The median of a set of 9 distinct observation | vedclass

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(A) Step-$1$: Identify the median position.For $n = 9$ observations (where $n$ is odd),the median is the $\frac{n+1}{2}^{	ext{th}}$ term.Median $= \f

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Remains the same as the original set

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(A) Step-$1$: Identify the median position.For $n = 9$ observations (where $n$ is odd),the median is the $\frac{n+1}{2}^{	ext{th}}$ term.Median $= \frac{9+1}{2} = 5^{	ext{th}}$ term.Step-$2$: Analyze the effect of the change.The four largest observations are the $6^{	ext{th}}, 7^{	ext{th}}, 8^{	ext{th}}$,and $9^{	ext{th}}$ terms.Since these terms are greater than the $5^{	ext{th}}$ term,increasing them by $2$ does not change the value or the position of the $5^{	ext{th}}$ term.Step-$3$: Conclusion.As the $5^{	ext{th}}$ term remains unchanged,the median of the new set remains the same as the original median,which is $20.5$.

$x_i$	$3$	$6$	$9$	$12$
$f_i$	$1$	$2$	$3$	$4$

The median of a set of $9$ distinct observations is $20.5$. If the four largest observations of the set are increased by $2$,what will be the median of the new set?

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