Median of distribution

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sgupta0827

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Why would median of a distribution is least likely to be equal to the third quintile if it is likely to be equal to the second quartile(4 groups) and fifth decile(10 groups). Could someone provide me an example explaining this? To me, all of them should be likely. In fact, I feel probability is more in case of third quintile(5 groups) due to odd number of groups and median is definitely be in the third quintile, unlike in other cases wherein it can be in two groups.
 
sgupta0827 Wrote:
——————————————————-
> Why would median of a distribution is least likely
> to be equal to the third quintile if it is likely
> to be equal to the second quartile(4 groups) and
> fifth decile(10 groups). Could someone provide me
> an example explaining this? To me, all of them
> should be likely. In fact, I feel probability is
> more in case of third quintile(5 groups) due to
> odd number of groups and median is definitely be
> in the third quintile, unlike in other cases
> wherein it can be in two groups.
Median, second quartile and fifth decile are all at 50%. Third quintile is 60%.
 
anish Wrote:
——————————————————-
> sgupta0827 Wrote:
> ————————————————–
> —–
> > Why would median of a distribution is least
> likely
> > to be equal to the third quintile if it is
> likely
> > to be equal to the second quartile(4 groups)
> and
> > fifth decile(10 groups). Could someone provide
> me
> > an example explaining this? To me, all of them
> > should be likely. In fact, I feel probability
> is
> > more in case of third quintile(5 groups) due to
> > odd number of groups and median is definitely
> be
> > in the third quintile, unlike in other cases
> > wherein it can be in two groups.
>
>
> Median, second quartile and fifth decile are all
> at 50%. Third quintile is 60%.
Please pardon my below average intellect, I would definitely need more information about this. Explanation given by you, I have already found in in notes and I was not able to understand this concept. That is the reason I posted it here.
 
Hi Sgupta,
Regarding your question and explanation, I think you may confuse about the Quantile and the Interval
Notice that Median, 2nd quartile, 3rd quintile, and 5th decile are points (not interval) that divided data into groups
Median is likely to be equal to the second quartile(4 groups) and fifth decile(10 groups) because they are the same POINT that cuts data set in half (50%)
Median is least likely to be equal to the third quintile, because 3rd quintile is the point that cuts data in (60% below and 40% above it)
You can also use the formula for the position of percentile in an array to prove it:
Ly= (n+1)*y/100
Where: y is the percentage point
Median = 2nd quartile = 5th decile = L50 = (n+1)*50/100
While: 3rd quintile = L60=(n+1)*60/100
 
the median is the middle number in a data set. ie half the data is above it, and half the data is below.
There are four quartiles, so the second quartile is the point at which half the data (ie two quartiles out of 4) is below, and half is above.
There are 10 deciles, so the fifth decile is the point at which half the data (ie five deciles out of 10) is below, and half is above.
there are five quintiles, so the third quintile is the point at which 60% of the data (ie three quintiles out of five) is below, and 40% is above.
See the difference?
Hope that helps….
 
Hai Hoang Wrote:
——————————————————-
> Hi Sgupta,
> Please read the below link which provides an
> example to explain mean, terciles, quartiles and
> so on, hope it can help
> http://www.metagora.org/training/encyclopedia/perc
> entile.html
Thanks Hoi Hoang for the link, the figure was really handy, now I will never forget the table :)
 
Kiakaha Wrote:
——————————————————-
> the median is the middle number in a data set. ie
> half the data is above it, and half the data is
> below.
>
> There are four quartiles, so the second quartile
> is the point at which half the data (ie two
> quartiles out of 4) is below, and half is above.
>
> There are 10 deciles, so the fifth decile is the
> point at which half the data (ie five deciles out
> of 10) is below, and half is above.
>
> there are five quintiles, so the third quintile is
> the point at which 60% of the data (ie three
> quintiles out of five) is below, and 40% is above.
>
>
> See the difference?
>
> Hope that helps….
After seeing the table everything makes sense..
 
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