I'm a bit confused about all the different "definitions" of uncertainty?
One can calculate "uncertainty" of a single measurement by simply checking how accurate the tool that is being used to do the measuring is.
One can also calculate "uncertainty" of a group of measurements by finding the standard deviation which means that any more measurements made will have a 70% chance of being within one standard deviation of the "true value".
Finally, there is also standard error which is also a measure of "uncertainty", but I'm not sure what it says.
Which "uncertainty" do I have to find in the following problem and would I go about finding it?
A particular 1.00-kg bag of rice consists of 2.00% "supergrains", each of which contains 5ppm of arsenic and the rest of the grains contain no arsenic. What is the average concentration?
A grain of rice weighs 20 mg. What is the uncertainty in the concentration due to sampling if a 10.00 g sample is taken for analysis from this bag?
If the entire contents of the bag were ground to spherical particles 100 micrometer in diameter, what would the uncertainty be if a 10.0 g sample were taken for analysis?
The first part is pretty straight forward. I calculated that the average concentration of arsenic in this bag of rice is 100ppb.
It's the next two questions I don't understand partly because as I said in the beginning, I'm not sure what "definition" of uncertainty they are asking for/about. How would I go about finding it?
Please correct any assumptions or definitions I've made if they are incorrect in any way. I'm really trying to learn and I know how important precision of language is.