The median of a set of 9 distinct observation | vedclass

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(D) Let the $9$ distinct observations in ascending order be $x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9$.Since the number of observations $n = 9$ is

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remains the same as that of the original set

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(D) Let the $9$ distinct observations in ascending order be $x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9$.Since the number of observations $n = 9$ is odd,the median is the $\left(\frac{n+1}{2}\right)^{th}$ observation,which is the $5^{th}$ observation,$x_5$.Given,$x_5 = 20.5$.When the largest $4$ observations $(x_6, x_7, x_8, x_9)$ are increased by $2$,the order of the observations remains unchanged because $x_5 The new set of observations is $x_1, x_2, x_3, x_4, x_5, x_6+2, x_7+2, x_8+2, x_9+2$.The median of the new set is still the $5^{th}$ observation,which is $x_5 = 20.5$.Thus,the median remains the same.

Column-$I$	Column-$II$
$(A)$ Blue-green algae	$(i)$ Spirogyra
$(B)$ Unicellular algae	$(ii)$ Nostoc
$(C)$ Filamentous algae	$(iii)$ Volvox
$(D)$ Colonial algae	$(iv)$ Chlamydomonas

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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