when trying to find uncertanty percent error and your given the number - 15 s^-2 m with a implied uncertanty of +/- 1 s^-2 m and you try to find the percent uncertanty and you do this

(- 15 s^2 m)^-1 1 s^-2 m (100 %) is the percent negative or positve

also when trying to find the average percent uncertanty of your data do you count that number as positive or negetive when you find the average by finding the mean?

In the example you mentioned, the relative uncertainty is +/- 1/15 = +/- 6.7%

I am not sure what you mean by your second question. When you make a series of measurements of something that should be a constant, the most probable value is the mean, unless there are systematic bias errors. Errors due to nonrepeatability are expressed as +/- about the mean in most cases. The error value can be estimated from the standard deviation, which is the square root of the average squared deviation from the mean.

To find the percent uncertainty, we need to divide the implied uncertainty by the given value and then multiply it by 100. Let's go through the steps to calculate the percent uncertainty for the given number of -15 s^-2 m with an implied uncertainty of +/- 1 s^-2 m:

1. Start by taking the absolute value of the given value, so |-15 s^-2 m| = 15 s^-2 m.
2. Divide the implied uncertainty by the absolute value: 1 s^-2 m / 15 s^-2 m = 1/15.
3. Multiply the result by 100 to obtain the percent uncertainty: (1/15) x 100 ≈ 6.67%.

Now, when considering the sign of the number, the percent uncertainty is always positive. This is because we are only concerned with the magnitude of the uncertainty relative to the value itself, not the direction.

Regarding your second question on finding the average percent uncertainty of data, you should treat each individual percent uncertainty as positive, regardless of whether the original values were positive or negative. Average percent uncertainty is determined by calculating the mean of all percent uncertainties, which would include both positive and negative values.