How to quickly determine a range of output values

[hallelu01]

i know this may seem to be on such a novice level and in the wrong section, but I hope someone here can help me. I was wondering if anyone can tell me how to quickly determine a range of output values, given a specific range for the input values that I can apply to any general spreadsheet. for example in excel, I have 10 values between 8 and 20 in cells A1:A10. In cell A15 I need to identify the range of the average of A1:A10. Besides trying every possible combination, is there a quick way to do this?

 

[Crumbles]

i know this may seem to be on such a novice level and in the wrong section, but I hope someone here can help me. I was wondering if anyone can tell me how to quickly determine a range of output values, given a specific range for the input values that I can apply to any general spreadsheet. for example in excel, I have 10 values between 8 and 20 in cells A1:A10. In cell A15 I need to identify the range of the average of A1:A10. Besides trying every possible combination, is there a quick way to do this?

What exactly do you mean by "the range of the average"? If you have numbers in cells A1 to A10, you can have an average for those numbers but I don't quite see what you mean by the range of that average?

 

[hallelu01]

What I mean by "range of the average" is this, and please excuse me if I am not communicating my question effectively: I have a range of what the numbers in A1:A10 are (between 8 and 20), not the exact numbers of each cell. I need a range of what the answer for the average in cell A15 could be between. For example, knowing that all 10 numbers in A1:A10 to be used in calculating an average are greater than or equal to 8 and less than or equal to 20, what can I expect the anticipated average in cell A15 to be, greater than or equal to WHAT NUMBER but less than or equal to WHAT NUMBER? And how do you come up with that range of numbers?

 

[theFuture]

I'm not sure I completely understand what you're going after here, but I'll take a shot. You have 10 numbers in 10 different cells. You know the value each that each number can take on (I am assuming you can repeat from the range 8-20 and each number has an equal probability of popping up). You want to find the expectation value of these numbers, meaninging, you want to know which number to expect to see or what the average is.

To calculate this We use first define X as a random variable that can take on any value 8-20.

$$\Sigma x_{i}P(X=x_{i})$$

for all x in the range of X. This will give the expectation value, or average, of your values. And because each of your values have an equal probability of occurring

$$P(X=x_{i}) = \frac{1}{20-8} = \frac{1}{12}$$

I'm not sure if this is what you're looking for, but this is how I read it. From here you can use excel to sum over the numbers 8-20, multiply by 1/12 and the answer should pop out. The more I think about it, the more I think this isn't what you want but I can't figure out exactly what you're looking for.

 

[HallsofIvy]

If you know that the numbers must all lie between 8 and 20 but have no other information about the numbers, then their average can lie between 8 and 20.

If all the numbers happen to be 8, their average is 8, if all numbers happen to be 20, their average is 20. Any other combination of numbers will give an average somewhere between 8 and 20.

 

[hallelu01]

Thank you all for your help.