Moving average using awk

Question 1

You could try the following script:

awk -vn=100 -f a.awk file

where a.awk is

BEGIN {
    m=int((n+1)/2)
}
{L[NR]=$2; sum+=$2}
NR>=m {d[++i]=$1}
NR>n {sum-=L[NR-n]}
NR>=n{
    a[++k]=sum/n
}
END {
    for (j=1; j<=k; j++)
        print d[j],a[j]
}

For example given test data:

and running awk -vn=5 -f a.awk file gives

Question 2

Without input it's really difficult to understand what you are trying to achieve, Here is an example of moving average of 5 point and index at 3, implement according to your need

awk '
 BEGIN{
         OFS = "\t"

         No_of_row = 20

         Average_Point = 5
         index_Point   = 3 

         print "Column1" OFS "Column2"

         for(i=1;i<=No_of_row;i++)
         {
             C1[i]=i
             C2[i]=i
             print i OFS i
         }
         print RS "index" OFS "Average" OFS "Data_used" OFS "Sum" OFS "No_of_Point"
      }
   END{ 
        for(i=1;i<=No_of_row;i++){
                                for(j=1;j<=Average_Point;j++){
                                                              flag = 0
                                                              if(C1[i+j] || j == 1 && C1[i])
                                                                {
                                                                 add = j==1 ? C2[i] : C2[(i+j)-1]
                                                                 sum += add
                                                                 ind  = j==index_Point ? C1[(i+j)-1] : ind
                                                                 flag = 1 
                                                                 s = s ? s "+" add : add
                                                                }
                                                              }

                                if(flag == 1){
                                              print ind,sum/Average_Point,s,sum,Average_Point
                                             }  

                                sum = ind = s = ""      
                                }          
      }
    '   /dev/null

Resulting

 Column1    Column2         
 1  1           
 2  2           
 3  3           
 4  4           
 5  5           
 6  6           
 7  7           
 8  8           
 9  9           
 10 10          
 11 11          
 12 12          
 13 13          
 14 14          
 15 15          
 16 16          
 17 17          
 18 18          
 19 19          
 20 20          

 index Average  Data_used   Sum No_of_Point
 3    3        1+2+3+4+5        15  5
 4    4        2+3+4+5+6        20  5
 5    5        3+4+5+6+7        25  5
 6    6        4+5+6+7+8        30  5
 7    7        5+6+7+8+9        35  5
 8    8        6+7+8+9+10       40  5
 9    9        7+8+9+10+11      45  5
 10   10       8+9+10+11+12     50  5
 11   11       9+10+11+12+13    55  5
 12   12       10+11+12+13+14   60  5
 13   13       11+12+13+14+15   65  5
 14   14       12+13+14+15+16   70  5
 15   15       13+14+15+16+17   75  5
 16   16       14+15+16+17+18   80  5
 17   17       15+16+17+18+19   85  5

Question 3

You have to modify the no. of rows to suit your file, the input shall contain two columns one as an index and the other will be averaged, output will be less by 100 points , 50 from each side.

# Moving average over the Second column of a data file 
    BEGIN{
             OFS = "\t"

             No_of_row = 10294
             Average_Point = 100
             index_Point   = 50


          }
       { 
            for(i=1;i<=No_of_row;i++){
                  NR == i &&
                  C1[i]= $1 
                  NR == i && 
                  C2[i]= $2 } }
    END {  for(i=1;i<=No_of_row - Average_Point;i++){
                                  for(j=1;j<=Average_Point;j++){
                                                                 if(C1[i+j] || j == 1 && C1[i])
                                                                    {
                                                                     add = j==1 ? C2[i] : C2[(i+j)-1]
                                                                     sum += add
                                                                     ind  = j==index_Point ? C1[(i+j)-1] : ind
                                                                     }
                                                               }
                                         {
                                                 print ind,sum/Average_Point
                                                               }
                                        sum = ind = ""
                                           }  
         }