Question: In a day, quartile deviation and the first quartile are 20 and 35 respectively. Find its third quartile and the coefficient of quartile deviation.

Solution:
Given,

Quartile Deviation (Q.D.) = 20
First Quartile ($Q_1$) = 35

To find: Third Quartile ($Q_3$) = ?

We know,

$Q.D. = \dfrac{Q_3 - Q_1}{2}$

$or, 20 = \dfrac{Q_3 - 35}{2}$

$or, 20 × 2 = Q_3 - 35$

$or, Q_3 - 35 = 40$

$or, Q_3 = 40+35$

$\therefore Q_3 = 75$

And,

$Coefficient of Q.D. = \dfrac{Q_3 - Q_1}{Q_3 + Q_1}$

$= \dfrac{75 - 35}{75+35}$

$= \dfrac{40}{110}$

$= 0.36$

Hence, the third quartile of the above data is 75 and the coefficient of quartile deviation is 0.36.

Related Notes and Solutions:

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

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