calculating averages w/non significant data
Message posted by wk (via 207.64.17.161) on November 29, 2001 at 12:22 PM (ET)

I am trying to find the "most correct" way to calculate an average of a data set that includes data which (from a scientific standpoint) is considered non detectable.

For example, a water sample analysis from the same source yielded the following results for Lead from analysis using an Inductively Coupled Plasma Mass Spectrometer.

<0.1 mg/L
<0.1 mg/L
0.5 mg/L
0.3 mg/L

The question is do you treat the less than reults as "0" an average with the other data? or do you report the average using 0.1 as your number? I have noted where some individuals use 1/2of the non detect data and average the set with those values. I find that to be unreliable since anything reported as less than 0.1 could be from 0.0 0.009.

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: calculating averages w/non significant data
Message posted by Tomi (via 213.133.214.2) on November 30, 2001 at 7:53 AM (ET)

So for your data:

<0.1 mg/L
<0.1 mg/L
0.5 mg/L
0.3 mg/L

We say the mean is (0.05+0.05+.5+.3)/4 = .9/4 = .225

This is just an approximation because of the assumption we have made. It is possible to get an idea of the range of values between which this answer lies by workingout the maximum and minimum possible values:

min = (0+0+.5+.3)/4 = .2
max = (.1+.1+.5+.3)/4 = .25
######################

Now in fact your data has probably been measured correct to the nearest 0.05
So <0.1 really means <0.05 (since anything greater than 0.5 would hae been recorded as 0.1)
0.5 really means between 0.45 and 0.55
.3 really means between 0.25 and 0.35

So min = (0+0+.45+.25)/4 = .7/4 = .175
max = (.05+.05+.55+.35)/4 = 1/4 = .25
mean = (.025+.025+.5+.3)/4 = .85/4 = .2125