Let's review what this is saying and let's pretend we are talking about rats or some small animal that doesn't live too many years.
It says that at age 0, there were 100 rats, and at age 1 there were only 65 rats. That means that 35 rats died when they were 0 years old or another way of saying it is 35 rats lived to be 0 years old. (100-65) = 35
It then says that 50 rats lived to be 2 years old, so that means of the 65 rats that were a year old, 50 of them lived another year while 65-50 = 15 rats died that year. So 15 rats lived to be 1.
We can continue with this method and find that 40 died at the age of two, 8 died at the age of three and 2 died at the age of four.
To recap then, we have 35 rats that lived to be zero and 15 rats that lived to be one, 40 rats that lived to be two, 8 rats that lived to be three, and 2 rats that lived to be four, while no rats lived past four so no rats were 5 years old.
Chart:
Age lived to Number of rats
0 35
1 15
2 40
3 8
4 2
5 0
The average is 0(35)+1(15)+2(40)+3(8)+4(2)+5(0) all divided by the 100 total rats we started with.
Simplified is 127/100
So the average age is 1.27 years
To find the median think about lining up all the rats in a line with a little card that says the age when they died. They are lined up in order from youngest age death to oldest age death. We want to know the age of the middle rat. Since there are 100 rats, which is an even number, then there will actually be two middle rats and we will average their ages.
so we have 0000000000000000000000000000000000011111111111111122222222222222222222222222222222222222223333333344
Since there are 100 numbers here, 50 from the start and 50 from the end will give us the middle numbers.
0000000000000000000000000000000000011111111111111 1 2 2222222222222222222222222222222222222223333333344
So 1 and 2 are the middle numbers.
To find the median of an odd number of numbers, it is just the one in the middle, but when there are an even number of numbers, then you will have 2 middle numbers and we must average them. Which is to say add them and divide by 2.
(1+2)/2 = 3/2 = 1.5years
**Interestingly enough, I work as an actuary and we use lx's similar to this, but on a larger scale and with humans. This is how companies like Allstate, Liberty Mutual, State Farm are able to calculate life insurance.
