The median of a set of 19 observations is 30. | vedclass

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(B) The original set has $19$ observations,so the median is the $10^{th}$ observation when arranged in ascending order.When two new observations $8$ a

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$30$

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(B) The original set has $19$ observations,so the median is the $10^{th}$ observation when arranged in ascending order.When two new observations $8$ and $32$ are added,the total number of observations becomes $21$.The new median will be the $\frac{21+1}{2} = 11^{th}$ observation.Since $8  30$,the original $10^{th}$ observation (which is $30$) remains the median of the new set because one smaller value is added to the left and one larger value is added to the right,shifting the position of the median by one index but keeping the value the same.

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

The median of a set of $19$ observations is $30$. If two observations with values $8$ and $32$ are added,what is the median of the new set of $21$ observations?

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