Question

In a data, quartile deviation and its coefficient and 15 and 3/7 respectively. Find the first quartile.​

Answer 1

In a data, the quartile deviation and its coefficient are 15 and 3/7 respectively. Find the first quartile. To find: First Quartile ($Q_1$) = ? Hence, the first quartile of the above data is 20.

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Answer 2

Solution:

Given,

Quartile Deviation (Q.D.) = 15

Coefficient of Q.D. = $\frac{3}{7}$

To find: First Quartile ($Q_1$) = ?

We know,

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

$or, 15 = \dfrac{Q_3 - Q_1}{2}$

$or, 15 × 2 = Q_3 - Q_1$

$or, Q_3 = 30 + Q_1$ - (i)

Also,

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

$or, \dfrac{3}{7} = \dfrac{Q_3 - Q_1}{Q_3 + Q_1}$

$or, 3(Q_3 + Q_1) = 7(Q_3 - Q_1)$

[ Put $Q_3$ = 30 + $Q_1$ from (i) ]

$or, 3(30 + Q_1 + Q_1) = 7(30+ Q_1 - Q_1)$

$or, 3(30+2Q_1) = 7×30$

$or, 90 + 6Q_1 = 210$

$or, 6Q_1 = 210-90$

$or, 6Q_1 = 120$

$or, Q_1 = \dfrac{120}{6}$

$\therefore Q_1 = 20$

Hence, the first quartile of the above data is 20.

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