# Finding the Uncertainty Limit from a data set

• MaroonR
In summary, the person is trying to find the uncertainty limit in their measurement of time for a physics lab report. They have 16 data subsets from testing 8 heights with two different masses, and each subset had 3 trials. They were initially told to use standard deviation, but their course syllabus says they need at least 10 trials for it to be accurate. They then ask if there is another way to find the uncertainty limit or if they are misusing standard deviation when using it for each subset. They also mention their professor's suggestion of using a graph to determine the uncertainty, but question the mathematical background of this method.
MaroonR
Hello everyone, I've run into a little issue with physics homework. During a lab we recently had, we were required to measure the amount of time it took for a ball to drop from different heights (2m, 1.5m, etc) using a photogate. Now that I'm writing the lab report, I have to find the uncertainty limit in my measurement of time. Here's my problem: I have 16 data subsets. We tested 8 heights with two different masses, and each of those had 3 trials. I was told to use the standard deviation, but when I looked at my course syllabus it told me I needed to have at least 10 trials in order for the standard deviation to be accurate. So as for my question, is there another way to go about finding the uncertainty limit? Or, could I possibly be misusing the standard deviation when I use it for each subset (each height)?

Edit: My professor listed an appendix online that says I should be able to see the uncertainty from a graph. If I graph a time squared vs distance graph, how can I determine the error from that? I'll include my graph

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To see the uncertainty from the graph, you could translate your graph (the line you draw), keeping the same slope, up and down until all your data points are inside those two lines. They then give you the uncertainty. However, this method doesn't have _any_ mathematical background; here it's usually only taught in schools since they don't teach statistics there.

## 1. What is the uncertainty limit in a data set?

The uncertainty limit in a data set is a measure of the range of values within which the true value of a measurement is likely to fall. It is also known as the margin of error and is influenced by factors such as the precision of the measurement instrument and the variability of the data.

## 2. How is the uncertainty limit calculated?

The uncertainty limit is typically calculated by taking the standard deviation of the data and multiplying it by a factor, usually 2 or 3. This factor represents the number of standard deviations that encompasses a certain percentage of the data, typically 95% or 99%. The resulting value is the uncertainty limit.

## 3. Why is it important to determine the uncertainty limit in a data set?

Determining the uncertainty limit allows us to understand the reliability and accuracy of our data. It also helps us to communicate the level of uncertainty associated with our measurements and results. This is crucial in making informed decisions and drawing meaningful conclusions from the data.

## 4. Can the uncertainty limit be reduced?

Yes, the uncertainty limit can be reduced by improving the precision of the measurement instrument or by increasing the sample size. However, it is important to note that certain sources of uncertainty, such as inherent variability in the data, cannot be eliminated completely.

## 5. How can one interpret the uncertainty limit in a data set?

The uncertainty limit should be interpreted as a range of values within which the true value of the measurement is likely to fall. This means that there is a certain level of uncertainty associated with the data, and the true value could be anywhere within this range. It is important to consider this uncertainty when making decisions or drawing conclusions based on the data.

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