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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: sachinmachin on October 07, 2009, 09:08:53 pm

Title: median
Post by: sachinmachin on October 07, 2009, 09:08:53 pm: can someone please tell me how to find the median when a discrete or continuous random variable is given??
any help would be great!!
Title: Re: median
Post by: Ilovemathsmeth on October 07, 2009, 09:23:08 pm: Discrete: usually from the table. Add the probabilities in a cumulative fashion from lowest number. Usually you need to cross 0.50 to obtain the median. Say you got 0.54 for X = 4; 4 is your median. IHowever, if the probability is equal to 0.5, then find the midway point between the two adjacent values of the variable. I.e. you got 0.5 for X=4, and 5 is the next number, median is 4.5.

Continuous: need to evaluate an integral, set up so that the lower limit is the lower value of the CRV and use m as your 'median' value; integrate the Continuous RV from the lower limit to m, and equate this integral to 0.5. You'll get some value for m, that's your median. Note that for cumulative distribution functions (not on course but briefly mentioned in Essentials), you need to equate the function to 0.5 as it is a function of cumulative probabilities of the probability density function.

Hope that helps!
Title: Re: median
Post by: Damo17 on October 07, 2009, 09:28:00 pm: Quote from: sachinmachin on October 07, 2009, 09:08:53 pm
can someone please tell me how to find the median when a discrete or continuous random variable is given??
any help would be great!!

Continuous:

$\int_{-\infty}^m f(x)dx=0.5$ , solve for m.

Discrete:
Use the probability distribution table to find the value of x that sums up to just over 0.5 or equals 0.5(median is halfway between next x-value.)

e.g

x 0 1 2 3
Pr(X=x) 0.2 0.4 0.3 0.1

The median is 1.

OR

x 0 1 2 3
Pr(X=x) 0.2 0.3 0.4 0.1

Median=1.5
Title: Re: median
Post by: sachinmachin on October 07, 2009, 09:32:41 pm: actually i understood continuous, but it was discrete that i could quite get my head around. this however, has cleared up any doubt. thank you to the both of you!! :)
Title: Re: median
Post by: Ilovemathsmeth on October 07, 2009, 09:50:38 pm: No problem!