Finding the median for probability distribution

[Violagirl]

The Palestinian Central Bureau of Statistics asked mothers of age 20-24 about the ideal number of children. For those living on the Gaza Strip, the probability distribution is approximately P(1)=.01, P(2)=.10, P(3)=.09, P(4)=.31, P(5)=.19, and P(6 or more)=.29. Because the last category is open-ended, it is not possible to calculate the mean exactly. Explain why you can find the median of the distribution, and find it.

So to find the median, do you take the values of each probability, find the number located in the middle of the data and then find the average of the two?

In doing that, I took the sums of .10 and .19 divided by two and got an answer of .195, is this correct. And the median can be found as there is a set number of 6 probablilities where as a mean would require a each specific set without the possibility of any additional numbers.

 

[tkhunny]

No p(0)? Maybe that's the missing 0.01. Anyway...

Median is not a probability. It is a value.

1) 0.01 - Nope.
2) 0.01+0.10 = 0.11 - Nope.
3) 0.11 + 0.09 = 0.20 - Nope.
4) 0.20 + 0.31 = 0.51 -- Ah! There it is.

See if it agrees the other way.

6) 0.29 - Nope.
5) 0.29 + 0.19 = 0.48 - Very close, but no.
4) 0.48 + 0.31 = 0.79 -- That did it!

Always check a given distribution for credibility. 0.01 + 0.10 + 0.09 + 0.31 + 0.19 + 0.29 = 0.99!! There seems to be a piece missing. Not good.