For the following frequency distribution find: (i) Lower quartile… - Vidyadip

Question

For the following frequency distribution find:
(i) Lower quartile
(ii) Upper quartile
(iii) Inter quartile range
(iv) Semi-inter quartile range.

$x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$y$	$3$	$5$	$9$	$15$	$20$	$16$	$10$	$2$

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Answer

(i) Lower quartile
($Q_1$) = The value of $\left(\frac{ n }{4}\right)^{\text {th }}$ observation
$=$ The value of (804)th observation
$=$ The value of $20^{\text {th }}$ observation $Q _1=4$.
(ii) Upper quartile
$\left(Q_3\right)=$ The value of $(3 n 4)$ th observation
$=$ The value of $(3 \times 804)$ th observation
$=$ The value of $60^{\text {th }}$ observation
$\therefore Q_3 = 6.$
(iii) Inter quartile range
$= Q_3 - Q_1$
$= 6 - 4$
$= 2.$
(iv) Semi-quartile range
$=\frac{Q_3-Q_1}{2}$
$=\frac{2}{2}$
$= 1.s$

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