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vjramana 04-20-2011 11:20 PM

awk syntax for calculating average and standard deviation
 
I have a data in a column.
Code:

2
4
7
3
5

I want to calculate average and standard deviation. As first step I want to calculate average for the data than calculate (del=data - avg) for all the data.

I suppose get
Code:

avg=4.2
x  x-avg(x)
2  -2.2
4  -0.2
7    2.8
3  -1.2
5    0.8

For this I use AWK and the code goes like this
Code:

#!/usr/bin/awk -f

{col=1}
{sum+=$col; avg=sum/NR;}
{delX=($col-avg)}
{print $col, delX}

But I get different answers.
Code:

x  x-avg(x)
2    0
4    1
7    2.66667
3  -1
5    0.8

Can anyone explain why the answers are so different? since this is wrong I can not continue calculating the standard deviation.

Many thanks in advance.

David the H. 04-21-2011 12:33 AM

I don't really understand the math that you want to do, but here's the math that you actually did.
Code:


$ cat file.txt
2
4
7
3
5

$ cat script.sh
#! /usr/bin/awk -f
{ col=1; }
{ sum+=$col; }
{ avg=(sum/NR); }
{ delX=($col-avg); }
{ print "col="$col,"sum="sum,"NR="NR,"avg="avg,"delX="delX; }

$ ./script.sh file.txt
col=2 sum=2 NR=1 avg=2 delX=0
col=4 sum=6 NR=2 avg=3 delX=1
col=7 sum=13 NR=3 avg=4.33333 delX=2.66667
col=3 sum=16 NR=4 avg=4 delX=-1
col=5 sum=21 NR=5 avg=4.2 delX=0.8

The numbers appear to be coming out exactly as you told the script to calculate them.
(e.g. line one: "delX" = "$col-avg" = "2-2" = "0").

Tinkster 04-21-2011 12:57 AM

As far as I'm concerned it doesn't make too much sense to use
an average that's a moving target (changes w/ each row) to
calculate anything :}

grail 04-21-2011 01:12 AM

I agree with the others that what you require mathematically is not clear, but this seems to give the results you want:
Code:

#!/usr/bin/awk -f

{ sum += num[NR] = $0 }

END{
    avg = sum / NR

    print "avg = "avg

    print "x (x - avg)"
    for(i = 1; i <= NR; i++)
        print num[i], num[i] - avg
}


David the H. 04-21-2011 02:33 AM

I also think it's risky to rely on NR for the calculation, if there's a possibility of blank lines or non-numeric data occurring in the input. It would be safer to test for proper input and keep a running tab of the number of lines processed.
Code:


#! /usr/bin/awk -f

{
if ( $1 ~ /^[[:digit:]]+$/ )
    { sum += num[++n] = $1 }
}

END{
    avg=( sum / n )
    print "avg = "avg
    print "x ( x - avg )"
    for ( i=1 ; i<=n ; i++ )
          print num[i] , ( num[i] - avg )
}

grail will probably come back and show me how to write it in half the space, of course. ;)

Edit: if there could be decimal or negative numbers, you'll have to widen the test. Something like this:
Code:

if ( $1 ~ /^-?[[:digit:]]+(\.[[:digit:]]+)?$/ )
Edit2: I just found an easier way to determine if a field is numeric.
Code:

if ( $1 + 0.0 == $1 )

vjramana 04-21-2011 04:55 AM

Thank you for the reply. Basically I want to calculate average and standard deviation from data as below:
Quote:

O11 0.115 0.096 0.138 0.106 0.001 0.009 0.000 0.000
O12 0.298 0.290 0.282 0.240 0.012 0.003 0.000 0.000
O13 0.450 0.451 0.418 0.362 0.052 0.038 0.000 0.000
O14 0.078 0.082 0.068 0.063 0.003 0.006 0.000 0.000
O15 0.138 0.136 0.182 0.201 0.001 0.000 0.000 0.000
O16 0.717 0.832 0.766 0.759 0.029 0.018 0.000 0.000
O22 0.390 0.373 0.381 0.373 0.159 0.129 0.000 0.000
O23 0.195 0.312 0.184 0.307 0.305 0.372 0.000 0.000
O24 0.358 0.472 0.465 0.497 0.146 0.175 0.000 0.000
O25 0.298 0.274 0.251 0.249 0.074 0.104 0.000 0.000
O26 0.777 0.771 0.775 0.697 0.296 0.262 0.000 0.000
I want to calculate average and standard deviation for each column starting from column 2 until 5 separately.
After that I want to calculate the average and standard deviation line by line starting from column 2 until column 5 from each line.

For achieve this I tried to work out from model data for calculating average and standard deviation. I just wonder how to write awk code for doing this.

thank you in advance.

grail 04-21-2011 09:36 AM

Well I had a bit of a play ... you can do what you will but this should get you going in some sort of direction :)
Code:

#!/usr/bin/awk -f

{
    row[NR] = $1
    for(i=2;i<=NF;i++){
        sum[NR]+=num[NR,i]=$i
        col[i]+=$i
    }

    avg[NR] = sum[NR] / (NF - 1)
}

END{
    printf "Column details:\n%-7s","RowID"

    for(x=2;x<=NF;x++){
        col_avg[x] = col[x] / NR
        printf "%-8s%s-(%2.8f)    ","Value","Dev", col_avg[x]
    }

    for(a=1;a<=NR;a++){
        printf "\n%-6s ", row[a]
        for(b=2;b<=NF;b++){
            d = num[a,b] >= col_avg[b]?8:7
            printf "%1.5f (%2.8f)%"d"s", num[a,b],num[a,b] - col_avg[b], " "
        }
    }

    printf "\n\nRow details:\n%-7s%-16s","RowID","(Dev)"
    for(x=2;x<=NF;x++)
        printf "%-8s%-16s","Value","Dev"

    for(a=1;a<=NR;a++){
        printf "\n%-7s(%2.8f)%3s", row[a], avg[a]," "
        for(b=2;b<=NF;b++){
            d = num[a,b] >= avg[b]?3:2
            printf " %1.5f (%2.8f)%"d"s", num[a,b],num[a,b] - avg[b], " "
        }
    }

    print ""
}

You can also implement David's test for digits if you require.

@David - looks good, only suggestion for shorter would be to just implement the 'if' as the test to sum:
Code:

$1+0==$1{sum+= num[++n] = $1 }


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