Let's say I have the following data:
$$1,2,3,1,4,0,6,4,3,2,46,7,5,7$$
I'd like to get a percentage based off some sort of average change of the data (in the order) to get an idea of what % the data appears to be increasing/decreasing on average.
The data above is obviously increasing from start to finish (with a few random changes). But what is the average increase in a percentage format?
My first thought was to take the difference between each consecutive number pair (ie: $2-1 = 1, 3-2 = 1, 1-3 = -2,$ etc), then taking the averages of all these difference values. This might get what I want. But I was wondering if there was some more clever formulas that might do this better.
Cheers!
Best Answer
A good measure of this is check the highest increasing chain.
$100*$(No of elements in the highest increasing chain)$/$No of total elements is a good measure of percentage of increasing trend in a particular data.
By the largest increasing chain of the sequence $a_1,a_2,a_3,....a_n$, what I meant is a subsequence with largest cardinality which is increasing, that is a subsequence $a_{k_1},a_{k_2},....a_{k_m}$ such that $k_1<k_2<....<k_m$ and $a_{k_1}<a_{k_2},....<a_{k_m}$