Post by: ElephantStew on August 11, 2008, 07:14:01 pm
thanks
Post by: Mao on August 11, 2008, 08:05:43 pm
generally just count up to 0.5
more formally, you'd use cumulative distribution function (cdf). the point where the probability passes 0.5 (or reaches it) is the median
Post by: excal on August 11, 2008, 08:09:05 pm
Post by: /0 on August 11, 2008, 08:52:24 pm
the point where the probability passes 0.5 (or reaches it) is the median
Won't this 'median' be as much in the current value of X as it is in the next value of X? i.e. the current and next values of X share the median. So then what do you do if it adds exactly up to 50%?
Post by: Mao on August 11, 2008, 10:02:14 pm
consider the following discrete distribution:
| X | 1 | 2 | 3 | 4 |
| p(X) | 0.1 | 0.4 | 0.3 | 0.2 |
in this case, the median is "shared" by 2 and 3. For the purposes of Maths Methods, you take an average. i.e. median is 2.5. [I am unsure as to if there is a more correct way of doing this]
if we have continuous random distribution however, the continuity of the variable means that we can sleep soundly knowing that there is no categorical jump from the left 0.5 and the right 0.5 (there is an infinitesimal difference if you'd like). Hence, we can soundly use this:
for the purposes of MM, p(x) would be simple to differentiate
the reverse would be the same:
more strictly however, probability density functions are usually defined from
Post by: /0 on August 11, 2008, 10:10:34 pm
Post by: Mao on August 11, 2008, 10:17:55 pm
If you'd like to be REAL pedantic, you'd try to calculate the regression by plotting the pdf, then integrating the curve of best fit and finding at which value half the area of the whole interval is achieved.
but if you require THAT kind of accuracy, you wouldn't be using discrete probability distribution anyways :P
Post by: excal on August 12, 2008, 05:49:01 pm
Lol, doesn't feel quite right doing that in a discrete probability distribution... but I guess whatever the VCAA says is gospel anyway
Medians and means are ways to find the 'centre' point of the data, with varying accuracy depending on the underlying factors in data collection (cf. robustness).
In cases of a 'tie' between two numbers in a median calculation, it is perfectly acceptable to find the centre point between these two using what is essentially a mean of those two - remembering that the purpose of the median is a measure of central tendency.