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13. statistics — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS13. statistics1 Mark
MCQ
If a variable takes the discrete values $\alpha - 4,\,\alpha - \frac{7}{2},\,\alpha - \frac{5}{2},\,\alpha - 3,\,\alpha - 2,\,\alpha + \frac{1}{2},\,\alpha - \frac{1}{2},\,\alpha + 5\,(\alpha > 0)$, then the median is
  • ✓
    $\alpha - \frac{5}{4}$
  • B
    $\alpha - \frac{1}{2}$
  • C
    $\alpha - 2$
  • D
    $\alpha + \frac{5}{4}$
✓

Answer

Correct option: A.
$\alpha - \frac{5}{4}$
a
(a) Arrange the data as

$\alpha - \frac{7}{2},\alpha - 3,\alpha - \frac{5}{2},\alpha - 2,\alpha - \frac{1}{2},\alpha + \frac{1}{2},\alpha + 4,\alpha + 5$

Median $ = \frac{1}{2}[{\rm{value\ of\ }}{{\rm{4}}^{{\rm{th}}}}{\rm{\ item}} + {\rm{value \ of\ }}{{\rm{5}}^{{\rm{th}}}}{\rm{\ item]}}$

Median $ = \frac{{\alpha - 2 + \alpha - \frac{1}{2}}}{2}$

$ = \frac{{2\alpha - \frac{5}{2}}}{2}$= $\alpha - \frac{5}{4}$.

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