I couldn't get the frostberg.edu site to load. However, I was thinking about this all day as a matter of magnitude. Each digit to the right introduces the possibility of error that is an order of magnitude 10 higher than the last digit.
In your example above where we are apparently averaging weights of a person (or persons.)
*** Adding up the weights gives a total weight of 763.6 lbs, which has 4 significant figures.
*** To get the average, divide by 5. The 5 is an exact number, so you don't lose any significant figures by doing this. The *** exact answer is 152.72 lbs
*** The answer rounded to 4 digits is 152.7 lbs.
We can be pretty certain that the first digit of 1, for 100 pounds is accurate. We are surely certain that the person (or persons) we weighed, weighed AT LEAST 100 pounds!
For the same reason, we are pretty certain about that 5 being at least 50 pounds.
Thus we have a high degree of certainty that we measured and average weight of at least 150 pounds!
Now we get to that 2. Well, we're pretty sure it was at least 2 pounds. So with a reasonable degree of certainty we can claim the average was at least 152 pounds.
Then comes that decimal point and that 7 and 2 following the decimal point. And we wonder, "Should we round up that 0.7 to the next 1?" Well, now that would make our average 153 instead of 152. Just how accurate is that 0.7? We study our measuring equipment, our measuring technique and even as you point out weather the subject being weighed was still, unbalanced or wiggling while being measured. And we find that we are not all that comfortable with the accuracy of that 0.7.
What it looks like is our "true" average is between 152 pounds and 153 pounds. Something like:
152.0 pounds
Sentiment: Hold