How do you calculate the uncertainty for the average diameter?
I have 3 different diamters, and its average! but i am struggling in calculating its uncertainty.
Thanks
I would recommend calculating the standard deviation from the mean. Google "stadard deviation" for more details, if you need them.
http://www.gcseguide.co.uk/standard_deviation.htm
To calculate the uncertainty for the average diameter, you need to compute the standard deviation of the individual measurements. Here's how you can do it step by step:
1. Take your three different diameter measurements.
2. Calculate the average of the three measurements by adding them up and dividing by 3. This will give you the mean diameter.
3. Calculate the difference between each individual measurement and the mean diameter. These differences are called deviations.
4. Square each deviation to get rid of negative values and emphasize differences from the mean.
5. Calculate the average of the squared deviations. This value is called the variance.
6. Take the square root of the variance to find the standard deviation. This is the measure of how spread out the individual measurements are from the mean diameter.
The standard deviation of the measurements represents the uncertainty in the individual measurements. However, since you are averaging the diameters, you also need to consider the uncertainty in the mean diameter. This is known as the standard error of the mean.
To calculate the standard error of the mean, divide the standard deviation by the square root of the number of measurements you have (3 in this case). This will give you the uncertainty in the average diameter.
Keep in mind that this approach assumes your measurements follow a normal distribution. If your data does not follow a normal distribution or if you have a large number of measurements, you might need to use different statistical methods to estimate uncertainty.