# Percentage uncertainty and percentage error

• david18
In summary, the conversation discusses the calculation of the percentage error and uncertainty in recorded data. The first scenario involves finding the percentage error in the average diameter of a set of measurements, while the second scenario is about calculating the percentage uncertainty in a measurement of length. The formula for calculating the percentage uncertainty is mentioned, but the speaker is unsure how to apply it to their specific problem.
david18
You record the following data Diameter/mm: 11.67, 12.67, 13.9, 12.67, 12.67, 12.66 You take the average of these values to be the diameter, but what is the percentage error in this value?

I tried working this problem out but I can't use the normal formula as it is spread over many values and there is no accepted value. I got some numbers; 17.55%, 1.5% but theyr all wrong.

W = T(x+y)/x

Where W is the weight of the stand and T is the Newton meter reading.

You measure and record the values of x, y (with a ruler) and T. The following data is recorded:

x = 12.8 cm , y = 30.2 cm, T= 2.2 N

What is the percentage uncertainty in y?

This one wants the percentage uncertainty which I'm unsure of how to find. I did try 30.25(max value) - 30.15(lowest value) / 2 = 0.05 and find it as a percentage but it turned out to be wrong...

Any help with these problems would be much appreciated.

Percentage Uncertainty

Uncertainties may be quoted as a percentage rather than absolute values. An uncertainty of 124 (+ or -) 1 means 1 in 124 ie.

Percentage Uncertainty = $$\frac{1}{124}\times100 = 0,08$$

I can help you understand the concepts of percentage uncertainty and percentage error.

Firstly, percentage uncertainty is a measure of the uncertainty or variability in a set of data. It is calculated by taking the standard deviation of the data and dividing it by the average value, and then multiplying by 100 to get a percentage. In your first problem, the percentage uncertainty would be the standard deviation of the diameter values divided by the average diameter, multiplied by 100.

On the other hand, percentage error is a measure of the difference between a measured value and the true or accepted value. It is calculated by taking the absolute value of the difference between the measured value and the true value, dividing it by the true value, and then multiplying by 100 to get a percentage. In your first problem, since there is no accepted value, the percentage error cannot be calculated.

For the second problem, the formula you mentioned (W = T(x+y)/x) is not relevant to finding the percentage uncertainty in y. To find the percentage uncertainty in y, you need to use the same formula as in the first problem - taking the standard deviation of the y values, dividing it by the average y value, and multiplying by 100. In this case, the standard deviation would be the difference between the maximum and minimum y values divided by 2, as you correctly calculated. However, you should divide this value by the average y value, which in this case would be (30.2+30.15)/2 = 30.175 cm. So the percentage uncertainty in y would be (30.25-30.15)/2 / 30.175 x 100 = 0.165%

I hope this helps you understand the concepts of percentage uncertainty and percentage error better. It is important to always consider both of these factors when analyzing data and drawing conclusions in scientific research.

## 1. What is percentage uncertainty?

Percentage uncertainty is a measure of the potential error or inaccuracy in a measurement. It is typically calculated by taking the absolute uncertainty (the smallest increment that can be measured on the instrument) and dividing it by the measured value, then multiplying by 100 to get a percentage.

## 2. How is percentage error different from percentage uncertainty?

Percentage error is a measure of how much a measured value differs from the true or accepted value. It is calculated by taking the absolute difference between the measured and accepted values, dividing by the accepted value, and multiplying by 100 to get a percentage. Percentage uncertainty, on the other hand, is a measure of the potential error in a measurement due to limitations in the instrument or method used.

## 3. What is an acceptable range for percentage uncertainty or error?

There is no specific acceptable range for percentage uncertainty or error, as it can vary depending on the specific measurement and its importance. However, in general, a lower percentage uncertainty or error is preferred as it indicates a more accurate measurement. A common rule of thumb is to aim for a percentage uncertainty or error of less than 5%.

## 4. How can percentage uncertainty or error be reduced?

Percentage uncertainty or error can be reduced by using more precise instruments, taking multiple measurements, and using proper techniques for measurement and calculation. Additionally, understanding the limitations and sources of error in a measurement can help in reducing the uncertainty or error.

## 5. Can percentage uncertainty or error be negative?

No, percentage uncertainty or error cannot be negative. It is always expressed as a positive value, as it represents the magnitude of the difference or potential error. A negative value would imply that the measured value is greater than the accepted value, which is not possible.

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