. statistics1 Mark
MCQ
Let $9 < x_1 < x_2 < \ldots < x_7$ be in an $A.P.$ with common difference $d$. If the standard deviation of $x_1, x_2 \ldots$, $x _7$ is $4$ and the mean is $\overline{ x }$, then $\overline{ x }+ x _6$ is equal to:
  • A
    $18\left(1+\frac{1}{\sqrt{3}}\right)$
  • ✓
    $34$
  • C
    $2\left(9+\frac{8}{\sqrt{7}}\right)$
  • D
    $25$
✓

Answer

Correct option: B.
$34$
b
$9=x_1 < x_2 < \ldots \ldots < x_7$

$9,9+d, 9+2 d, \ldots \ldots .9+6 d$

$0, d, 2 d, \ldots \ldots \cdot 6$

$\bar{x}_{\text {new }}=\frac{21 d }{7}=3 d$

$16=\frac{1}{7}\left(0^2+1^2+\ldots \ldots+6^2\right) d^2-9 d^2$

$=\frac{1}{7}\left(\frac{6 \times 7 \times 13}{6}\right) d ^2-9 d ^2$

$16=4 d^2$

$d^2=4$

$d=2$

$\bar{x}+x_6=6+9+10+9$

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