# Statistics question?

## 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) = 0.01, P(2) = 0.10, P(3) = 0.09, P(4) = 0.31, P(5) = 0.019, and P(6 or more) = 0.29. 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. Answer is: The median would be the score that falls at 50%. If we add the probabilities from either end, we find that 4 falls at 0.50. The median is 4. But I don't get it

May 21, 2018

Because 0.01 + 0.10 + 0.09 + 0.31 = 0.51
0.51 > 0.5
Thus, median = 4

#### Explanation:

I am assuming that there is a typo and P(5) = 0.19

The median of a distribution is the number that falls in the exact middle of the distribution.

Law of probability says that P(E) = # favorable Outcomes /total Outcomes

For example, let's say there are 100 women (you can pick any number, the amount would be proportional) , then
$\setminus \because P \left(1\right) = 0.01$, frequency $= 100 \cdot 0.01 = 1$
there would 1 mother who says the ideal number is 1,

$\setminus \because P \left(1\right) = 0.10$ , frequency $= 100 \cdot 0.10 = 10$
10 who say the ideal is 2,

And continuing with this formula:
9 who say the ideal is 3, 31 who say 4, 20 who say 5 and 29 who say 6 or more.

Once you order these numbers from smallest to largest you will something like get this set of data:

1,2,2,2,...3,3,3...,4,4,4,4,4,4,4,4,4,4 ..., 5,5,5,5,5, ... 6,6,6,6 ... 7,7,7, .. etc

You will find that the numbers in the 50th and 51st position are both 4 and thus the median of the set is 4.