Median Value of a Discrete Random Value

[barydos]

suppose you had a probability table:

X      1          2           3             4
p(x)   0.2       0.2         0.1          0.5

Is the median value 3 or 3.5 or 4? :O
I'm really confused

[Homer]

I would say its 3.5 :/

[b^3]

To find the median, we keep adding the probabilities until they exceed 0.5. If we add them and they end up on 0.5 exactly, then the median is halfway between the value of X for when we hit 0.5, and the next value.

I.e.
so the median would be

EDIT: made into the respective parts

[barydos]

So as a discrete random variable, the answer is definitely 3.5? Just want to triple-check!

[Jenny_2108]

If you still doubt, go to p535 essential

[BubbleWrapMan]

Yeah, it's only for discrete variables where you take the midpoint.

If you want to know why we take the midpoint, it's the same thing we do when we have an even number of data points in a data set, e.g.:

3, 4, 4, 6, 7, 9, 10, 11

The median would be 6.5. Same sort of thing with discrete random variables.

[barydos]

Alright awesome, thanks everyone.
I just got kind of confused because the teacher said something about not taking halfway between because it's discrete. Must have been an accidental mistake on her behalf.
Once again, thanks everyone

[Jenny_2108]

Alright awesome, thanks everyone.
I just got kind of confused because the teacher said something about not taking halfway between because it's discrete. Must have been an accidental mistake on her behalf.
Once again, thanks everyone

Name "discrete" because its countable :p
Forget what your teacher said about "discrete" then. I haven't listened to my methods teacher for a long time

[TrueTears]

Alright awesome, thanks everyone.
I just got kind of confused because the teacher said something about not taking halfway between because it's discrete. Must have been an accidental mistake on her behalf.
Once again, thanks everyone

Exactly what Ennjy said, but I want to re-emphasize further.

A DISCRETE random variable is NOT a random variable that can only take "whole numbers" or any intuitive correspondence with the word "discrete".

The formal definition of discrete is a random variable that is countable (as Ennjy pointed out) OR countably INFINITE. The latter case does not tend to appear in high school mathematics but is quite interesting.

Say we have a DRV X, X takes on the values 1.1, 1.2, 1.3, 1.4 and so on, we say that X is a countably infinite because for each output of X we can "pair" it up with an integer value. Eg:

1.1 -> 1

1.2 -> 2

1.3 -> 3

1.4 -> 4

and so on, and we can "count" all possible values of X up to "infinity", thus it is still a DISCRETE random variable.

[Special At Specialist]

The answer is 3.5
You always take the midpoint of the two discrete values when that happens.
eg. If the values are 1, 2, 3 and 4, then the median is 2.5.