Correct to use an average 99th percentile value?

[kerrymaid]

Hi,

I have been asked to plot the 99th percentile for a graph of hop count values.

Basically I have run 5 simulations each for different numbers of nodes (10, 20, 30) i.e. 15 simulations in total and I am plotting the batch mean value in a graph (i.e. 3 points on the graph showing the batch mean value for the 10, 20 and 30 network).

As I said I am being asked for the 99th percentile also. So for example for the 10 node network I calculated the 99th percentile (using excel) for each of the 5 simulations runs and got the following answers.

Sim run 1: 6
Sim run 2: 5.34
Sim run 3: 5
Sim run 4: 5.34
Sim run 5: 5.31

My question is this: Does it even make sense to plot an average 99th percentile value on the final graph? From my understanding the whole purpose of the 99th percentile is to show that 99% of the values are at or below a certain value i.e. to emphasise that values don’t pass a certain threshold value such as 6 (is this correct?). But if I plot an average 99th percentile value of 5.398 well this will be misleading really values higher than this could have been noted…..

I would really appreciate if someone could clarify this for me.

 

[tkhunny]

There are some who argue that Medians should be a value actually in your set. Not everyone agreees with this view.

I explain...

{1 2 3 4 5 6 7 8}

What is the Median?

Some might say 5, since
----- 1 is greater than 0% - Obviously NOT the median
----- 2 is greater than 12.5% - Obviously NOT the median
----- 3 is greater than 25% - Obviously NOT the median
----- 4 is greater than 37.5% - Obviously NOT the median
----- 5 is greater than 50% - Okay, that seems reasonable.

Not everyone likes this, since 5 is less than only 37.5% of the values in the set.

Most, I think, would say 4.5. That is not in the set. However, if you are willing to accept 4.5, you must also be willing to accept 4.1, 4.2, 4.3512154, 4.6518, \(\displaystyle \sqrt{17}\), and infinitely other values.

Having said that, I must ask only, "Why do you care that other values 'could have been noted'?" A cow may have jumped over the moon, too, but that isn't in your data, either.