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13. statistics — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS13. statistics1 Mark
MCQ
In a series of $3n$ observations, if $n$ observations are equal $a$ and remaining observations are equal $-2a$, then the mean deviation of observations about their mean will be:-
  • A
    $0$
  • B
    $\frac{a}{3}$
  • ✓
    $\frac{4a}{3}$
  • D
    $4a$
✓

Answer

Correct option: C.
$\frac{4a}{3}$
c
Here, given observatios are $a, a$ $\ldots \ldots$ $n$ times, $-$ $2 a,-2 a \ldots 2 n$ times

No. of observations $=3 \mathrm{n}$

mean $(\bar X) = \frac{{n \times a + 2n \times ( - 2a)}}{{3n}} =  - a$

$\therefore $ Mean deviation about mean $ = \frac{{\Sigma \left| {{{\rm{x}}_1} - {\rm{\bar x}}} \right|}}{{3{\rm{n}}}}$

$\frac{\mathrm{n} \times 2 \mathrm{a}+2 \mathrm{n} \times \mathrm{a}}{3 \mathrm{n}}=\frac{4 \mathrm{a}}{3}$

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