Question: In a data, the first quartile is 35 and the third quartile is 75. Find the quartile deviation and its coefficient.

Solution:
Given,

First quartile ($Q_1$) = 35
Third quartile ($Q_3$) = 75

Now,

Quartile Deviation (Q.D.) = $\dfrac{Q_3 - Q_1}{2}$

$= \dfrac{75-35}{2}$

$= \dfrac{40}{2}$

$= 20

And,

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

$= \dfrac{75-35}{75+45}$

$= \dfrac{40}{110}$

$= 0.36$

Hence, the quartile deviation of the above data is 40 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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