Question: The third quartile and inter-quartile range of a data are 58 and 28 respectively. Find the coefficient of the quartile deviation.


Solution:
Given,

Third quartile ($Q_3$) = 58
Inter-quartile range = 28

To find: Coefficient of Quartile Deviation = ?

We know,

Inter-quartile range = $Q_3 - Q_1$

$or, 28 = 58 - Q_1$

$or, Q_1 = 58-28$

$\therefore, Q_1 = 30$

Now,

Coefficient of Quartile Deviation
$= \dfrac{Q_3 - Q_1}{Q_3 + Q_1}$

$= \dfrac{58-30}{58+30}$

$= \dfrac{28}{88}$

$= 0.318$

$= 0.32$

Hence, the coefficient of quartile deviation of the above data is 0.32.

Related Notes and Solutions:

Here is the website link to the notes of Statistics of Class 10.

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