probability distribution

[letsride]

I'm having trouble with this extended question, how would you go about finding the median and IQR of the probability distribution (sorry for my poor drawing, don't have a scanner)

the equations of the two lines are:
y=0.1x-0.2 2≤x≤6
y=-0.4x+2.8 6≤x≤7

btw they intersect and (6,0.4)

any help will be appreciated

[Martoman]

My reasoning for them is thus

Median is where the area under the graph will be half way.

You have a big triangle, base 5 and height 0.4

This means whole area is 2.

Median will be the X point where area is 1.

So you set up a triangle with base x and height 0.4 with a area of 1.

This leads to 5/2 = x but we start the triangle at 2 so 2+5/2 = 4.5 that is ur median.

IQR is 75% under -25% under see what you can do there.

[letsride]

its okay, already done the q a while ago.
btw the area is 1.
anyway first eqn of the line y=0.1x-0.2 2≤x≤6 has an area of 0.8 so therefore 0.5 would fall under here and you wouldn't have to take the second eqn into mind.
from there set a bound a to 2 and let eqn 1 equal 0.5 and solve from there

atleast what i think this is right

[Mao]

That is the correct method letsride, martoman got a bit too smart there and assumed height is at a constant 0.4.