The median of a set of 13 observations which | vedclass

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(D) For a set of $13$ observations arranged in decreasing order,the median is the $7^{th}$ observation.Let the observations be $x_1 \ge x_2 \ge \dots

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remains unchanged

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(D) For a set of $13$ observations arranged in decreasing order,the median is the $7^{th}$ observation.Let the observations be $x_1 \ge x_2 \ge \dots \ge x_7 \ge \dots \ge x_{13}$.The median is $x_7 = 18.6$.When the first two observations $(x_1, x_2)$ are increased and the last three observations $(x_{11}, x_{12}, x_{13})$ are decreased,the relative order of the $7^{th}$ observation remains unaffected because the changes occur at the extreme ends of the sorted list.Since the $7^{th}$ observation remains the same,the median remains unchanged.

Class	Frequency
$10-20$	$180$
$20-30$	$82$
$30-40$	$34$
$40-50$	$180$
$50-60$	$136$
$60-70$	$23$
$70-80$	$50$

$x_i$	$5$	$15$	$25$	$35$	$45$	$55$
$f_i$	$12$	$18$	$27$	$20$	$17$	$6$

The median of a set of $13$ observations which are in decreasing order is $18.6$. If the first two observations are increased by $1$ and the last three observations are decreased by $5$,then the median of the set of new observations is-

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Find the median for the following distribution:
Class Frequency
$10-20$ $180$
$20-30$ $82$
$30-40$ $34$
$40-50$ $180$
$50-60$ $136$
$60-70$ $23$
$70-80$ $50$

Find the mean of the following frequency distribution:

$x_i$ $5$ $15$ $25$ $35$ $45$ $55$

$f_i$ $12$ $18$ $27$ $20$ $17$ $6$

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