bash awk moving average with skipping - bash

Question

I am trying to calculate a moving average with a data set. But in addition, I want it to skip a few number of data each time the average 'window' moves. For example, if my data set is a column from 1 to 20 and my average window is 5, then the current calculation is the average of (1-5), (2-6), (3-7), (4-8).....
But I want to skip a few data each time the window moves, say I want to skip 2. then the new average will be (1-5), (4-8), (6-10), (8-12)......
Here is the current awk file I am using, can anyone help me edit it so that I can skip a few data each time the window moves? I want to change the skip size and window size as well. Thank you very much!
#!/bin/awk
BEGIN {
N=5 # the window size
}
{
n[NR]=$1 # store the value in an array
}
NR>=N { # for records where NR >= N
x=0 # reset the sum variable
delete n[NR-N] # delete the one out the window of N
for(i in n) # all array elements
x+=n[i] # ... must be summed
print x/N # print the row from the beginning of window
}

Answer 1

I think your ranges are not well specified, but you wanted to achieve can be done by parallel windowing as below
awk '{sum[1]+=$1}
!(NR%5){print NR-4"-"NR, sum[1]/5; sum[1]=0}
NR>3{sum[4]+=$1}
NR>3 && !((NR-3)%5){print NR-4"-"NR, sum[4]/5; sum[4]=0}' <(seq 15)
will give, you can remove printing ranges which it there for debugging.
1-5 3
4-8 6
6-10 8
9-13 11
11-15 13
for making window size and skip count variable
awk -v w=5 -v s=3 'function pr(x) {print (NR-s-1)"-"NR, sum[x]/w; sum[x]=0}
{sum[1]+=$1}
NR>s {sum[s+1]+=$1}
!(NR%w) {pr(1)}
NR>s && !((NR-s)%w){pr(s+1)}' file
first window always start at 1, second window starts at s+1. This can be generalize for more than 2 windows as well, perhaps you can find someone to do it...

Answer 2

I see that you want to print MA every K ticks instead of printing for every tick (K=1). So you could add a condition NR%K==0 before printing in your existing code.
But it would be better to keep an array of N elements and overwrite them instead of deleting. Using NR%N as array index. This way, when K is not 1 and want not to calculate the MA, you will avoid checking how many elements to delete etc.
awk -v n=5 -v k=2 '{ a[NR%n]=$0 }
NR>=n && (NR-n)%k==0 { s=0; for (i in a) s+=a[i]; print NR ":\t" s/n }' file
update condition to (NR-n)%k==0 for always starting from first tick where MA is calculated (that is for NR=n).