How to calculate the average with uncertainties?

In summary, when calculating the average with uncertainties in each measurement, the values should be added and divided by the number of measurements. The absolute uncertainties should also be added together and divided by the square of the number of measurements to obtain the appropriate weight for each measurement.
  • #1
Tyler S
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Homework Statement


How to calculate the average given the uncertainties in each measurement 8.70 +/- 0.28, 9.680 +/- 0.046, 9.700 +/- 0.055, 9.720 +/- 0.067?

Homework Equations

The Attempt at a Solution


I know I add the values and divide by 4. I also know I add the absolute uncertainties but idk if I divide them by 4. Please help I've gotten 9.45 +/- 0.448 meters
 
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  • #2
Hello Tyler, :welcome:

In the case off different accuracies, you have to weight the measurements when averaging. The appropriate weight of a measurement is ##1\over \sigma^2##.
Here, ##\sigma## is the (estimated) inaccuracy
 
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  • #3
BvU said:
It's "weight the measurements".
BvU said:
Here, σ is the (estimated) accuracy
Well, it's not so much the accuracy as the inaccuracy.
 
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FAQ: How to calculate the average with uncertainties?

How do I calculate the average with uncertainties using Excel?

To calculate the average with uncertainties using Excel, use the AVERAGE function. This function takes a range of values as its argument and returns the average of those values. Then, use the STDEV function to calculate the standard deviation of the data set. Finally, use the formula =AVERAGE ± STDEV to calculate the average with uncertainties.

What is the formula for calculating the average with uncertainties?

The formula for calculating the average with uncertainties is: average ± (standard deviation / √n), where n is the number of data points in the data set. This formula takes into account the uncertainty or variability of the data set and provides a more accurate representation of the average.

How do I interpret the average with uncertainties result?

The average with uncertainties result represents the estimated range of values that the true average of the data set lies within. This means that there is a certain level of uncertainty in the calculated average due to the variability of the data points. The larger the standard deviation, the larger the uncertainty in the average.

Why is it important to calculate the average with uncertainties?

Calculating the average with uncertainties allows for a more accurate representation of the data set. It takes into account the variability of the data, which can affect the overall average. This is especially important in scientific research as it helps to provide a more precise understanding of the data and its implications.

Can I calculate the average with uncertainties for non-numerical data?

No, the average with uncertainties can only be calculated for numerical data. This is because the formula for calculating the average with uncertainties involves taking the standard deviation, which can only be calculated for numerical data. Non-numerical data can be analyzed using other statistical measures such as mode or median.

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