The median of a set of 9 distinct observation | vedclass

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(D) Given that the number of observations $n = 9$.The median of $9$ observations is the $\left( \frac{9+1}{2} \right)^{th} = 5^{th}$ observation.Let t

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Remains the same as that of the original set

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(D) Given that the number of observations $n = 9$.The median of $9$ observations is the $\left( \frac{9+1}{2} \right)^{th} = 5^{th}$ observation.Let the ordered observations be $x_1 The median is $x_5 = 20.5$.If the largest $4$ observations $(x_6, x_7, x_8, x_9)$ are increased by $2$,the new set of observations is $x_1, x_2, x_3, x_4, x_5, (x_6+2), (x_7+2), (x_8+2), (x_9+2)$.Since $x_5$ is smaller than $x_6$,and $x_6 Therefore,the $5^{th}$ observation remains $x_5$,which is $20.5$.Thus,the median remains the same as that of the original set.

Marks	$2$	$3$	$5$	$7$
Frequency	$(x+1)^2$	$2x-5$	$x^2-3x$	$x$

The median of a set of $9$ distinct observations is $20.5$. If each of the largest $4$ observations of the set is increased by $2$,then the median of the new set:

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