# B "Strength" of the mean of the distribution curve

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1. Apr 15, 2017

### icakeov

My understanding of the distribution curves is very basic but I do have a couple of somewhat generic questions. I looked up a number of definitions but have had a hard time finding these specific answers:

- Is there an agreed on minimum number of samples that one needs to take to deem a result to be viable? Or does the result more depend on the data we get?

- Additionally, is there a certain "percentile" value of how far the standard deviation is from the mean (i.e. how "far" it is from it, or how low its value is), that would conclude that the mean value is "very likely" to happen?

What I am really aiming for with these questions is:

- If in science we are to declare something a "fact", how "precise" does the distribution curve have to be in order for us to declare it a fact? Does it have to occur 100% times? Or is there some "window" of probability that we take into account and what is that?

Apologies if the questions is sloppy or if it makes no sense.
Thanks for any feedback!

2. Apr 15, 2017

### FactChecker

You have to decide how accurate you want your estimate of the mean to be and what probability you want that the true mean is within that range. Typically, you use the data to find a "confidence interval" where you can say that the mean is 95%, 97.5% or 99% like to be within that interval. The probabilities are assuming that you know the general form of the distribution of the thing you are measuring (like normal, poisson, etc.)

3. Apr 15, 2017

### icakeov

Perfect! Thanks FactChecker!
I am guessing that 95% and over would be the value at which the mean value starts becoming a "fact"?
Not sure if this is the right forum for this question, but is this the step to conclude something is a fact? Or do facts have to have 100% confidence interval?

4. Apr 15, 2017

### FactChecker

For most things, you can never get 100% confidence. 95% is probably low because that will be wrong one out of every 20 times. There is a trade-off between the size of the confidence interval (the accuracy you want from your estimated mean) and the level of confidence that the interval contains the true mean. Different applications require different standards as far as the level of confidence and accuracy. You have to use your own judgment. An extremely conservative example (although they are not talking about a mean) is the level of confidence that a new particle has been found. For high-energy physics, they like 99.7% confidence before they say they have found "evidence of a particle" and 99.99997% confidence before they say that a new particle has been discovered.

Last edited: Apr 15, 2017
5. Apr 15, 2017

### Staff: Mentor

Each individual measured value is a fact. The mean of any collection of such values is also a fact. There is no lower limit, even the smallest piece of data is a fact.

6. Apr 16, 2017

### Stephen Tashi

What do you mean by "it"? In order for something to be a fact, it would at least have to be expressed as a complete sentence.

If we consider a population of things, we can can make many different statements about the population. For example:

1) All the objects in the population have weight 102.3 and measurements that show a different value than 102.3 have errors in them.

or

2) The mean value of the objects in the population is 102.3, but there are objects in the population that have a weight different than the mean value.

7. Apr 16, 2017