Max & Min values

[Gareth56]

If you're given an average value and the sample size can you determine from those values what the maximum & minimum values were that gave the average value?

 

Thanks

[DrP]

I do not believe so. For example, the mean average is '4' from 5 samples.

 

You could have 2, 2, 4, 6 and 6. You could have 1, 2, 4, 6 and 7. You could have 1, 1, 1, 3, 7 and 7. In each case the average if 4 and the number of values is 5, but there is no way of knowing what the min and max values are - they are different in each case.

[ajb]

As DrP, I can't see how you could do it, not without some (probability) distribution being given.

[chitrangda]

you need to know the dristribution for knowing the max nad min values.

[Gareth56]

Many thanks for your input. What it was was I heard an advertisment on the radio about a company blowing its own trumpet for check in times at an airport and was just wondering if they had given us the whole picture

 

Averages can be so much removed from reality I suppose.

 

Thanks again

[ajb]

Indeed one has to be very careful with averages. Usually the distribution is more interesting and fundamental.

[Kyrisch]

Well, given certain restraints like "the number cannot be negative", which is feasible in many real-world scenarios (number of siblings, number of cars, and other "survey questions") it can be done. Say the average is 8 of ten samples. Since the numbers have to be positive, the minimum is automatically zero. So, we have the equation [math]\frac{0 +0+0+0+0+0+0+0+0+x}{10}=8[/math] or [math]\frac{x}{10}=8[/math]. The maximum would then be 80.

[the tree]

Say the average is 8 of ten samples. Since the numbers have to be positive, the minimum is automatically zero.

I'm fairly sure that the OP meant the min/max of either the population or the sample, not the min/max possible.

 

Although you can often make reasonable assumptions about the distribution (i.e. that it's Normal or Possion or whatever depending on the situation) you'd need to know both the mean and the variance to come up with some reasonable guesses about min/max values which you may as well declare to be the boundaries of a confidence interval.