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13. statistics — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS13. statistics1 Mark
MCQ
Let $a, b \in R$. Let the mean and the variance of $6$ observations $-3,4,7,-6$, $a,\ b$ be $2$ and $23$ , respectively. The mean deviation about the mean of these $6$ observations is :
  • ✓
    $\frac{13}{3}$
  • B
    $\frac{16}{3}$
  • C
    $\frac{11}{3}$
  • D
    $\frac{14}{3}$
✓

Answer

Correct option: A.
$\frac{13}{3}$
a
$ \frac{\sum x_i}{6}=2 \text { and } \frac{\sum x_i^2}{N}-\mu^2=23 $

$ \alpha+\beta=10 $

$ \alpha^2+\beta^2=52$

solving we get $\alpha=4, \beta=6$

$\frac{\sum\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{6}=\frac{5+2+5+8+2+4}{6}=\frac{13}{3}$

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