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Display the standard deviation of a column of numbers with awk

Terminal - Display the standard deviation of a column of numbers with awk
awk '{sum+=$1; sumsq+=$1*$1} END {print sqrt(sumsq/NR - (sum/NR)**2)}' file.dat
2009-03-24 21:56:40
User: kaan
Functions: awk
6
Display the standard deviation of a column of numbers with awk

Alternatives

There are 8 alternatives - vote for the best!

Terminal - Alternatives
awk '{delta = $1 - avg; avg += delta / NR; mean2 += delta * ($1 - avg); } END { print sqrt(mean2 / NR); }'
2009-09-11 04:46:01
User: ashawley
Functions: awk delta
Tags: awk
4

This will calculate a running standard deviation in one pass and should never have the possibility for overflow that can happen with other implementations. I suppose there is a potential for underflow in the corner case where the deltas are small or the values themselves are small.

Know a better way?

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What others think

I was finding that this was 'blowing up' when processing a large number (1000's) of lat/long positions with an error message about attempting to SQRT a negative number.

Apparently the correct way is to do two passes, compute the mean first, sum the difference between value & mean.

You can do this with:

awk '{sum+=$1; array[NR]=$1} END {for(x=1;x<=NR;x++){sumsq+=((array[x]-(sum/NR))**2);}print sqrt(sumsq/NR)}' file.dat
Comment by mungewell 269 weeks and 3 days ago

can you help me how to edit this command, if I have the values in 2nd column?

Comment by siti 229 weeks and 4 days ago

siti: Just replace all occurrences of $1 with $2 (in either version).

Thanks to mungewell for pointing out the overflow problem, and to ashawley for the elegant code.

Comment by kaan 229 weeks and 3 days ago

Can someone help me to modify this code to be able to normalize each value of the column. I guess, after having the mean and the standard deviation, this should be pretty easy.

thanks in advance.

Comment by anurag_bagaria 194 weeks and 3 days ago

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