If the quartile deviation of a set of observations is $10$ and the third quartile is $35$ , then the first quartile is :

24

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30

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17

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15

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Solution

The correct option is D $15$
Quartile Deviation ( $Q_{D}$ ) means the semi variation between the upper quartile or third quartile ( $Q_{3}$ ) and lower quartile or first quartile ( $Q_{1}$ ) in a distribution.
Formula = $Q_{D} = \frac{Q_{3} - Q_{1}}{2}$
Given, $Q_{D}$ $= 10$ and $Q_{3}$ $= 35$
$10 = \frac{35 - Q_{1}}{2}$
$Q_{1}$ $= 15$

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