# S2: finding the medians with cdf?Watch

#1
Can someone help me with a past paper question? Q. 8 (d)

https://eiewebvip.edexcel.org.uk/Rep...e_20070611.pdf

The mark scheme is below [for reference to the cdf formula]

https://eiewebvip.edexcel.org.uk/Rep...s_20070815.pdf

I'm not sure why they used the second part of the cdf to find the median (0<x<3), instead of the third part (3<x<4).

I always thought that, to find the median using the cdf, you just plug F(m)=0.5 into the last/longest equation/the last part (before 1), while here in this paper you have to plug it in the second part (0<x<3).

That's what we were taught in class anyway.

I know that the answer you get when you use the 3rd part is out of the range, but how would you know when to use which part, generally?
0
9 years ago
#2
the median will be where F(x)=0.5, so to get this you need to add up the cdf until you get to 0.5.

looking at the first bound (0-3) if you sub in 3, you get 9/12 = 3/4 (more than 0.5) so the median must be in that part.
(if this came to less than 0.5 the median would be in the second part, so you would sub in 0.5 - F(1st region) to then second region formula)

then as you say 'just plug it in'

also: drawing a quick sketch is very useful
0
9 years ago
#3
This exact same question came up a couple of days ago:
http://www.thestudentroom.co.uk/show...7#post19059497
0
#4
Thank you both very much!
0
8 years ago
#5
(Original post by 2^1/2)
the median will be where F(x)=0.5, so to get this you need to add up the cdf until you get to 0.5.

looking at the first bound (0-3) if you sub in 3, you get 9/12 = 3/4 (more than 0.5) so the median must be in that part.
(if this came to less than 0.5 the median would be in the second part, so you would sub in 0.5 - F(1st region) to then second region formula)

then as you say 'just plug it in'

also: drawing a quick sketch is very useful

yeah but for the second fuction, if you sub in the higher limit [ (2)(4) - (16/4) - (3)] you get 1 and thats higher than .5 aswell! so how would you know which one to use?
0
8 years ago
#6
(Original post by kelly316)
yeah but for the second fuction, if you sub in the higher limit [ (2)(4) - (16/4) - (3)] you get 1 and thats higher than .5 aswell! so how would you know which one to use?
you always do them in order (as it's cumulative)

0
8 years ago
#7
(Original post by 2^1/2)
you always do them in order (as it's cumulative)

no worries... i get it!
0
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