Question: The third quartile of a data is 15. If the coefficient of quartile deviation is 1/4, find the first quartile and the inter-quartile range of the data.


Solution:
Given,

Third quartile ($Q_3$) = 15
Coefficient of Quartile Deviation = $\frac{1}{4}$

To find: First Quartile = ? And Inter-quartile range= ?

We know,

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

$or, \dfrac{1}{4} = \dfrac{15 -Q_1}{15+Q_1}$

$or, 1(15 + Q_1) = 4(15 - Q_1)$

$or, 15 + Q_1 = 60 - 4Q_1$

$or, 4Q_1 + Q_1 = 60-15$

$or, 5 Q_1 = 45$

$or, Q_1 = \dfrac{45}{5}$

$\therefore Q_1 = 9$

Now,

Inter-quartile range of data = $Q_3 - Q_1$

$= 15 - 9$

$= 6$

Hence, the first quartile of the above data is 9 and the coefficient of quartile deviation is 6.

Related Notes and Solutions:

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

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