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#{ AVERAGE -- Compute the average and standard deviation of a list of numbers.
# Numeric input is via the standard input (one number per line). The mean,
# sigma, and number of samples are written to the standard output.
#
# By default (Average called with no arguments), the sample is taken
# to be the set of numbers in the standard input when Average is run.
# Additional points can be added to or deleted from the sample by
# rerunning Average with one of the following arguments:
#
# add - add points to the sample, recalculate mean and sigma
# sub - subtract points from the sample
{
if ($nargs == 0) # if no arguments, don't query
opstring = "new_sample"
else
opstring = option # get parameter "option"
if (opstring == "add") # add, subtract, or start over?
addsub_flag = 1
else if (opstring == "sub" || opstring == "subtract")
addsub_flag = -1
else { # new sample (default)
addsub_flag = 1
n = 0 # number of points in sample
sum = 0
sumsqrs = 0
}
# Process data; print mean, sigma, and the sample size on
# the standard output.
while (scan (data_value) != EOF)
if (nscan() == 1 && data_value != INDEF) {
n += addsub_flag
sum += addsub_flag * data_value
sumsqrs += addsub_flag * data_value * data_value
}
if (n <= 0)
print ("INDEF ", "INDEF ", n)
else if (n == 1)
print (sum, "INDEF ", 1)
else {
mean = sum / n
variance = (n * sumsqrs - sum * sum) / (n * (n-1))
if (variance < 0) # possible with roundoff error
sigma = 0.0
else
sigma = sqrt (variance)
print (mean, sigma, n)
}
}
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