Qbank id 1745 mistake? following, question, solution, believe, mistake

lunarfollies

Hello Guys
I believe there is a mistake in question id 1745.
Problem: What are the median and the third quintile of the following data points?
9.2% 10.1% 11.5% 11.9% 12.2% 12.8% 13.1% 13.6% 13.9% 14.2% 14.8% 14.9% 15.4%
Qbank solution is 13.1% median and third quintile is 13.7%
Qbank interpolation is: 0.136 + (o.4)(0.1390.136)= o.1372 =>13.7%
My solution is: 0.136 + (0.6 due to third quintile)(0.1390.136) = 0.1378 =13.8%, but not given as one of the solution options.
third quintile is 0.6.

Feedback welcomed

dcfox83

I would have thought it to be 13.7 as well. Arriving this way:
(n+1)(3/5) = (13+1)*3/5 = 8.4
8th is .136
0.4th is (0.4)(0.1390.136)
I think you are trying to use 0.6 directly in the linear interpolation.

eoin

For finding the solution, You are rite, median is 13.1%.
Now,
For finding quintile,
it is Ly= ((n+1)*y)/100;
so here y=75%.
It is coming out as 10.6
so it will be,
14.2+ 0.6*(14.814.2)=14.56.
So third quantile will be 14.56.

Iginla2011

Yes no doubt…but why are you using 0.4 in the interpolation instead 0.6?
I used 0.6 because 3/5 = 0.6
How are you getting 0.4 to calculate L?

former

Prasenjith your way is right, but y = 60% in this question and not 75% ;) But you used just like I did 0.6 as y. y =0.6
Thanks for all the replies

Houjichasan

I am using 0.4 because I arrived at 8.4 ; that is the 0.4 fractions from the 8th to 9th element.
When calculating 8.4, you have already used the 3/5 logic.

FVPV

Yes Guys, I did a mistake….I thought it to be 1/4 th part….I have not seen as quintile…sorry…it will be 60%( 100*3/5)…
And then ratio will be
Ly= (14*(60))/100
=8.4( hope I pressed calculator accurately)
In that case it will be
=13.6+0.4(13.913.6)
=13.72 (hope I pressed calculator accurately
Thanks a lot

d2rockstar

Ok thank you very much you both. I understand it now. the 0.4 is taken from the 8.4 and used for the interpolation and not the 60% ;).
13.72 is correct!
Once again thanks for the help.